diff --git a/LeanPool.lean b/LeanPool.lean
index c42ffb54..9fdc1f32 100644
--- a/LeanPool.lean
+++ b/LeanPool.lean
@@ -795,6 +795,95 @@ import LeanPool.Erdos403
 import LeanPool.Erdos403.Basic
 import LeanPool.Erdos403.FactBase
 import LeanPool.Erdos403.Sharp
+import LeanPool.Erdos97ConvexOctagon
+import LeanPool.Erdos97ConvexOctagon.Basic
+import LeanPool.Erdos97ConvexOctagon.CayleyMenger
+import LeanPool.Erdos97ConvexOctagon.Certificates
+import LeanPool.Erdos97ConvexOctagon.Classification
+import LeanPool.Erdos97ConvexOctagon.CoverageBranches
+import LeanPool.Erdos97ConvexOctagon.CoverageData
+import LeanPool.Erdos97ConvexOctagon.CoverageData00
+import LeanPool.Erdos97ConvexOctagon.CoverageData01
+import LeanPool.Erdos97ConvexOctagon.CoverageData02
+import LeanPool.Erdos97ConvexOctagon.CoverageData03
+import LeanPool.Erdos97ConvexOctagon.CoverageData04
+import LeanPool.Erdos97ConvexOctagon.CoverageData05
+import LeanPool.Erdos97ConvexOctagon.CoverageData06
+import LeanPool.Erdos97ConvexOctagon.CoverageData07
+import LeanPool.Erdos97ConvexOctagon.CoverageData08
+import LeanPool.Erdos97ConvexOctagon.CoverageData09
+import LeanPool.Erdos97ConvexOctagon.CoverageData10
+import LeanPool.Erdos97ConvexOctagon.CoverageData11
+import LeanPool.Erdos97ConvexOctagon.CoverageData12
+import LeanPool.Erdos97ConvexOctagon.CoverageData13
+import LeanPool.Erdos97ConvexOctagon.CoverageData14
+import LeanPool.Erdos97ConvexOctagon.CoverageData15
+import LeanPool.Erdos97ConvexOctagon.CoverageData16
+import LeanPool.Erdos97ConvexOctagon.CoverageData17
+import LeanPool.Erdos97ConvexOctagon.CoverageData18
+import LeanPool.Erdos97ConvexOctagon.CoverageData19
+import LeanPool.Erdos97ConvexOctagon.CoverageData20
+import LeanPool.Erdos97ConvexOctagon.CoverageData21
+import LeanPool.Erdos97ConvexOctagon.CoverageData22
+import LeanPool.Erdos97ConvexOctagon.CoverageData23
+import LeanPool.Erdos97ConvexOctagon.CoverageData24
+import LeanPool.Erdos97ConvexOctagon.CoverageData25
+import LeanPool.Erdos97ConvexOctagon.CoverageData26
+import LeanPool.Erdos97ConvexOctagon.CoverageData27
+import LeanPool.Erdos97ConvexOctagon.CoverageData28
+import LeanPool.Erdos97ConvexOctagon.CoverageData29
+import LeanPool.Erdos97ConvexOctagon.CoverageData30
+import LeanPool.Erdos97ConvexOctagon.CoverageData31
+import LeanPool.Erdos97ConvexOctagon.CoverageDataTypes
+import LeanPool.Erdos97ConvexOctagon.CoverageFormula
+import LeanPool.Erdos97ConvexOctagon.CycleStrip
+import LeanPool.Erdos97ConvexOctagon.EquidistantFour
+import LeanPool.Erdos97ConvexOctagon.FiniteModel
+import LeanPool.Erdos97ConvexOctagon.GeometryReduction
+import LeanPool.Erdos97ConvexOctagon.Gram
+import LeanPool.Erdos97ConvexOctagon.Incidence
+import LeanPool.Erdos97ConvexOctagon.LRAT.Elab
+import LeanPool.Erdos97ConvexOctagon.LRAT.Format
+import LeanPool.Erdos97ConvexOctagon.LRAT.Semantics
+import LeanPool.Erdos97ConvexOctagon.Main
+import LeanPool.Erdos97ConvexOctagon.MasterCertificate
+import LeanPool.Erdos97ConvexOctagon.MasterCertificateData0
+import LeanPool.Erdos97ConvexOctagon.MasterCertificateData1
+import LeanPool.Erdos97ConvexOctagon.MasterCertificateData2
+import LeanPool.Erdos97ConvexOctagon.MasterCertificateData3
+import LeanPool.Erdos97ConvexOctagon.MasterCertificateData4
+import LeanPool.Erdos97ConvexOctagon.MasterCertificateData5
+import LeanPool.Erdos97ConvexOctagon.MasterCertificateData6
+import LeanPool.Erdos97ConvexOctagon.MasterCertificateData7
+import LeanPool.Erdos97ConvexOctagon.MasterCertificateData8
+import LeanPool.Erdos97ConvexOctagon.MasterCertificateManifest
+import LeanPool.Erdos97ConvexOctagon.MasterCertificateStage00
+import LeanPool.Erdos97ConvexOctagon.MasterCertificateStage01
+import LeanPool.Erdos97ConvexOctagon.MasterCertificateStage02
+import LeanPool.Erdos97ConvexOctagon.MasterFormula
+import LeanPool.Erdos97ConvexOctagon.MasterFormulaData
+import LeanPool.Erdos97ConvexOctagon.Obstructions
+import LeanPool.Erdos97ConvexOctagon.Pentagon
+import LeanPool.Erdos97ConvexOctagon.Radius
+import LeanPool.Erdos97ConvexOctagon.Regenerate
+import LeanPool.Erdos97ConvexOctagon.Relabelling
+import LeanPool.Erdos97ConvexOctagon.ResidualAlgebra00
+import LeanPool.Erdos97ConvexOctagon.ResidualAlgebra01
+import LeanPool.Erdos97ConvexOctagon.ResidualAlgebra02
+import LeanPool.Erdos97ConvexOctagon.ResidualAlgebra03
+import LeanPool.Erdos97ConvexOctagon.ResidualAlgebra04
+import LeanPool.Erdos97ConvexOctagon.ResidualAlgebra05
+import LeanPool.Erdos97ConvexOctagon.ResidualAlgebra06
+import LeanPool.Erdos97ConvexOctagon.ResidualAlgebra07
+import LeanPool.Erdos97ConvexOctagon.ResidualAlgebra08
+import LeanPool.Erdos97ConvexOctagon.ResidualAlgebra09
+import LeanPool.Erdos97ConvexOctagon.ResidualAlgebra10
+import LeanPool.Erdos97ConvexOctagon.ResidualAlgebra11
+import LeanPool.Erdos97ConvexOctagon.ResidualAlgebra12
+import LeanPool.Erdos97ConvexOctagon.ResidualObstructions
+import LeanPool.Erdos97ConvexOctagon.ResidualRepresentatives
+import LeanPool.Erdos97ConvexOctagon.RhombusFan
+import LeanPool.Erdos97ConvexOctagon.RowSymmetry
 import LeanPool.ErdosMoser
 import LeanPool.ErdosMoser.Basic
 import LeanPool.ErdosMoser.Bounds
diff --git a/LeanPool/Erdos97ConvexOctagon.lean b/LeanPool/Erdos97ConvexOctagon.lean
new file mode 100644
index 00000000..52e0a59e
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon.lean
@@ -0,0 +1,18 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.Main
+
+/-!
+# The Convex-Octagon Case of Erdős Problem 97
+
+Source: doi:10.1080/00029890.1946.11991674, url:https://www.erdosproblems.com/97
+Authors: Egor Lyfar
+Status: verified
+Main declarations: `Erdos97Octagon.erdos97_convex_octagon`
+Tags: discrete-geometry, distance-geometry, erdos-problems, convexity
+MSC: 51K05, 52A10
+-/
diff --git a/LeanPool/Erdos97ConvexOctagon/Basic.lean b/LeanPool/Erdos97ConvexOctagon/Basic.lean
new file mode 100644
index 00000000..1cab0edc
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/Basic.lean
@@ -0,0 +1,22 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import Mathlib.Analysis.InnerProductSpace.PiL2
+import Mathlib.Analysis.InnerProductSpace.Basic
+import Mathlib.LinearAlgebra.Dimension.Finite
+import Mathlib.LinearAlgebra.LinearIndependent.Defs
+
+/-! # Erdős 97 convex-octagon formalization: Basic -/
+
+namespace Erdos97Octagon
+
+open scoped InnerProductSpace
+open Module
+
+/-- The Euclidean plane, represented as `EuclideanSpace ℝ (Fin 2)`. -/
+abbrev Plane := EuclideanSpace ℝ (Fin 2)
+
+end Erdos97Octagon
diff --git a/LeanPool/Erdos97ConvexOctagon/CayleyMenger.lean b/LeanPool/Erdos97ConvexOctagon/CayleyMenger.lean
new file mode 100644
index 00000000..bc9d18cc
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/CayleyMenger.lean
@@ -0,0 +1,84 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.Gram
+
+/-! # Erdős 97 convex-octagon formalization: Cayley Menger -/
+
+namespace Erdos97Octagon
+
+open scoped InnerProductSpace
+
+/-- Squared Euclidean distance. -/
+noncomputable def sqDist (a b : Plane) : ℝ := dist a b ^ 2
+
+/-- The four-point Cayley--Menger polynomial in its six squared distances. -/
+def cm4 (A B C D E F : ℝ) : ℝ :=
+  -2 * A ^ 2 * F - 2 * A * B * D + 2 * A * B * E + 2 * A * B * F +
+    2 * A * C * D - 2 * A * C * E + 2 * A * C * F + 2 * A * D * F +
+    2 * A * E * F - 2 * A * F ^ 2 - 2 * B ^ 2 * E + 2 * B * C * D +
+    2 * B * C * E - 2 * B * C * F + 2 * B * D * E - 2 * B * E ^ 2 +
+    2 * B * E * F - 2 * C ^ 2 * D - 2 * C * D ^ 2 + 2 * C * D * E +
+    2 * C * D * F - 2 * D * E * F
+
+/-- Polarisation expresses an inner product through three squared distances. -/
+theorem inner_sub_sub_eq
+    (a b c : Plane) :
+    ⟪b - a, c - a⟫_ℝ = (sqDist a b + sqDist a c - sqDist b c) / 2 := by
+  have hsub : (b - a) - (c - a) = b - c := by abel
+  have h := norm_sub_sq_real (b - a) (c - a)
+  rw [hsub, ← dist_eq_norm, ← dist_eq_norm, ← dist_eq_norm] at h
+  simp only [sqDist]
+  rw [dist_comm b a, dist_comm c a] at h
+  nlinarith
+
+/-- Four planar points have vanishing Cayley--Menger determinant. -/
+theorem cm4_sqDist_eq_zero (a b c d : Plane) :
+    cm4 (sqDist a b) (sqDist a c) (sqDist a d)
+      (sqDist b c) (sqDist b d) (sqDist c d) = 0 := by
+  have h := gram_det_eq_zero ![b - a, c - a, d - a]
+  rw [gram3_expand] at h
+  have n1 : ⟪b - a, b - a⟫_ℝ = sqDist a b := by
+    rw [real_inner_self_eq_norm_sq, ← dist_eq_norm]
+    simp only [sqDist, dist_comm b a]
+  have n2 : ⟪c - a, c - a⟫_ℝ = sqDist a c := by
+    rw [real_inner_self_eq_norm_sq, ← dist_eq_norm]
+    simp only [sqDist, dist_comm c a]
+  have n3 : ⟪d - a, d - a⟫_ℝ = sqDist a d := by
+    rw [real_inner_self_eq_norm_sq, ← dist_eq_norm]
+    simp only [sqDist, dist_comm d a]
+  have i12 := inner_sub_sub_eq a b c
+  have i13 := inner_sub_sub_eq a b d
+  have i23 := inner_sub_sub_eq a c d
+  have i21 : ⟪c - a, b - a⟫_ℝ =
+      (sqDist a b + sqDist a c - sqDist b c) / 2 := by
+    rw [real_inner_comm]
+    exact i12
+  have i31 : ⟪d - a, b - a⟫_ℝ =
+      (sqDist a b + sqDist a d - sqDist b d) / 2 := by
+    rw [real_inner_comm]
+    exact i13
+  have i32 : ⟪d - a, c - a⟫_ℝ =
+      (sqDist a c + sqDist a d - sqDist c d) / 2 := by
+    rw [real_inner_comm]
+    exact i23
+  rw [n1, n2, n3, i12, i13, i23, i21, i31, i32] at h
+  dsimp [cm4]
+  ring_nf at h ⊢
+  linarith
+
+/-- The Cayley--Menger identity remains zero after dividing all squared
+distances by one common nonzero scale. -/
+theorem cm4_normalized_eq_zero
+    (a b c d : Plane) {s : ℝ} (hs : s ≠ 0) :
+    cm4 (sqDist a b / s) (sqDist a c / s) (sqDist a d / s)
+      (sqDist b c / s) (sqDist b d / s) (sqDist c d / s) = 0 := by
+  have h := cm4_sqDist_eq_zero a b c d
+  dsimp [cm4] at h ⊢
+  field_simp [hs]
+  nlinarith
+
+end Erdos97Octagon
diff --git a/LeanPool/Erdos97ConvexOctagon/Certificates.lean b/LeanPool/Erdos97ConvexOctagon/Certificates.lean
new file mode 100644
index 00000000..27a40025
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/Certificates.lean
@@ -0,0 +1,408 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.FiniteModel
+import LeanPool.Erdos97ConvexOctagon.Obstructions
+import LeanPool.Erdos97ConvexOctagon.ResidualObstructions
+
+/-! # Erdős 97 convex-octagon formalization: Certificates -/
+
+namespace Erdos97Octagon
+
+namespace RawIncidence
+
+/-- A finite witness emitted by the obstruction classifier. -/
+inductive Certificate where
+  | k4 (root : Vertex) (component : List Vertex) (a b c d : Vertex)
+  | hubPentagon (root : Vertex) (component : List Vertex) (o a b c d e : Vertex)
+  | sharedThree (a b q1 q2 q3 : Vertex)
+  | cycleStrip (root : Vertex) (component : List Vertex) (o x1 x2 x3 x4 x5 x6 : Vertex)
+  | residual (payload : UInt64)
+  deriving DecidableEq
+
+/-- The two obstruction shapes that remain valid when incidences are added. -/
+inductive PrefixCertificate where
+  | k4 (root : Vertex) (component : List Vertex) (a b c d : Vertex)
+  | sharedThree (a b q1 q2 q3 : Vertex)
+  deriving DecidableEq
+
+/-- Regard a monotone prefix witness as a general obstruction certificate. -/
+def PrefixCertificate.toCertificate : PrefixCertificate → Certificate
+  | .k4 root component a b c d => .k4 root component a b c d
+  | .sharedThree a b q1 q2 q3 => .sharedThree a b q1 q2 q3
+
+/-- Validate the tail of an ordered mutual-edge spanning tree. -/
+def extendsTreeB
+    (R : RawIncidence) (reached : Finset Vertex) : List Vertex → Bool
+  | [] => true
+  | v :: todo =>
+      decide (v ∉ reached) &&
+        decide (∃ u ∈ reached, v ∈ R u ∧ u ∈ R v) &&
+        extendsTreeB R (insert v reached) todo
+
+/-- Check that the listed vertices form an ordered mutual-edge spanning tree. -/
+def componentTreeB (R : RawIncidence) (root : Vertex) : List Vertex → Bool
+  | [] => false
+  | first :: rest => decide (first = root) && extendsTreeB R {root} rest
+
+/-- A selected edge whose selecting endpoint occurs in a validated tree. -/
+def TreeLabelledEdge (R : RawIncidence) (component : List Vertex) (a b : Vertex) : Prop :=
+  (a ∈ component ∧ b ∈ R a) ∨ (b ∈ component ∧ a ∈ R b)
+
+private def treeLabelledEdgeB
+    (R : RawIncidence) (component : List Vertex) (a b : Vertex) : Bool :=
+  (decide (a ∈ component) && decide (b ∈ R a)) ||
+    (decide (b ∈ component) && decide (a ∈ R b))
+
+/-- The class number stored in a residual-isomorphism payload. -/
+def payloadClass (payload : UInt64) : ℕ :=
+  (payload &&& 15).toNat
+
+/-- The forward permutation stored in a residual-isomorphism payload. -/
+def payloadForwardCode (payload : UInt64) : UInt64 :=
+  (payload >>> 4) &&& 0xffffff
+
+/-- The inverse permutation stored in a residual-isomorphism payload. -/
+def payloadInverseCode (payload : UInt64) : UInt64 :=
+  (payload >>> 28) &&& 0xffffff
+
+/-- Decode one three-bit entry of a packed permutation. -/
+def decodeMap (code : UInt64) (v : Vertex) : Vertex :=
+  Fin.ofNat 8 (((code >>> UInt64.ofNat (3 * v.val)) &&& 7).toNat)
+
+/-- The mathematical proposition checked for each emitted finite witness. -/
+def Certificate.Valid (R : RawIncidence) : Certificate → Prop
+  | .k4 root component a b c d =>
+      componentTreeB R root component = true ∧ [a, b, c, d].Nodup ∧
+        TreeLabelledEdge R component a b ∧ TreeLabelledEdge R component a c ∧
+        TreeLabelledEdge R component a d ∧ TreeLabelledEdge R component b c ∧
+        TreeLabelledEdge R component b d ∧ TreeLabelledEdge R component c d
+  | .hubPentagon root component o a b c d e =>
+      componentTreeB R root component = true ∧ [o, a, b, c, d, e].Nodup ∧
+        TreeLabelledEdge R component o a ∧ TreeLabelledEdge R component o b ∧
+        TreeLabelledEdge R component o c ∧ TreeLabelledEdge R component o d ∧
+        TreeLabelledEdge R component o e ∧ TreeLabelledEdge R component a b ∧
+        TreeLabelledEdge R component b c ∧ TreeLabelledEdge R component c d ∧
+        TreeLabelledEdge R component d e ∧ TreeLabelledEdge R component e a
+  | .sharedThree a b q1 q2 q3 =>
+      a ≠ b ∧ q1 ≠ q2 ∧ q1 ≠ q3 ∧ q2 ≠ q3 ∧
+        q1 ∈ R a ∧ q2 ∈ R a ∧ q3 ∈ R a ∧
+        q1 ∈ R b ∧ q2 ∈ R b ∧ q3 ∈ R b
+  | .cycleStrip root component o x1 x2 x3 x4 x5 x6 =>
+      componentTreeB R root component = true ∧ [o, x1, x2, x3, x4, x5, x6].Nodup ∧
+        TreeLabelledEdge R component o x1 ∧ TreeLabelledEdge R component o x2 ∧
+        TreeLabelledEdge R component o x6 ∧ TreeLabelledEdge R component x1 x2 ∧
+        TreeLabelledEdge R component x1 x3 ∧ TreeLabelledEdge R component x2 x3 ∧
+        TreeLabelledEdge R component x2 x4 ∧ TreeLabelledEdge R component x3 x4 ∧
+        TreeLabelledEdge R component x3 x5 ∧ TreeLabelledEdge R component x4 x5 ∧
+        TreeLabelledEdge R component x4 x6 ∧ TreeLabelledEdge R component x5 x6
+  | .residual payload =>
+      let classIndex := payloadClass payload
+      let forward := decodeMap (payloadForwardCode payload)
+      let inverse := decodeMap (payloadInverseCode payload)
+      classIndex < 13 ∧
+        (∀ v, inverse (forward v) = v) ∧
+        (∀ v, forward (inverse v) = v) ∧
+        ∀ v w, w ∈ R v ↔
+          forward w ∈ (residualRepresentative (Fin.ofNat 13 classIndex)).targets (forward v)
+
+private def residualValidB (R : RawIncidence) (payload : UInt64) : Bool :=
+  let classIndex := payloadClass payload
+  let forward := decodeMap (payloadForwardCode payload)
+  let inverse := decodeMap (payloadInverseCode payload)
+  decide (classIndex < 13) &&
+    (List.finRange 8).all (fun v => decide (inverse (forward v) = v)) &&
+    (List.finRange 8).all (fun v => decide (forward (inverse v) = v)) &&
+    (List.finRange 8).all (fun v =>
+      (List.finRange 8).all (fun w => decide (w ∈ R v ↔
+        forward w ∈
+          (residualRepresentative (Fin.ofNat 13 classIndex)).targets (forward v))))
+
+/-- Kernel-check the mathematical content of an emitted witness. -/
+def Certificate.validB (R : RawIncidence) : Certificate → Bool
+  | .k4 root component a b c d =>
+      componentTreeB R root component && decide [a, b, c, d].Nodup &&
+        treeLabelledEdgeB R component a b && treeLabelledEdgeB R component a c &&
+        treeLabelledEdgeB R component a d && treeLabelledEdgeB R component b c &&
+        treeLabelledEdgeB R component b d && treeLabelledEdgeB R component c d
+  | .hubPentagon root component o a b c d e =>
+      componentTreeB R root component && decide [o, a, b, c, d, e].Nodup &&
+        treeLabelledEdgeB R component o a && treeLabelledEdgeB R component o b &&
+        treeLabelledEdgeB R component o c && treeLabelledEdgeB R component o d &&
+        treeLabelledEdgeB R component o e && treeLabelledEdgeB R component a b &&
+        treeLabelledEdgeB R component b c && treeLabelledEdgeB R component c d &&
+        treeLabelledEdgeB R component d e && treeLabelledEdgeB R component e a
+  | .sharedThree a b q1 q2 q3 =>
+      decide (a ≠ b) && decide (q1 ≠ q2) && decide (q1 ≠ q3) && decide (q2 ≠ q3) &&
+        decide (q1 ∈ R a) && decide (q2 ∈ R a) && decide (q3 ∈ R a) &&
+        decide (q1 ∈ R b) && decide (q2 ∈ R b) && decide (q3 ∈ R b)
+  | .cycleStrip root component o x1 x2 x3 x4 x5 x6 =>
+      componentTreeB R root component && decide [o, x1, x2, x3, x4, x5, x6].Nodup &&
+        treeLabelledEdgeB R component o x1 && treeLabelledEdgeB R component o x2 &&
+        treeLabelledEdgeB R component o x6 && treeLabelledEdgeB R component x1 x2 &&
+        treeLabelledEdgeB R component x1 x3 && treeLabelledEdgeB R component x2 x3 &&
+        treeLabelledEdgeB R component x2 x4 && treeLabelledEdgeB R component x3 x4 &&
+        treeLabelledEdgeB R component x3 x5 && treeLabelledEdgeB R component x4 x5 &&
+        treeLabelledEdgeB R component x4 x6 && treeLabelledEdgeB R component x5 x6
+  | .residual payload => residualValidB R payload
+
+/-- The Boolean validator implies the mathematical certificate predicate. -/
+theorem Certificate.valid_of_validB
+    {R : RawIncidence} {certificate : Certificate}
+    (hvalid : certificate.validB R = true) : certificate.Valid R := by
+  cases certificate with
+  | residual payload =>
+      simp only [Certificate.validB, residualValidB, Bool.and_eq_true] at hvalid
+      rcases hvalid with ⟨⟨⟨hclass, hleft⟩, hright⟩, hedges⟩
+      refine ⟨of_decide_eq_true hclass, ?_, ?_, ?_⟩
+      · intro v
+        exact of_decide_eq_true ((List.all_eq_true.mp hleft) v (List.mem_finRange v))
+      · intro v
+        exact of_decide_eq_true ((List.all_eq_true.mp hright) v (List.mem_finRange v))
+      · intro v w
+        have hv := (List.all_eq_true.mp hedges) v (List.mem_finRange v)
+        exact of_decide_eq_true ((List.all_eq_true.mp hv) w (List.mem_finRange w))
+  | k4 root component a b c d =>
+      simpa only [Certificate.validB, Bool.and_eq_true, decide_eq_true_eq,
+        treeLabelledEdgeB, TreeLabelledEdge, Certificate.Valid, Bool.or_eq_true,
+        and_assoc] using hvalid
+  | hubPentagon root component o a b c d e =>
+      simpa only [Certificate.validB, Bool.and_eq_true, decide_eq_true_eq,
+        treeLabelledEdgeB, TreeLabelledEdge, Certificate.Valid, Bool.or_eq_true,
+        and_assoc] using hvalid
+  | sharedThree a b q1 q2 q3 =>
+      simpa only [Certificate.validB, Bool.and_eq_true, decide_eq_true_eq,
+        Certificate.Valid, and_assoc] using hvalid
+  | cycleStrip root component o x1 x2 x3 x4 x5 x6 =>
+      simpa only [Certificate.validB, Bool.and_eq_true, decide_eq_true_eq,
+        treeLabelledEdgeB, TreeLabelledEdge, Certificate.Valid, Bool.or_eq_true,
+        and_assoc] using hvalid
+
+/-- One incidence table extends another when it contains every selected edge. -/
+def Extends (R S : RawIncidence) : Prop :=
+  ∀ centre target, target ∈ R centre → target ∈ S centre
+
+private theorem extendsTreeB_mono {R S : RawIncidence} (hRS : Extends R S) :
+    ∀ reached todo, extendsTreeB R reached todo = true →
+      extendsTreeB S reached todo = true := by
+  intro reached todo
+  induction todo generalizing reached with
+  | nil => simp [extendsTreeB]
+  | cons v todo ih =>
+      intro htree
+      simp only [extendsTreeB, Bool.and_eq_true, decide_eq_true_eq] at htree ⊢
+      rcases htree with ⟨⟨hv, u, hu, hvu, huv⟩, hrest⟩
+      exact ⟨⟨hv, u, hu, hRS u v hvu, hRS v u huv⟩,
+        ih (insert v reached) hrest⟩
+
+private theorem componentTreeB_mono {R S : RawIncidence} (hRS : Extends R S)
+    {root component} (htree : componentTreeB R root component = true) :
+    componentTreeB S root component = true := by
+  cases component with
+  | nil => simp [componentTreeB] at htree
+  | cons first rest =>
+      simp only [componentTreeB, Bool.and_eq_true] at htree ⊢
+      exact ⟨htree.1, extendsTreeB_mono hRS {root} rest htree.2⟩
+
+private theorem treeLabelledEdge_mono {R S : RawIncidence} (hRS : Extends R S)
+    {component a b} (hedge : TreeLabelledEdge R component a b) :
+    TreeLabelledEdge S component a b := by
+  rcases hedge with ⟨ha, hab⟩ | ⟨hb, hba⟩
+  · exact Or.inl ⟨ha, hRS a b hab⟩
+  · exact Or.inr ⟨hb, hRS b a hba⟩
+
+/-- A prefix certificate remains valid in every incidence extension. -/
+theorem PrefixCertificate.valid_mono
+    {R S : RawIncidence} {certificate : PrefixCertificate}
+    (hRS : Extends R S) (hvalid : certificate.toCertificate.Valid R) :
+    certificate.toCertificate.Valid S := by
+  cases certificate with
+  | k4 root component a b c d =>
+      simp only [PrefixCertificate.toCertificate, Certificate.Valid] at hvalid ⊢
+      rcases hvalid with ⟨htree, hnodup, hab, hac, had, hbc, hbd, hcd⟩
+      exact ⟨componentTreeB_mono hRS htree, hnodup,
+        treeLabelledEdge_mono hRS hab, treeLabelledEdge_mono hRS hac,
+        treeLabelledEdge_mono hRS had, treeLabelledEdge_mono hRS hbc,
+        treeLabelledEdge_mono hRS hbd, treeLabelledEdge_mono hRS hcd⟩
+  | sharedThree a b q1 q2 q3 =>
+      simp only [PrefixCertificate.toCertificate, Certificate.Valid] at hvalid ⊢
+      rcases hvalid with ⟨hab, h12, h13, h23, ha1, ha2, ha3, hb1, hb2, hb3⟩
+      exact ⟨hab, h12, h13, h23, hRS a q1 ha1, hRS a q2 ha2,
+        hRS a q3 ha3, hRS b q1 hb1, hRS b q2 hb2, hRS b q3 hb3⟩
+
+private theorem extendsTree_sameComponent
+    (Q : OctagonIncidence) (root : Vertex) :
+    ∀ (reached : Finset Vertex) (todo : List Vertex),
+      (∀ v ∈ reached, Q.SameComponent root v) →
+      extendsTreeB Q.targets reached todo = true →
+      ∀ v ∈ todo, Q.SameComponent root v := by
+  intro reached todo
+  induction todo generalizing reached with
+  | nil => simp
+  | cons v todo ih =>
+      intro hreach htree
+      simp only [extendsTreeB, Bool.and_eq_true, decide_eq_true_eq] at htree
+      obtain ⟨u, hu, huv⟩ := htree.1.2
+      have hv : Q.SameComponent root v := (hreach u hu).tail huv
+      have hreach' : ∀ w ∈ insert v reached, Q.SameComponent root w := by
+        intro w hw
+        rcases Finset.mem_insert.mp hw with rfl | hw
+        · exact hv
+        · exact hreach w hw
+      have htodo := ih (insert v reached) hreach' htree.2
+      intro w hw
+      rcases List.mem_cons.mp hw with rfl | hw
+      · exact hv
+      · exact htodo w hw
+
+/-- Every vertex in a validated ordered tree belongs to the root component. -/
+theorem componentTree_sameComponent
+    (Q : OctagonIncidence) {root : Vertex} {component : List Vertex}
+    (htree : componentTreeB Q.targets root component = true)
+    {v : Vertex} (hv : v ∈ component) :
+    Q.SameComponent root v := by
+  cases component with
+  | nil => simp [componentTreeB] at htree
+  | cons first rest =>
+      simp only [componentTreeB, Bool.and_eq_true, decide_eq_true_eq] at htree
+      have hfirst : first = root := htree.1
+      subst first
+      rcases List.mem_cons.mp hv with rfl | hv
+      · exact Relation.ReflTransGen.refl
+      · apply extendsTree_sameComponent Q root {root} rest
+          (fun w hw => by
+            have : w = root := by simpa using hw
+            subst w
+            exact Relation.ReflTransGen.refl) htree.2 v hv
+
+/-- Every tree-labelled checker edge is a genuine component-radius edge. -/
+theorem treeLabelledEdge_sound
+    (Q : OctagonIncidence) {root : Vertex} {component : List Vertex}
+    (htree : componentTreeB Q.targets root component = true)
+    {a b : Vertex} (h : TreeLabelledEdge Q.targets component a b) :
+    Q.LabelledEdge root a b := by
+  rcases h with ⟨ha, hab⟩ | ⟨hb, hba⟩
+  · exact Or.inl ⟨componentTree_sameComponent Q htree ha, hab⟩
+  · exact Or.inr ⟨componentTree_sameComponent Q htree hb, hba⟩
+
+private theorem finOfNat_eq_of_lt {n a : ℕ} [NeZero n] (h : a < n) :
+    Fin.ofNat n a = ⟨a, h⟩ := by
+  apply Fin.ext
+  simp [Nat.mod_eq_of_lt h]
+
+private theorem residual_relabel_eq
+    (Q : OctagonIncidence) (payload : UInt64)
+    (hvalid : (Certificate.residual payload).Valid Q.targets) :
+    ∃ classIndex : Fin 13, ∃ e : Vertex ≃ Vertex,
+      Q.relabel e = residualRepresentative classIndex := by
+  simp only [Certificate.Valid] at hvalid
+  let classIndex : Fin 13 := ⟨payloadClass payload, hvalid.1⟩
+  let forward := decodeMap (payloadForwardCode payload)
+  let inverse := decodeMap (payloadInverseCode payload)
+  let e : Vertex ≃ Vertex := Equiv.mk forward inverse
+    (left_inv := hvalid.2.1) (right_inv := hvalid.2.2.1)
+  have hright (x : Vertex) : forward (inverse x) = x := hvalid.2.2.1 x
+  refine ⟨classIndex, e, ?_⟩
+  apply OctagonIncidence.ext
+  funext v
+  ext w
+  have hedge := hvalid.2.2.2 (e.symm v) (e.symm w)
+  have hindex : Fin.ofNat 13 (payloadClass payload) = classIndex :=
+    finOfNat_eq_of_lt hvalid.1
+  change w ∈ (Q.targets (e.symm v)).map e.toEmbedding ↔
+    w ∈ (residualRepresentative classIndex).targets v
+  rw [Finset.mem_map]
+  constructor
+  · rintro ⟨x, hx, hxw⟩
+    have hxeq : x = e.symm w := by
+      apply e.injective
+      simpa using hxw
+    subst x
+    have := hedge.mp hx
+    change forward (inverse w) ∈
+      (residualRepresentative (Fin.ofNat 13 (payloadClass payload))).targets
+        (forward (inverse v)) at this
+    rw [hright w, hright v, hindex] at this
+    exact this
+  · intro hw
+    refine ⟨e.symm w, ?_, by simp⟩
+    apply hedge.mpr
+    change forward (inverse w) ∈
+      (residualRepresentative (Fin.ofNat 13 (payloadClass payload))).targets
+        (forward (inverse v))
+    rw [hright w, hright v, hindex]
+    exact hw
+
+/-- Every validated finite witness contradicts a convex planar realisation. -/
+theorem Certificate.not_convex_realises
+    {Q : OctagonIncidence} (certificate : Certificate)
+    (hvalid : certificate.Valid Q.targets)
+    {p : Vertex → Plane} (hC : ConvexIndependent ℝ p) (hR : Realises p Q) :
+    False := by
+  cases certificate with
+  | k4 root component a b c d =>
+      simp only [Certificate.Valid] at hvalid
+      rcases hvalid with ⟨htree, hnodup, hab, hac, hadge, hbc, hbd, hcd⟩
+      have had : a ≠ d := by
+        intro had
+        subst d
+        simp at hnodup
+      exact no_labelled_k4 hC.injective hR had
+        (treeLabelledEdge_sound Q htree hab)
+        (treeLabelledEdge_sound Q htree hac)
+        (treeLabelledEdge_sound Q htree hadge)
+        (treeLabelledEdge_sound Q htree hbc)
+        (treeLabelledEdge_sound Q htree hbd)
+        (treeLabelledEdge_sound Q htree hcd)
+  | hubPentagon root component o a b c d e =>
+      simp only [Certificate.Valid] at hvalid
+      rcases hvalid with
+        ⟨htree, _hnodup, hoa, hob, hoc, hod, hoe, hab, hbc, hcd, hde, hea⟩
+      exact no_labelled_hub_pentagon hC.injective hR
+        (treeLabelledEdge_sound Q htree hoa)
+        (treeLabelledEdge_sound Q htree hob)
+        (treeLabelledEdge_sound Q htree hoc)
+        (treeLabelledEdge_sound Q htree hod)
+        (treeLabelledEdge_sound Q htree hoe)
+        (treeLabelledEdge_sound Q htree hab)
+        (treeLabelledEdge_sound Q htree hbc)
+        (treeLabelledEdge_sound Q htree hcd)
+        (treeLabelledEdge_sound Q htree hde)
+        (treeLabelledEdge_sound Q htree hea)
+  | sharedThree a b q1 q2 q3 =>
+      simp only [Certificate.Valid] at hvalid
+      exact no_three_shared_targets hC hR hvalid.1 hvalid.2.1
+        hvalid.2.2.1 hvalid.2.2.2.1 hvalid.2.2.2.2.1
+        hvalid.2.2.2.2.2.1 hvalid.2.2.2.2.2.2.1
+        hvalid.2.2.2.2.2.2.2.1 hvalid.2.2.2.2.2.2.2.2.1
+        hvalid.2.2.2.2.2.2.2.2.2
+  | cycleStrip root component o x1 x2 x3 x4 x5 x6 =>
+      simp only [Certificate.Valid] at hvalid
+      rcases hvalid with
+        ⟨htree, _hnodup, e01, e02, e06, e12, e13, e23, e24, e34, e35, e45, e46, e56⟩
+      exact no_labelled_cycle_square_strip hC.injective hR
+        (treeLabelledEdge_sound Q htree e01)
+        (treeLabelledEdge_sound Q htree e02)
+        (treeLabelledEdge_sound Q htree e06)
+        (treeLabelledEdge_sound Q htree e12)
+        (treeLabelledEdge_sound Q htree e13)
+        (treeLabelledEdge_sound Q htree e23)
+        (treeLabelledEdge_sound Q htree e24)
+        (treeLabelledEdge_sound Q htree e34)
+        (treeLabelledEdge_sound Q htree e35)
+        (treeLabelledEdge_sound Q htree e45)
+        (treeLabelledEdge_sound Q htree e46)
+        (treeLabelledEdge_sound Q htree e56)
+  | residual payload =>
+      obtain ⟨classIndex, e, he⟩ := residual_relabel_eq Q payload hvalid
+      have hC' := convexIndependent_relabel hC e
+      have hR' := realises_relabel hR e
+      rw [he] at hR'
+      exact residualRepresentative_not_convex_realises classIndex hC' hR'
+
+end RawIncidence
+
+end Erdos97Octagon
diff --git a/LeanPool/Erdos97ConvexOctagon/Classification.lean b/LeanPool/Erdos97ConvexOctagon/Classification.lean
new file mode 100644
index 00000000..6afb8f8c
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/Classification.lean
@@ -0,0 +1,43 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.CoverageBranches
+
+/-!
+# Exhaustive normalized-incidence classification
+
+The 35 possible first rows reduce to seven symmetry orbits.  One master LRAT
+certificate excludes all seven canonical rows, and every clause has an audited
+semantic proof in `CoverageFormula`.
+-/
+
+namespace Erdos97Octagon
+
+open RawIncidence
+
+/-- No normalized octagon incidence table has a convex planar realisation. -/
+theorem normalized_convex_realisation_impossible
+    {p : Vertex → Plane} {Q : OctagonIncidence}
+    (hC : ConvexIndependent ℝ p) (hR : Realises p Q) (hN : Q.Normalized) :
+    False := by
+  obtain ⟨rowOneIndex, hrowOne⟩ := exists_rowOneIndex Q
+  obtain ⟨orbit, p', Q', hC', hR', hN', hSparse', hBalanced', hcanonical⟩ :=
+    canonicalize_rowOne hC hR hN rowOneIndex hrowOne
+  exact canonicalBranch_impossible hC' hR' hN' hSparse' hBalanced'
+    orbit hcanonical
+
+/-- A convex-independent labelled octagon has a vertex that does not have
+four other labelled vertices at one common distance. -/
+theorem erdos97_convex_octagon
+    {p : Vertex → Plane} (hC : ConvexIndependent ℝ p) :
+    ∃ vertex, ¬HasFourEquidistant p vertex := by
+  by_contra hall
+  push Not at hall
+  obtain ⟨p', Q, hC', hR', hN, _hSparse, _hBalanced⟩ :=
+    normalized_reduction_of_all_hasFour hC hall
+  exact normalized_convex_realisation_impossible hC' hR' hN
+
+end Erdos97Octagon
diff --git a/LeanPool/Erdos97ConvexOctagon/CoverageBranches.lean b/LeanPool/Erdos97ConvexOctagon/CoverageBranches.lean
new file mode 100644
index 00000000..7195cf3f
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/CoverageBranches.lean
@@ -0,0 +1,31 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.MasterCertificate
+
+/-!
+# Master coverage contradiction
+
+One kernel-checked certificate excludes all seven canonical first rows at once.
+-/
+
+namespace Erdos97Octagon.RawIncidence
+
+open LRAT
+
+/-- Every normalized counterexample with a canonical first row contradicts
+the master LRAT certificate. -/
+theorem canonicalBranch_impossible
+    {p : Vertex → Plane} {Q : OctagonIncidence}
+    (hC : ConvexIndependent ℝ p) (hR : Realises p Q)
+    (hN : Q.Normalized) (hSparse : Q.PairSparse) (hBalanced : Q.Balanced)
+    (rowOneIndex : Fin 7)
+    (hrowOne : Q.targets 1 = packedRow (canonicalRowMask rowOneIndex)) :
+    False :=
+  masterFormula_unsatisfiable (valuation Q.targets)
+    (masterFormula_satisfied hC hR hN hSparse hBalanced rowOneIndex hrowOne)
+
+end Erdos97Octagon.RawIncidence
diff --git a/LeanPool/Erdos97ConvexOctagon/CoverageData.lean b/LeanPool/Erdos97ConvexOctagon/CoverageData.lean
new file mode 100644
index 00000000..db451f2b
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/CoverageData.lean
@@ -0,0 +1,144 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.CoverageData00
+import LeanPool.Erdos97ConvexOctagon.CoverageData01
+import LeanPool.Erdos97ConvexOctagon.CoverageData02
+import LeanPool.Erdos97ConvexOctagon.CoverageData03
+import LeanPool.Erdos97ConvexOctagon.CoverageData04
+import LeanPool.Erdos97ConvexOctagon.CoverageData05
+import LeanPool.Erdos97ConvexOctagon.CoverageData06
+import LeanPool.Erdos97ConvexOctagon.CoverageData07
+import LeanPool.Erdos97ConvexOctagon.CoverageData08
+import LeanPool.Erdos97ConvexOctagon.CoverageData09
+import LeanPool.Erdos97ConvexOctagon.CoverageData10
+import LeanPool.Erdos97ConvexOctagon.CoverageData11
+import LeanPool.Erdos97ConvexOctagon.CoverageData12
+import LeanPool.Erdos97ConvexOctagon.CoverageData13
+import LeanPool.Erdos97ConvexOctagon.CoverageData14
+import LeanPool.Erdos97ConvexOctagon.CoverageData15
+import LeanPool.Erdos97ConvexOctagon.CoverageData16
+import LeanPool.Erdos97ConvexOctagon.CoverageData17
+import LeanPool.Erdos97ConvexOctagon.CoverageData18
+import LeanPool.Erdos97ConvexOctagon.CoverageData19
+import LeanPool.Erdos97ConvexOctagon.CoverageData20
+import LeanPool.Erdos97ConvexOctagon.CoverageData21
+import LeanPool.Erdos97ConvexOctagon.CoverageData22
+import LeanPool.Erdos97ConvexOctagon.CoverageData23
+import LeanPool.Erdos97ConvexOctagon.CoverageData24
+import LeanPool.Erdos97ConvexOctagon.CoverageData25
+import LeanPool.Erdos97ConvexOctagon.CoverageData26
+import LeanPool.Erdos97ConvexOctagon.CoverageData27
+import LeanPool.Erdos97ConvexOctagon.CoverageData28
+import LeanPool.Erdos97ConvexOctagon.CoverageData29
+import LeanPool.Erdos97ConvexOctagon.CoverageData30
+import LeanPool.Erdos97ConvexOctagon.CoverageData31
+
+/-! # Erdős 97 convex-octagon formalization: Coverage Data -/
+
+namespace Erdos97Octagon.RawIncidence
+
+/-- The 32 generated groups containing all 256 pattern hash buckets. -/
+def patternBucketGroups : Array (Array (List PatternEntry)) := #[
+  patternBuckets00,
+  patternBuckets01,
+  patternBuckets02,
+  patternBuckets03,
+  patternBuckets04,
+  patternBuckets05,
+  patternBuckets06,
+  patternBuckets07,
+  patternBuckets08,
+  patternBuckets09,
+  patternBuckets10,
+  patternBuckets11,
+  patternBuckets12,
+  patternBuckets13,
+  patternBuckets14,
+  patternBuckets15,
+  patternBuckets16,
+  patternBuckets17,
+  patternBuckets18,
+  patternBuckets19,
+  patternBuckets20,
+  patternBuckets21,
+  patternBuckets22,
+  patternBuckets23,
+  patternBuckets24,
+  patternBuckets25,
+  patternBuckets26,
+  patternBuckets27,
+  patternBuckets28,
+  patternBuckets29,
+  patternBuckets30,
+  patternBuckets31
+]
+
+/-- The 32 generated groups containing all 256 exact-table hash buckets. -/
+def hardBucketGroups : Array (Array (List HardEntry)) := #[
+  hardBuckets00,
+  hardBuckets01,
+  hardBuckets02,
+  hardBuckets03,
+  hardBuckets04,
+  hardBuckets05,
+  hardBuckets06,
+  hardBuckets07,
+  hardBuckets08,
+  hardBuckets09,
+  hardBuckets10,
+  hardBuckets11,
+  hardBuckets12,
+  hardBuckets13,
+  hardBuckets14,
+  hardBuckets15,
+  hardBuckets16,
+  hardBuckets17,
+  hardBuckets18,
+  hardBuckets19,
+  hardBuckets20,
+  hardBuckets21,
+  hardBuckets22,
+  hardBuckets23,
+  hardBuckets24,
+  hardBuckets25,
+  hardBuckets26,
+  hardBuckets27,
+  hardBuckets28,
+  hardBuckets29,
+  hardBuckets30,
+  hardBuckets31
+]
+
+/-- Retrieve one pattern hash bucket. -/
+def patternBucket (index : Fin 256) : List PatternEntry :=
+  let group := patternBucketGroups.getD (index.val / 8) #[]
+  group.getD (index.val % 8) []
+
+/-- Retrieve one exact-table hash bucket. -/
+def hardBucket (index : Fin 256) : List HardEntry :=
+  let group := hardBucketGroups.getD (index.val / 8) #[]
+  group.getD (index.val % 8) []
+
+/-- Look up a monotone obstruction entry by its source identifier. -/
+def patternEntry (origin : ℕ) : Option PatternEntry :=
+  (patternBucket (Fin.ofNat 256 origin)).find? (fun entry => entry.origin == origin)
+
+/-- Look up an exact-table obstruction entry by its source identifier. -/
+def hardEntry (origin : ℕ) : Option HardEntry :=
+  (hardBucket (Fin.ofNat 256 origin)).find? (fun entry => entry.origin == origin)
+
+theorem patternEntry_sound {origin : ℕ} {entry : PatternEntry}
+    (hfind : patternEntry origin = some entry) :
+    entry.origin = origin := by
+  simpa using List.find?_some hfind
+
+theorem hardEntry_sound {origin : ℕ} {entry : HardEntry}
+    (hfind : hardEntry origin = some entry) :
+    entry.origin = origin := by
+  simpa using List.find?_some hfind
+
+end Erdos97Octagon.RawIncidence
diff --git a/LeanPool/Erdos97ConvexOctagon/CoverageData00.lean b/LeanPool/Erdos97ConvexOctagon/CoverageData00.lean
new file mode 100644
index 00000000..029dd30c
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/CoverageData00.lean
@@ -0,0 +1,155 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.CoverageDataTypes
+
+/-! # Coverage certificate data, buckets 0–7 -/
+
+namespace Erdos97Octagon.RawIncidence
+
+/-- Generated monotone-obstruction entries for this hash-bucket group. -/
+def patternBuckets00 : Array (List PatternEntry) := #[
+  [
+    ⟨0, 7196, .sharedThree 0 1 2 3 4⟩,
+    ⟨1280, 11272194355625984, .k4 2 [2, 3, 5, 6] 2 3 5 6⟩,
+    ⟨2048, 42785027821404184, .k4 0 [0, 3, 4, 6] 3 4 6 7⟩,
+    ⟨6656, 6777829138759680, .k4 2 [2, 5, 4, 6, 3] 1 2 3 4⟩
+  ],
+  [
+    ⟨1, 1703962, .sharedThree 0 2 1 3 4⟩,
+    ⟨257, 286851100, .k4 0 [0, 2, 3] 0 2 3 4⟩,
+    ⟨513, 10770815905719296, .k4 1 [1, 6, 5] 1 2 5 6⟩,
+    ⟨1793, 7036875513593884, .k4 0 [0, 2, 3, 6] 0 2 4 6⟩,
+    ⟨2049, 42785061912707096, .k4 0 [0, 3, 4, 6] 3 4 6 7⟩,
+    ⟨6657, 6777846117826560, .k4 2 [2, 5, 4, 6, 3] 1 2 3 4⟩
+  ],
+  [
+    ⟨514, 11259000712620032, .k4 1 [1, 3, 6] 1 3 5 6⟩,
+    ⟨770, 50922766, .k4 0 [0, 1, 2, 3] 0 1 2 3⟩,
+    ⟨1026, 1970324837187846, .k4 0 [0, 1, 2, 6] 0 1 2 6⟩,
+    ⟨1282, 11272194890399744, .k4 2 [2, 3, 5, 6] 2 3 5 6⟩,
+    ⟨1794, 7036875793500442, .k4 0 [0, 1, 3, 6] 0 3 4 6⟩,
+    ⟨2050, 45108564053910528, .k4 1 [1, 2, 5, 6] 1 2 6 7⟩,
+    ⟨4610, 76965868563468, .k4 0 [0, 2, 3, 1, 5] 1 2 5 6⟩,
+    ⟨8450, 13583693067657502, .k4 0 [0, 1, 2, 5, 6, 4] 0 2 3 4⟩,
+  ],
+  [
+    ⟨771, 50924558, .k4 0 [0, 2, 3, 1] 0 1 2 3⟩,
+    ⟨1027, 1970324837188614, .k4 0 [0, 2, 1, 6] 0 1 2 6⟩,
+    ⟨1795, 7036875827642396, .k4 0 [0, 2, 3, 6] 0 3 4 6⟩,
+    ⟨2819, 26560699629596, .k4 0 [0, 2, 3, 5, 4] 0 2 3 4⟩,
+    ⟨4355, 5805140522122608640, .k4 2 [2, 3, 4, 7, 6] 2 3 4 6⟩,
+    ⟨6659, 7036875513660702, .k4 0 [0, 1, 3, 2, 6] 0 2 4 6⟩
+  ],
+  [
+    ⟨772, 50988302, .k4 0 [0, 1, 3, 2] 0 1 2 3⟩,
+    ⟨1028, 1970324841235718, .k4 0 [0, 1, 2, 6] 0 1 2 6⟩,
+    ⟨1284, 11285698464186368, .k4 3 [3, 4, 5, 6] 3 4 5 6⟩,
+    ⟨6148, 79165430787084, .k4 0 [0, 2, 3, 1, 5] 1 2 5 6⟩,
+    ⟨7428, 4792955903484264718, .k4 0 [0, 1, 3, 7, 6, 2] 0 1 2 3⟩,
+  ],
+  [
+    ⟨261, 337182748, .k4 0 [0, 2, 3] 0 2 3 4⟩,
+    ⟨517, 11340362928908288, .k4 1 [1, 5, 6] 1 3 5 6⟩,
+    ⟨773, 50990094, .k4 0 [0, 3, 1, 2] 0 1 2 3⟩,
+    ⟨1029, 1970324841251846, .k4 0 [0, 2, 6, 1] 0 1 2 6⟩,
+    ⟨4101, 1513210028855821334, .k4 0 [0, 4, 7, 2, 1] 0 1 2 7⟩,
+    ⟨4357, 5805791526348939264, .k4 1 [1, 6, 7, 4, 5] 1 4 5 6⟩,
+    ⟨9221, 5922249353749534, .k4 0 [0, 3, 4, 5, 6, 1] 0 1 2 6⟩,
+    ⟨9989, 4940472293295006982, .k4 0 [0, 1, 2, 7, 6, 4, 5] 0 1 2 5⟩
+  ],
+  [
+    ⟨6, 6381824, .sharedThree 1 2 0 5 6⟩,
+    ⟨262, 353435676, .k4 0 [0, 2, 3] 0 2 3 4⟩,
+    ⟨518, 11342561958952960, .k4 2 [2, 5, 6] 2 3 5 6⟩,
+    ⟨1030, 1970324841301254, .k4 0 [0, 1, 2, 6] 0 1 2 6⟩,
+    ⟨1286, 11285835366268928, .k4 3 [3, 4, 6, 5] 3 4 5 6⟩,
+    ⟨1542, 72997271643136, .k4 1 [1, 2, 5, 4] 2 4 5 6⟩,
+    ⟨4358, 5806354484898562048, .k4 2 [2, 6, 7, 4, 5] 2 4 5 6⟩,
+    ⟨4870, 150242816163864, .k4 0 [0, 3, 4, 5, 2] 2 4 5 7⟩,
+    ⟨6662, 7037153590856734, .k4 0 [0, 2, 4, 1, 6] 0 1 3 6⟩,
+    ⟨7430, 4792955916319359254, .k4 0 [0, 1, 4, 7, 6, 2] 0 1 2 4⟩
+  ],
+  [
+    ⟨7, 6842368, .sharedThree 1 2 3 5 6⟩,
+    ⟨263, 353894428, .k4 0 [0, 3, 2] 0 2 3 4⟩,
+    ⟨519, 11356202768269312, .k4 4 [4, 5, 6] 3 4 5 6⟩,
+    ⟨775, 84085774, .k4 0 [0, 2, 3, 1] 0 1 2 3⟩,
+    ⟨1031, 1970324841316614, .k4 0 [0, 1, 6, 2] 0 1 2 6⟩,
+    ⟨1799, 7037200836395036, .k4 0 [0, 2, 4, 6] 0 3 4 6⟩,
+    ⟨4359, 5807480403589595136, .k4 3 [3, 6, 7, 4, 5] 3 4 5 6⟩
+  ]
+]
+
+/-- Generated exact-table entries for this hash-bucket group. -/
+def hardBuckets00 : Array (List HardEntry) := #[
+  [
+    ⟨0, 8697799730556775710, .cycleStrip 0 [0, 1, 2, 3, 4, 5, 6, 7] 0 1 3 5 7 6 4⟩,
+    ⟨768, 6020701831342613790, .residual 104390639921009⟩,
+    ⟨1024, 8153717281279011870, .residual 1339015425089107⟩,
+    ⟨1280, 3870992639438515230, .residual 3018991752198694⟩,
+    ⟨5376, 5590592674009309470, .residual 3915966730421769⟩,
+    ⟨5632, 6428199806150304030, .residual 1734974158594661⟩
+  ],
+  [
+    ⟨1, 8697795349690133790, .hubPentagon 0 [0, 1, 2, 3, 4, 5, 6, 7] 2 0 1 5 6 4⟩,
+    ⟨769, 3717101826386453790, .residual 605269692606434⟩,
+    ⟨1025, 8190575647154334750, .residual 307506372826355⟩,
+    ⟨1281, 3148396054435752990, .residual 3302134262631687⟩,
+    ⟨5377, 7824238863525208350, .residual 199278788155888⟩,
+    ⟨5633, 6141095329905434910, .residual 3035551636309698⟩
+  ],
+  [
+    ⟨2, 8410689778228604190, .residual 4411689737676934⟩,
+    ⟨770, 8256726681708422430, .residual 4409479976808705⟩,
+    ⟨1026, 5418893192665328670, .residual 3746517855920788⟩,
+    ⟨1282, 3139951933983452190, .residual 347141178295410⟩,
+    ⟨5378, 5599249129591660830, .residual 208055910283760⟩,
+    ⟨5634, 6425956802429640990, .residual 4231650588109506⟩
+  ],
+  [
+    ⟨3, 8693859081117707550, .hubPentagon 0 [0, 1, 2, 3, 4, 5, 6, 7] 1 0 2 6 5 3⟩,
+    ⟨771, 3717098527901902110, .residual 4411689737676933⟩,
+    ⟨1027, 5418892097448668190, .residual 3746517855920785⟩,
+    ⟨1283, 5996977923177999390, .residual 2317586278089825⟩,
+    ⟨5379, 8398447679112864030, .residual 199276909050352⟩,
+    ⟨5635, 5564643373695033630, .residual 2920824465876805⟩
+  ],
+  [
+    ⟨4, 7397959300637994270, .residual 4411689737676931⟩,
+    ⟨772, 7652624885687543070, .residual 4189839890960416⟩,
+    ⟨1028, 3145293499375119390, .residual 3253936643007124⟩,
+    ⟨1284, 5158251776292449310, .residual 3893577870611859⟩,
+    ⟨5380, 3865946433514103070, .residual 1013831082619824⟩,
+    ⟨5636, 5563521871834702110, .residual 3528256976411330⟩
+  ],
+  [
+    ⟨5, 7684223732869704990, .residual 4349139977733382⟩,
+    ⟨773, 8226825029383906590, .residual 4251412542173216⟩,
+    ⟨1029, 3145012028693376030, .residual 3253936643007121⟩,
+    ⟨1285, 5452051303426452510, .residual 4408292418399751⟩,
+    ⟨5381, 3862342896896958750, .residual 4350102050465026⟩,
+    ⟨5637, 3141636414015463710, .residual 1441062780320802⟩
+  ],
+  [
+    ⟨6, 8693009180154604830, .residual 155917796596467⟩,
+    ⟨774, 7690130066659042590, .residual 3916673252471171⟩,
+    ⟨1030, 4158170209613736990, .residual 4317250646643984⟩,
+    ⟨1286, 5163820944454609950, .residual 3884919216541330⟩,
+    ⟨5382, 7798428910396104990, .residual 3364939598947586⟩,
+    ⟨5638, 3285736200573477150, .residual 2489030601069602⟩
+  ],
+  [
+    ⟨7, 7399917398290279710, .residual 4411689737676932⟩,
+    ⟨775, 3150432644676936990, .residual 157994266016500⟩,
+    ⟨1031, 3871062447718886430, .hubPentagon 0 [0, 2, 3, 4, 1, 5, 7, 6] 0 1 2 7 4 3⟩,
+    ⟨1287, 2858261605449231390, .residual 3331727417808275⟩,
+    ⟨5383, 4154172000913056030, .residual 1013834873746352⟩,
+    ⟨5639, 7653121739334017310, .residual 1076505035839408⟩
+  ]
+]
+
+end Erdos97Octagon.RawIncidence
diff --git a/LeanPool/Erdos97ConvexOctagon/CoverageData01.lean b/LeanPool/Erdos97ConvexOctagon/CoverageData01.lean
new file mode 100644
index 00000000..05320331
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/CoverageData01.lean
@@ -0,0 +1,134 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.CoverageDataTypes
+
+/-! # Coverage certificate data, buckets 8–15 -/
+
+namespace Erdos97Octagon.RawIncidence
+
+/-- Generated monotone-obstruction entries for this hash-bucket group. -/
+def patternBuckets01 : Array (List PatternEntry) := #[
+  [
+    ⟨520, 11550371277176832, .k4 3 [3, 5, 6] 0 3 5 6⟩,
+    ⟨1288, 11331567406311424, .k4 1 [1, 3, 5, 6] 1 3 5 6⟩,
+    ⟨4104, 1513210061336936460, .k4 0 [0, 2, 7, 4, 3] 0 2 3 7⟩
+  ],
+  [
+    ⟨265, 606743552, .k4 1 [1, 2, 3] 1 2 3 5⟩,
+    ⟨777, 84544526, .k4 0 [0, 3, 2, 1] 0 1 2 3⟩,
+    ⟨1033, 2533275885699084, .k4 0 [0, 2, 3, 6] 0 2 3 6⟩,
+    ⟨1289, 11331568446498816, .k4 1 [1, 5, 6, 3] 1 3 5 6⟩,
+    ⟨4361, 5810792234088398848, .k4 2 [2, 5, 6, 7, 4] 2 4 5 6⟩,
+    ⟨7433, 4794081804510527758, .k4 0 [0, 1, 2, 7, 6, 3] 0 1 2 3⟩,
+  ],
+  [
+    ⟨1546, 74768437111808, .k4 1 [1, 2, 3, 5] 1 3 5 6⟩,
+    ⟨7434, 4794081817596559642, .k4 0 [0, 1, 4, 7, 6, 3] 0 1 3 4⟩
+  ],
+  [
+    ⟨11, 10592512, .sharedThree 1 2 0 5 7⟩,
+    ⟨779, 100862990, .k4 0 [0, 2, 1, 3] 0 1 2 3⟩,
+    ⟨1035, 2533275914486026, .k4 0 [0, 1, 3, 6] 0 1 3 6⟩,
+    ⟨1291, 11331568480051200, .k4 1 [1, 5, 6, 3] 1 3 5 6⟩,
+    ⟨4107, 1729382826329571356, .k4 0 [0, 2, 3, 7, 4] 0 2 3 4⟩,
+    ⟨5899, 12116106420510, .k4 0 [0, 1, 4, 5, 2] 0 2 3 5⟩,
+  ],
+  [
+    ⟨524, 11821949592299520, .k4 1 [1, 3, 6] 1 3 5 6⟩,
+    ⟨780, 101254414, .k4 0 [0, 1, 2, 3] 0 1 2 3⟩,
+    ⟨1036, 2533275914487818, .k4 0 [0, 3, 1, 6] 0 1 3 6⟩,
+    ⟨4364, 5814226972846325760, .k4 3 [3, 5, 6, 7, 4] 3 4 5 6⟩,
+  ],
+  [
+    ⟨525, 11821950632486912, .k4 1 [1, 6, 3] 1 3 5 6⟩,
+    ⟨781, 101256206, .k4 0 [0, 2, 3, 1] 0 1 2 3⟩,
+    ⟨1037, 2533275936030732, .k4 0 [0, 2, 3, 6] 0 2 3 6⟩
+  ],
+  [
+    ⟨14, 12697856, .sharedThree 1 2 0 6 7⟩,
+    ⟨270, 1112165376, .k4 1 [1, 2, 3] 1 2 3 6⟩,
+    ⟨1038, 2533275952283660, .k4 0 [0, 2, 3, 6] 0 2 3 6⟩,
+    ⟨4110, 1729382843258306588, .k4 0 [0, 2, 3, 7, 4] 0 2 3 4⟩,
+    ⟨7438, 4796333903797518614, .k4 0 [0, 1, 2, 7, 6, 4] 0 1 2 4⟩
+  ],
+  [
+    ⟨527, 11821950666039296, .k4 1 [1, 6, 3] 1 3 5 6⟩,
+    ⟨1039, 2533275952742412, .k4 0 [0, 3, 2, 6] 0 2 3 6⟩,
+    ⟨2319, 5811896283073347584, .k4 3 [3, 6, 7, 4] 3 4 5 6⟩,
+    ⟨7439, 4796333921027522842, .k4 0 [0, 1, 3, 7, 6, 4] 0 1 3 4⟩
+  ]
+]
+
+/-- Generated exact-table entries for this hash-bucket group. -/
+def hardBuckets01 : Array (List HardEntry) := #[
+  [
+    ⟨8, 8697799730289388830, .hubPentagon 0 [0, 1, 2, 3, 4, 5, 6, 7] 2 0 1 5 6 4⟩,
+    ⟨776, 8266581603606816030, .residual 3916658220028291⟩,
+    ⟨1032, 5420594277881441310, .residual 768639863790514⟩,
+    ⟨1288, 3140075081450941470, .residual 4346719763574279⟩,
+    ⟨5384, 3285891231469789470, .residual 4349139977733378⟩,
+    ⟨5640, 3146988536760295710, .residual 263033069355504⟩
+  ],
+  [
+    ⟨9, 8410694158827859230, .residual 3918988239981702⟩,
+    ⟨777, 3726884181624710430, .residual 157979233573620⟩,
+    ⟨1033, 5419406806330076190, .residual 1203547363024721⟩,
+    ⟨1289, 2851844722479098910, .residual 3323068763737746⟩,
+    ⟨5385, 4154163606970425630, .residual 1022613787071408⟩,
+    ⟨5641, 7654234419566403870, .residual 3300225149774344⟩
+  ],
+  [
+    ⟨10, 8697795349422746910, .cycleStrip 0 [0, 1, 2, 3, 4, 5, 6, 7] 0 1 2 5 6 7 4⟩,
+    ⟨778, 3150432618907526430, .residual 157994266016497⟩,
+    ⟨1034, 3713174884401638430, .residual 1343842705006036⟩,
+    ⟨1290, 5130667230218972190, .residual 3746380685381268⟩,
+    ⟨5386, 8374880746683490590, .residual 3363977526215938⟩,
+    ⟨5642, 7650869913985409310, .residual 3300225149774345⟩
+  ],
+  [
+    ⟨11, 8689069625664810270, .hubPentagon 0 [0, 1, 2, 4, 3, 5, 6, 7] 0 1 2 6 4 3⟩,
+    ⟨779, 8693867215323751710, .hubPentagon 0 [0, 1, 2, 3, 4, 5, 6, 7] 1 0 2 6 5 4⟩,
+    ⟨1035, 5446490936687815710, .residual 236284790560113⟩,
+    ⟨1291, 5130666135002311710, .residual 3746380685381265⟩,
+    ⟨5387, 3289485261948576030, .residual 1022609995944880⟩,
+    ⟨5643, 8659741810657255710, .residual 3362744870465794⟩
+  ],
+  [
+    ⟨12, 6168184248254803230, .residual 4403991276775443⟩,
+    ⟨780, 7654313722328474910, .residual 1167913026665954⟩,
+    ⟨1036, 5455147529172249630, .residual 1703548918296290⟩,
+    ⟨1292, 2858189038789094430, .residual 3253799472467604⟩,
+    ⟨5388, 3857276638301118750, .residual 209140128487920⟩,
+    ⟨5644, 4149307752152490270, .residual 3035688894908098⟩
+  ],
+  [
+    ⟨13, 8688509961394924830, .residual 708974291475411⟩,
+    ⟨781, 4154171992331347230, .residual 2471328076515536⟩,
+    ⟨1037, 8189464194495114270, .residual 3299984631541254⟩,
+    ⟨1293, 2857907568107351070, .residual 3253799472467601⟩,
+    ⟨5389, 3865933230785552670, .residual 4346975314200073⟩,
+    ⟨5645, 3862203275907621150, .residual 1734838808404581⟩
+  ],
+  [
+    ⟨14, 6454721393713163550, .residual 4278891759698982⟩,
+    ⟨782, 6463102686283326750, .residual 1243631141429042⟩,
+    ⟨1038, 8192693988426869790, .residual 1831459452811859⟩,
+    ⟨1294, 5132297947931765790, .residual 1766497048060753⟩,
+    ⟨5390, 3289481274575151390, .residual 4346975314200072⟩,
+    ⟨5646, 4147064748431827230, .residual 2920841436030789⟩
+  ],
+  [
+    ⟨15, 6175167135772519710, .residual 4403991276775444⟩,
+    ⟨783, 8262233563400398110, .residual 3254039990700688⟩,
+    ⟨1039, 6451358515895823390, .residual 4410442049490187⟩,
+    ⟨1295, 3714161027419499550, .residual 1734880180889185⟩,
+    ⟨5391, 3280824408286552350, .residual 209138249382384⟩,
+    ⟨5647, 3285751319697219870, .residual 3668700697602754⟩
+  ]
+]
+
+end Erdos97Octagon.RawIncidence
diff --git a/LeanPool/Erdos97ConvexOctagon/CoverageData02.lean b/LeanPool/Erdos97ConvexOctagon/CoverageData02.lean
new file mode 100644
index 00000000..051808ae
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/CoverageData02.lean
@@ -0,0 +1,141 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.CoverageDataTypes
+
+/-! # Coverage certificate data, buckets 16–23 -/
+
+namespace Erdos97Octagon.RawIncidence
+
+/-- Generated monotone-obstruction entries for this hash-bucket group. -/
+def patternBuckets02 : Array (List PatternEntry) := #[
+  [
+    ⟨784, 12886017302, .k4 0 [0, 1, 2, 4] 0 1 2 4⟩,
+    ⟨1040, 2533555322224664, .k4 0 [0, 3, 4, 6] 0 3 4 6⟩,
+    ⟨1552, 76965818230022, .k4 0 [0, 1, 2, 5] 1 2 5 6⟩,
+    ⟨6416, 1708821463985152, .k4 1 [1, 5, 6, 4, 2] 1 2 3 4⟩
+  ],
+  [
+    ⟨17, 14737408, .sharedThree 1 2 5 6 7⟩,
+    ⟨529, 11901113859074048, .k4 1 [1, 6, 5] 1 3 5 6⟩,
+    ⟨1041, 2533585386995736, .k4 0 [0, 3, 4, 6] 0 3 4 6⟩,
+    ⟨1553, 76965818360070, .k4 0 [0, 1, 2, 5] 1 2 5 6⟩,
+    ⟨2321, 5850670421308866560, .k4 4 [4, 6, 7, 5] 0 5 6 7⟩
+  ],
+  [
+    ⟨18, 369098774, .sharedThree 0 3 1 2 4⟩,
+    ⟨530, 12384899586064384, .k4 2 [2, 3, 6] 2 3 5 6⟩,
+    ⟨786, 12886082838, .k4 0 [0, 1, 4, 2] 0 1 2 4⟩,
+    ⟨2322, 5882142704703373312, .k4 4 [4, 5, 7, 6] 0 5 6 7⟩,
+    ⟨3602, 10487141910012934, .k4 0 [0, 2, 6, 5, 1] 0 1 2 6⟩,
+    ⟨10002, 4945031556302507278, .k4 0 [0, 1, 2, 7, 6, 5, 3] 0 1 2 3⟩
+  ],
+  [
+    ⟨19, 589496320, .sharedThree 2 3 0 1 5⟩,
+    ⟨1043, 2533589665185816, .k4 0 [0, 4, 3, 6] 0 3 4 6⟩,
+    ⟨3859, 13598923026482176, .k4 1 [1, 2, 4, 5, 6] 1 2 4 6⟩,
+  ],
+  [
+    ⟨20, 620766464, .sharedThree 1 3 0 2 5⟩,
+    ⟨532, 12384900655611904, .k4 2 [2, 3, 6] 2 3 5 6⟩,
+    ⟨788, 13170116890, .k4 0 [0, 1, 3, 4] 0 1 3 4⟩,
+    ⟨4116, 1729401672863580184, .k4 0 [0, 3, 7, 4, 5] 0 3 4 5⟩,
+    ⟨4372, 6958853218688327680, .k4 1 [1, 6, 7, 5, 4] 1 4 5 6⟩,
+    ⟨4628, 79166464814092, .k4 0 [0, 2, 3, 1, 5] 1 3 5 6⟩,
+    ⟨10772, 6954279246022396958, .k4 0 [0, 2, 4, 5, 7, 6, 1] 0 1 2 3⟩
+  ],
+  [
+    ⟨3861, 13598941576710144, .k4 1 [1, 3, 4, 5, 6] 1 3 4 6⟩,
+    ⟨10773, 6954279246105693214, .k4 0 [0, 3, 4, 5, 7, 6, 1] 0 1 2 3⟩
+  ],
+  [
+    ⟨22, 825294848, .sharedThree 2 3 0 4 5⟩,
+    ⟨534, 12459667443679232, .k4 3 [3, 6, 5] 2 3 5 6⟩,
+    ⟨790, 13186894106, .k4 0 [0, 1, 4, 3] 0 1 3 4⟩,
+    ⟨1046, 2814750912302080, .k4 1 [1, 2, 6, 3] 1 2 3 6⟩,
+    ⟨2070, 504403179749900310, .k4 0 [0, 4, 2, 7] 0 1 2 7⟩,
+    ⟨2326, 5947003903903006720, .k4 3 [3, 6, 7, 4] 1 3 4 7⟩,
+    ⟨2582, 10995670526990, .k4 0 [0, 2, 3, 5, 1] 0 1 2 3⟩,
+    ⟨4630, 79166498366476, .k4 0 [0, 2, 3, 1, 5] 1 3 5 6⟩,
+  ],
+  [
+    ⟨23, 1128464384, .sharedThree 2 3 0 1 6⟩,
+    ⟨535, 12464063819284480, .k4 2 [2, 6, 5] 2 3 5 6⟩,
+    ⟨2071, 504403720914665494, .k4 0 [0, 2, 4, 7] 0 1 4 7⟩,
+    ⟨6423, 1970364900983070, .k4 0 [0, 1, 4, 6, 3] 0 2 3 6⟩,
+    ⟨7703, 79186873181208, .k4 0 [0, 3, 4, 5, 2, 1] 1 2 5 6⟩,
+  ]
+]
+
+/-- Generated exact-table entries for this hash-bucket group. -/
+def hardBuckets02 : Array (List HardEntry) := #[
+  [
+    ⟨16, 7397963681003285790, .residual 3918988239981699⟩,
+    ⟨784, 8693728118512968990, .hubPentagon 0 [0, 1, 3, 4, 2, 5, 6, 7] 0 1 2 3 4 5⟩,
+    ⟨1040, 6136111352343260190, .residual 3045388487022112⟩,
+    ⟨1296, 5420526107913907230, .residual 257256841594482⟩,
+    ⟨5392, 8369814334206501150, .residual 191580323985904⟩,
+    ⟨5648, 3858838770326626590, .residual 4091069608319682⟩
+  ],
+  [
+    ⟨17, 7688989032892673310, .hubPentagon 0 [0, 1, 2, 3, 4, 5, 6, 7] 1 0 2 5 7 3⟩,
+    ⟨785, 5996980126964409630, .residual 712033508203473⟩,
+    ⟨1041, 8184531214588800030, .residual 1805483491652404⟩,
+    ⟨1297, 5132295748942064670, .residual 3489747765103381⟩,
+    ⟨5393, 3865932820079304990, .residual 3361812862682632⟩,
+    ⟨5649, 6428199532346138910, .residual 2675518563356242⟩
+  ],
+  [
+    ⟨18, 5445915077183089950, .residual 4411689737676928⟩,
+    ⟨786, 8693858838493881630, .hubPentagon 0 [0, 1, 2, 3, 4, 5, 6, 7] 1 0 2 6 5 3⟩,
+    ⟨1042, 7175740291220597790, .residual 2049895082094273⟩,
+    ⟨1298, 5130613496151567390, .residual 3486425606329121⟩,
+    ⟨5394, 3289480863868903710, .residual 3361812862682633⟩,
+    ⟨5650, 6141095056101269790, .residual 3035311114012359⟩
+  ],
+  [
+    ⟨19, 7391473148990926110, .residual 4411689737676929⟩,
+    ⟨787, 4154163606945096990, .residual 1978746867214544⟩,
+    ⟨1043, 5419468377941437470, .residual 1823071514850097⟩,
+    ⟨1299, 6454719482227092510, .residual 2983541482437160⟩,
+    ⟨5395, 7793362241094017310, .residual 191582203091440⟩,
+    ⟨5651, 6425956528625475870, .residual 3363992558602380⟩
+  ],
+  [
+    ⟨20, 6464014315383041310, .hubPentagon 0 [0, 1, 3, 4, 2, 5, 7, 6] 0 1 2 4 7 3⟩,
+    ⟨788, 3726884181390746910, .residual 157979233573617⟩,
+    ⟨1044, 8180738470737177630, .residual 1839048902310592⟩,
+    ⟨1300, 6024062767859788830, .residual 4409479976808714⟩,
+    ⟨5396, 5600390815133917470, .residual 4409615268393218⟩,
+    ⟨5652, 5564643099890868510, .residual 1620093009165906⟩
+  ],
+  [
+    ⟨21, 6168179867137486110, .residual 3911289779080211⟩,
+    ⟨789, 8230765558615860510, .residual 1159119080898018⟩,
+    ⟨1045, 6460014971478174750, .residual 3487524849550112⟩,
+    ⟨1301, 2852284528975703070, .residual 1765399672906577⟩,
+    ⟨5397, 3284769712112328990, .residual 4348042613567746⟩,
+    ⟨5653, 6137730550520275230, .residual 2042461542408786⟩
+  ],
+  [
+    ⟨22, 5450438317695970590, .residual 4403991276775440⟩,
+    ⟨790, 6460859425737565470, .residual 1244713473302322⟩,
+    ⟨1046, 7184465745452559390, .residual 3794595216460161⟩,
+    ⟨1302, 3139951938027678750, .residual 266035765757554⟩,
+    ⟨5398, 6455296734412857630, .residual 4408397645048329⟩,
+    ⟨5654, 6425393587261989150, .residual 1442160232545314⟩
+  ],
+  [
+    ⟨23, 6170945011122842910, .residual 4403991276775441⟩,
+    ⟨791, 7688024503822214430, .residual 3253902820010640⟩,
+    ⟨1047, 7175740154318515230, .residual 3795707613169029⟩,
+    ⟨1303, 5996977927222225950, .residual 1743538842297953⟩,
+    ⟨5399, 6168192258167988510, .residual 4408397645048328⟩,
+    ⟨5655, 6425941135697568030, .residual 2488068499035170⟩
+  ]
+]
+
+end Erdos97Octagon.RawIncidence
diff --git a/LeanPool/Erdos97ConvexOctagon/CoverageData03.lean b/LeanPool/Erdos97ConvexOctagon/CoverageData03.lean
new file mode 100644
index 00000000..03d9c48c
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/CoverageData03.lean
@@ -0,0 +1,136 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.CoverageDataTypes
+
+/-! # Coverage certificate data, buckets 24–31 -/
+
+namespace Erdos97Octagon.RawIncidence
+
+/-- Generated monotone-obstruction entries for this hash-bucket group. -/
+def patternBuckets03 : Array (List PatternEntry) := #[
+  [
+    ⟨24, 1157645568, .sharedThree 1 3 0 2 6⟩,
+    ⟨1560, 79165414075392, .k4 1 [1, 2, 3, 5] 1 2 5 6⟩,
+    ⟨10008, 4945040515000239382, .k4 0 [0, 1, 2, 7, 6, 5, 4] 0 1 2 4⟩
+  ],
+  [
+    ⟨1049, 2814750946247680, .k4 1 [1, 6, 3, 2] 1 2 3 6⟩,
+    ⟨1305, 11340364036202496, .k4 1 [1, 5, 6, 3] 1 3 5 6⟩,
+    ⟨1561, 79165448152064, .k4 1 [1, 2, 3, 5] 1 2 5 6⟩,
+    ⟨3865, 13599060463330304, .k4 1 [1, 2, 4, 6, 5] 1 2 4 5⟩,
+    ⟨7449, 4936508141643844622, .k4 0 [0, 2, 3, 7, 6, 1] 0 1 2 3⟩
+  ],
+  [
+    ⟨26, 1364262912, .sharedThree 2 3 0 4 6⟩,
+    ⟨282, 12886147094, .k4 0 [0, 2, 4] 0 1 2 4⟩,
+    ⟨3610, 10768616884610310, .k4 0 [0, 1, 2, 5, 6] 1 2 5 6⟩,
+    ⟨4122, 1734168193745813528, .k4 0 [0, 3, 7, 4, 6] 0 3 4 6⟩,
+    ⟨5146, 5629778711940126, .k4 0 [0, 4, 6, 2, 1] 0 1 2 3⟩,
+    ⟨5914, 12283607589150, .k4 0 [0, 1, 2, 5, 4] 0 3 4 5⟩,
+    ⟨10522, 2605543504651354142, .k4 0 [0, 3, 4, 6, 5, 7, 2] 0 1 2 4⟩
+  ],
+  [
+    ⟨27, 1627414784, .sharedThree 1 3 0 5 6⟩,
+    ⟨283, 13203669018, .k4 0 [0, 3, 4] 0 1 3 4⟩,
+    ⟨1307, 11342562562408448, .k4 2 [2, 5, 3, 6] 2 3 5 6⟩,
+    ⟨3867, 13599078478784512, .k4 1 [1, 3, 4, 6, 5] 1 3 4 5⟩,
+  ],
+  [
+    ⟨540, 13603157866184704, .k4 2 [2, 5, 6] 2 4 5 6⟩,
+    ⟨796, 21760639004, .k4 0 [0, 2, 3, 4] 0 2 3 4⟩,
+    ⟨6172, 83563492630790, .k4 0 [0, 1, 2, 3, 5] 1 2 5 6⟩,
+  ],
+  [
+    ⟨29, 1650589696, .sharedThree 2 3 1 5 6⟩,
+    ⟨285, 21827158044, .k4 0 [0, 3, 4] 0 2 3 4⟩,
+    ⟨541, 13607557784403968, .k4 3 [3, 5, 6] 3 4 5 6⟩,
+    ⟨797, 21761622044, .k4 0 [0, 3, 4, 2] 0 2 3 4⟩,
+    ⟨6429, 1970651539718430, .k4 0 [0, 1, 3, 6, 4] 0 2 4 6⟩
+  ],
+  [
+    ⟨30, 1677747200, .sharedThree 1 3 2 5 6⟩,
+    ⟨542, 13811382168322048, .k4 4 [4, 5, 6] 0 4 5 6⟩,
+    ⟨798, 21810970652, .k4 0 [0, 2, 4, 3] 0 2 3 4⟩,
+    ⟨3102, 3659175792100366, .k4 0 [0, 3, 6, 2, 1] 0 1 2 6⟩,
+    ⟨4382, 6963854063864643584, .k4 2 [2, 6, 7, 5, 4] 2 4 5 6⟩,
+    ⟨4638, 79205404533010, .k4 0 [0, 1, 4, 3, 5] 1 3 5 6⟩,
+  ],
+  [
+    ⟨287, 25771048982, .k4 0 [0, 2, 4] 0 1 2 4⟩,
+    ⟨543, 13864158726455296, .k4 4 [4, 6, 5] 0 4 5 6⟩,
+    ⟨799, 21811953692, .k4 0 [0, 4, 2, 3] 0 2 3 4⟩,
+    ⟨2335, 6999582281887145984, .k4 1 [1, 5, 6, 7] 0 5 6 7⟩,
+    ⟨6175, 83564010038538, .k4 0 [0, 1, 3, 2, 5] 1 3 5 6⟩,
+    ⟨7455, 4940449091881600278, .k4 0 [0, 1, 2, 7, 6, 4] 0 1 2 4⟩
+  ]
+]
+
+/-- Generated exact-table entries for this hash-bucket group. -/
+def hardBuckets03 : Array (List HardEntry) := #[
+  [
+    ⟨24, 7184589160277617950, .residual 226406619532019⟩,
+    ⟨792, 5420528452980860190, .residual 711896337513425⟩,
+    ⟨1048, 8189394926319528990, .residual 3331710506259856⟩,
+    ⟨1304, 2853403831846333470, .residual 2923477778371361⟩,
+    ⟨5400, 4148893111707951390, .residual 349875201253872⟩,
+    ⟨5656, 3290606744473493790, .residual 1023692327717808⟩
+  ],
+  [
+    ⟨25, 7180660618116476190, .residual 3793888694448390⟩,
+    ⟨793, 8693719202631148830, .hubPentagon 0 [0, 1, 3, 4, 2, 5, 6, 7] 0 1 2 4 3 5⟩,
+    ⟨1049, 7175177204398648350, .residual 1877999719610674⟩,
+    ⟨1305, 2851721579055836190, .residual 2927897312299797⟩,
+    ⟨5401, 5995936581807694110, .residual 342176711443952⟩,
+    ⟨5657, 3869310384852230430, .residual 1015995746266032⟩
+  ],
+  [
+    ⟨26, 6031663275072564510, .residual 779463114410963⟩,
+    ⟨794, 7688081784408925470, .residual 4348042613567745⟩,
+    ⟨1050, 3713035248555617310, .residual 1343842705006033⟩,
+    ⟨1306, 4153888184988625950, .residual 3546491193113128⟩,
+    ⟨5402, 5564712493871980830, .residual 3794715475545346⟩,
+    ⟨5658, 3284062743641514270, .residual 1871244612204578⟩
+  ],
+  [
+    ⟨27, 6022943160021822750, .residual 3723640476413990⟩,
+    ⟨795, 5455140781798483230, .residual 595511780550626⟩,
+    ⟨1051, 6454735958723619870, .residual 3917740551801216⟩,
+    ⟨1307, 3721549217830824990, .residual 4347907321983242⟩,
+    ⟨5403, 3862203671239123230, .residual 4231802802030274⟩,
+    ⟨5659, 5419393472641163550, .residual 2425263122528290⟩
+  ],
+  [
+    ⟨28, 6019002510582754590, .residual 3918988239981696⟩,
+    ⟨796, 5454296369753253150, .residual 4349155010119813⟩,
+    ⟨1052, 5419400209260702750, .residual 3489764676551445⟩,
+    ⟨5404, 4147065143763329310, .residual 3527997568727746⟩,
+    ⟨5660, 7650865515905736990, .residual 1094060979620784⟩
+  ],
+  [
+    ⟨29, 7171934894358539550, .residual 3911289779080208⟩,
+    ⟨797, 3147054906303079710, .residual 112070295373681⟩,
+    ⟨1053, 5418839458330536990, .residual 3487524849550113⟩,
+    ⟨5405, 3285751715028721950, .residual 4038065412876101⟩,
+    ⟨5661, 5993610964398301470, .residual 1871109262014498⟩
+  ],
+  [
+    ⟨30, 5442550541537783070, .residual 4411689737676937⟩,
+    ⟨798, 6029358286390191390, .residual 604170434734050⟩,
+    ⟨1054, 3713030747899653150, .residual 1171932374908513⟩,
+    ⟨5406, 3858839165658128670, .residual 2315224306631269⟩,
+    ⟨5662, 8229569156284473630, .residual 1086364398169008⟩
+  ],
+  [
+    ⟨31, 5155446065292913950, .residual 4411689737676936⟩,
+    ⟨799, 8262299143542170910, .residual 4347907321983233⟩,
+    ⟨1055, 5131169850288860190, .residual 186890244864626⟩,
+    ⟨5407, 3284630213168390430, .residual 3035658830072514⟩,
+    ⟨5663, 3858262609255522590, .residual 2425398472718370⟩
+  ]
+]
+
+end Erdos97Octagon.RawIncidence
diff --git a/LeanPool/Erdos97ConvexOctagon/CoverageData04.lean b/LeanPool/Erdos97ConvexOctagon/CoverageData04.lean
new file mode 100644
index 00000000..67cb8222
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/CoverageData04.lean
@@ -0,0 +1,132 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.CoverageDataTypes
+
+/-! # Coverage certificate data, buckets 32–39 -/
+
+namespace Erdos97Octagon.RawIncidence
+
+/-- Generated monotone-obstruction entries for this hash-bucket group. -/
+def patternBuckets04 : Array (List PatternEntry) := #[
+  [
+    ⟨32, 1886388224, .sharedThree 2 3 4 5 6⟩,
+    ⟨288, 30064772374, .k4 0 [0, 1, 4] 0 1 2 4⟩,
+    ⟨1056, 2887318104991744, .k4 1 [1, 3, 5, 6] 1 3 5 6⟩,
+    ⟨1568, 81364984553738, .k4 0 [0, 1, 3, 5] 1 3 5 6⟩,
+    ⟨6176, 83564077539594, .k4 0 [0, 1, 3, 2, 5] 1 3 5 6⟩
+  ],
+  [
+    ⟨33, 2206400512, .sharedThree 2 3 0 1 7⟩,
+    ⟨1057, 2887319145179136, .k4 1 [1, 5, 6, 3] 1 3 5 6⟩,
+    ⟨4385, 6964984363154931712, .k4 3 [3, 6, 7, 5, 4] 3 4 5 6⟩
+  ],
+  [
+    ⟨290, 30064967702, .k4 0 [0, 2, 4] 0 1 2 4⟩,
+    ⟨802, 25770919190, .k4 0 [0, 1, 2, 4] 0 1 2 4⟩,
+    ⟨1826, 9662671393678336, .k4 1 [1, 6, 5, 4] 1 2 4 5⟩,
+    ⟨4386, 6967229435707678720, .k4 1 [1, 5, 7, 6, 4] 1 4 5 6⟩,
+    ⟨5410, 11259000696040460, .k4 0 [0, 2, 3, 1, 6] 1 3 5 6⟩,
+    ⟨10786, 6958204639972502558, .k4 0 [0, 2, 4, 6, 7, 5, 1] 0 1 2 3⟩
+  ],
+  [
+    ⟨291, 30065950742, .k4 0 [0, 4, 2] 0 1 2 4⟩,
+    ⟨2083, 792633575521386522, .k4 0 [0, 4, 3, 7] 0 1 3 7⟩,
+    ⟨2339, 7026533510907191296, .k4 1 [1, 5, 6, 7] 0 5 6 7⟩,
+    ⟨10787, 6958204640055798814, .k4 0 [0, 3, 4, 6, 7, 5, 1] 0 1 2 3⟩
+  ],
+  [
+    ⟨36, 2442199040, .sharedThree 2 3 0 4 7⟩,
+    ⟨804, 25770984726, .k4 0 [0, 1, 2, 4] 0 1 2 4⟩,
+    ⟨1060, 2893915174758400, .k4 1 [1, 3, 6, 5] 1 3 5 6⟩,
+    ⟨1316, 11356169213837312, .k4 3 [3, 5, 4, 6] 3 4 5 6⟩,
+    ⟨1828, 9667086620059648, .k4 1 [1, 6, 5, 4] 1 3 4 5⟩,
+    ⟨2084, 792634099222183962, .k4 0 [0, 3, 4, 7] 0 1 4 7⟩,
+    ⟨4132, 1801440420124688396, .k4 0 [0, 3, 7, 4, 2] 0 2 3 7⟩,
+    ⟨7460, 5224738519868066830, .k4 0 [0, 2, 3, 7, 6, 1] 0 1 2 3⟩,
+  ],
+  [
+    ⟨37, 2701172992, .sharedThree 1 3 0 5 7⟩,
+    ⟨293, 38656344092, .k4 0 [0, 2, 4] 0 2 3 4⟩,
+    ⟨549, 14074169742352384, .k4 1 [1, 6, 4] 1 4 5 6⟩,
+    ⟨1317, 11356169750708224, .k4 3 [3, 6, 5, 4] 3 4 5 6⟩,
+    ⟨8741, 4945032655210096910, .k4 0 [0, 1, 2, 7, 6, 5] 0 1 3 5⟩
+  ],
+  [
+    ⟨38, 2711683072, .sharedThree 2 3 0 5 7⟩,
+    ⟨1574, 83563492566016, .k4 1 [1, 2, 3, 5] 1 2 5 6⟩,
+    ⟨2086, 864691130661994510, .k4 0 [0, 3, 7, 2] 0 1 2 3⟩,
+  ],
+  [
+    ⟨39, 2728525824, .sharedThree 2 3 1 5 7⟩,
+    ⟨295, 43268440090, .k4 0 [0, 3, 4] 0 1 3 4⟩,
+    ⟨1063, 2893916248498176, .k4 1 [1, 6, 3, 5] 1 3 5 6⟩,
+    ⟨2087, 864691130711867406, .k4 0 [0, 2, 7, 3] 0 1 2 3⟩,
+    ⟨4135, 2450101136024808448, .k4 1 [1, 2, 5, 3, 7] 1 2 3 7⟩,
+  ]
+]
+
+/-- Generated exact-table entries for this hash-bucket group. -/
+def hardBuckets04 : Array (List HardEntry) := #[
+  [
+    ⟨32, 5442549446321122590, .residual 3124966165754280⟩,
+    ⟨800, 6028513861510391070, .residual 4350117082851461⟩,
+    ⟨1056, 5157704203357547550, .residual 712285307943888⟩,
+    ⟨5408, 6141095451432771870, .residual 2042187201179218⟩,
+    ⟨5664, 6164798601768330270, .residual 2923892976750376⟩
+  ],
+  [
+    ⟨33, 5155444970076253470, .residual 4411689737676938⟩,
+    ⟨801, 7680136727664026910, .residual 4189975189770272⟩,
+    ⟨1057, 6163132537773911070, .residual 1203904415154000⟩,
+    ⟨5409, 6425956923956977950, .residual 2745992379589202⟩,
+    ⟨5665, 5590589649278592030, .residual 4408547969025546⟩
+  ],
+  [
+    ⟨34, 7180591349940890910, .residual 1988155130967488⟩,
+    ⟨802, 8254336871360390430, .residual 4251547840983072⟩,
+    ⟨1058, 6166509980601707550, .residual 4410442049490185⟩,
+    ⟨5410, 5564643495222370590, .residual 4411689737676940⟩,
+    ⟨5666, 6164798327964165150, .residual 3915966730421770⟩
+  ],
+  [
+    ⟨35, 5451206997120134430, .residual 138098946286448⟩,
+    ⟨803, 3725758281434031390, .residual 103291382048625⟩,
+    ⟨1059, 6022957742479272990, .residual 4410442049490184⟩,
+    ⟨5411, 6137730945851777310, .residual 4231425101817543⟩,
+    ⟨5667, 5590589375474426910, .residual 2923891068342056⟩
+  ],
+  [
+    ⟨36, 6022942894774037790, .residual 2059468769785392⟩,
+    ⟨804, 6455296725831148830, .residual 4409479976808704⟩,
+    ⟨1060, 3862349361617464350, .residual 350147663258736⟩,
+    ⟨5412, 5563521993362039070, .residual 1549893534162514⟩,
+    ⟨5668, 3865088805855421470, .residual 3486842687426344⟩
+  ],
+  [
+    ⟨37, 5446490925729066270, .residual 629718082397152⟩,
+    ⟨805, 6425393974011782430, .residual 4251412542173217⟩,
+    ⟨1061, 6427714773259545630, .residual 342449173455088⟩,
+    ⟨5413, 5132297956764606750, .residual 1994254564389922⟩,
+    ⟨5669, 3288636849645020190, .residual 4346975314200074⟩
+  ],
+  [
+    ⟨38, 8410695253242359070, .cycleStrip 0 [0, 1, 2, 3, 4, 5, 7, 6] 0 1 3 5 6 7 4⟩,
+    ⟨806, 5420528307154740510, .residual 4255832076101653⟩,
+    ⟨1062, 6166493488178949150, .residual 3045114133599784⟩,
+    ⟨5414, 6453044909064249630, .residual 936850218047408⟩,
+    ⟨5670, 3865088395149173790, .residual 3361812862682634⟩
+  ],
+  [
+    ⟨39, 8410690872375717150, .hubPentagon 0 [0, 1, 2, 3, 4, 5, 7, 6] 2 0 1 5 7 4⟩,
+    ⟨807, 3714161027670631710, .residual 621177753307105⟩,
+    ⟨1063, 6022941250056514590, .residual 4410442049490186⟩,
+    ⟨5415, 5564641296232669470, .residual 1379760778107938⟩,
+    ⟨5671, 3288636438938772510, .residual 3486838896299816⟩
+  ]
+]
+
+end Erdos97Octagon.RawIncidence
diff --git a/LeanPool/Erdos97ConvexOctagon/CoverageData05.lean b/LeanPool/Erdos97ConvexOctagon/CoverageData05.lean
new file mode 100644
index 00000000..49f259d6
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/CoverageData05.lean
@@ -0,0 +1,139 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.CoverageDataTypes
+
+/-! # Coverage certificate data, buckets 40–47 -/
+
+namespace Erdos97Octagon.RawIncidence
+
+/-- Generated monotone-obstruction entries for this hash-bucket group. -/
+def patternBuckets05 : Array (List PatternEntry) := #[
+  [
+    ⟨40, 2751505408, .sharedThree 1 3 2 5 7⟩,
+    ⟨296, 47244642586, .k4 0 [0, 1, 4] 0 1 3 4⟩,
+    ⟨552, 14636853415116800, .k4 2 [2, 4, 6] 2 4 5 6⟩,
+    ⟨808, 38739705884, .k4 0 [0, 2, 3, 4] 0 2 3 4⟩,
+    ⟨1064, 3096224794165514, .k4 0 [0, 1, 3, 6] 0 1 3 6⟩,
+    ⟨4136, 2450101136058231808, .k4 1 [1, 3, 5, 2, 7] 1 2 3 7⟩,
+    ⟨7720, 88102720924696, .k4 0 [0, 3, 4, 1, 5, 2] 1 2 5 6⟩,
+    ⟨10024, 5228679453010429214, .k4 0 [0, 1, 3, 2, 7, 6, 4] 0 1 2 4⟩
+  ],
+  [
+    ⟨809, 38740164636, .k4 0 [0, 3, 4, 2] 0 2 3 4⟩,
+    ⟨1321, 11901114429497344, .k4 1 [1, 6, 5, 3] 1 3 5 6⟩,
+    ⟨2089, 864691130881081372, .k4 0 [0, 2, 7, 3] 0 2 3 4⟩,
+    ⟨2345, 12936350750, .k4 0 [0, 2, 3, 4, 1] 0 1 2 4⟩,
+    ⟨6697, 9646015560838158, .k4 0 [0, 3, 1, 6, 5] 0 1 2 5⟩,
+    ⟨8745, 5224738520187355422, .k4 0 [0, 1, 2, 6, 7, 3] 0 2 3 4⟩
+  ],
+  [
+    ⟨42, 2964324352, .sharedThree 2 3 4 5 7⟩,
+    ⟨298, 47294971930, .k4 0 [0, 3, 4] 0 1 3 4⟩,
+    ⟨554, 14637128288829440, .k4 2 [2, 4, 6] 2 4 5 6⟩,
+    ⟨1066, 3096225834338570, .k4 0 [0, 1, 3, 6] 0 1 3 6⟩,
+    ⟨1322, 11901114966353920, .k4 1 [1, 3, 6, 5] 1 3 5 6⟩,
+    ⟨2346, 12936416286, .k4 0 [0, 3, 4, 1, 2] 0 1 2 4⟩,
+    ⟨2858, 27659925520412, .k4 0 [0, 2, 3, 4, 5] 0 3 4 5⟩
+  ],
+  [
+    ⟨43, 3238052096, .sharedThree 1 3 0 6 7⟩,
+    ⟨299, 47546630170, .k4 0 [0, 4, 3] 0 1 3 4⟩,
+    ⟨1067, 3096225834354698, .k4 0 [0, 3, 6, 1] 0 1 3 6⟩,
+    ⟨1323, 11901114966368256, .k4 1 [1, 6, 3, 5] 1 3 5 6⟩,
+  ],
+  [
+    ⟨44, 3250651136, .sharedThree 2 3 0 6 7⟩,
+    ⟨300, 51541245980, .k4 0 [0, 2, 4] 0 2 3 4⟩,
+    ⟨556, 14711895076372480, .k4 4 [4, 6, 5] 2 4 5 6⟩,
+    ⟨812, 38991364124, .k4 0 [0, 2, 4, 3] 0 2 3 4⟩,
+    ⟨1068, 3096225851115786, .k4 0 [0, 1, 3, 6] 0 1 3 6⟩,
+  ],
+  [
+    ⟨45, 3267493888, .sharedThree 2 3 1 6 7⟩,
+    ⟨301, 51891929116, .k4 0 [0, 3, 4] 0 2 3 4⟩,
+    ⟨557, 14724659726516224, .k4 2 [2, 6, 5] 2 4 5 6⟩,
+    ⟨813, 38991822876, .k4 0 [0, 4, 3, 2] 0 2 3 4⟩,
+    ⟨1069, 3096225851130122, .k4 0 [0, 1, 6, 3] 0 1 3 6⟩,
+    ⟨4397, 7211547920209805312, .k4 2 [2, 6, 7, 5, 4] 2 4 6 7⟩
+  ],
+  [
+    ⟨46, 3288384512, .sharedThree 1 3 2 6 7⟩,
+    ⟨302, 55835164700, .k4 0 [0, 2, 4] 0 2 3 4⟩,
+    ⟨558, 15762772373536768, .k4 3 [3, 4, 6] 3 4 5 6⟩,
+    ⟨1326, 12459667381288960, .k4 2 [2, 6, 3, 5] 2 3 5 6⟩,
+    ⟨2862, 844425018884366, .k4 0 [0, 1, 3, 6, 2] 0 1 2 6⟩,
+    ⟨10030, 5233255336936811534, .k4 0 [0, 2, 3, 7, 6, 5, 1] 0 1 2 3⟩
+  ],
+  [
+    ⟨303, 55836147740, .k4 0 [0, 4, 2] 0 2 3 4⟩,
+    ⟨2095, 936748743977861148, .k4 0 [0, 4, 2, 7] 0 2 3 7⟩,
+    ⟨2863, 844425018885134, .k4 0 [0, 3, 2, 1, 6] 0 1 2 6⟩,
+    ⟨8751, 5225301482995253278, .k4 0 [0, 2, 4, 6, 7, 3] 0 1 3 4⟩
+  ]
+]
+
+/-- Generated exact-table entries for this hash-bucket group. -/
+def hardBuckets05 : Array (List HardEntry) := #[
+  [
+    ⟨40, 8697794253403925790, .residual 3919108499073158⟩,
+    ⟨808, 5420526108165039390, .residual 128355992864626⟩,
+    ⟨1064, 6452484415601863710, .residual 1766852221134672⟩,
+    ⟨5416, 6463953189995208990, .residual 348792862155248⟩,
+    ⟨5672, 6176849385392563230, .residual 4403716935715220⟩
+  ],
+  [
+    ⟨41, 7401888936946248990, .hubPentagon 0 [0, 1, 2, 3, 4, 5, 7, 6] 1 0 2 7 5 3⟩,
+    ⟨809, 4157549558708593950, .residual 4347907321983232⟩,
+    ⟨1065, 6461191191255936030, .residual 2396827539183955⟩,
+    ⟨5417, 4157549567290302750, .residual 4346824990222857⟩,
+    ⟨5673, 5157704223821521950, .residual 4377740973378195⟩
+  ],
+  [
+    ⟨42, 7685063775813315870, .residual 3919108499073155⟩,
+    ⟨810, 4149305811566880030, .residual 4251547840983073⟩,
+    ⟨1066, 7171799521858513950, .residual 2509119394140465⟩,
+    ⟨5418, 3869323589185102110, .residual 4346824990222856⟩,
+    ⟨5674, 3860667531440808990, .residual 4334447695825300⟩
+  ],
+  [
+    ⟨43, 7181790898371636510, .residual 3794986058614022⟩,
+    ⟨811, 3140514888198677790, .residual 4254869999757333⟩,
+    ⟨1067, 6424318531947555870, .residual 2526707417338164⟩,
+    ⟨5419, 3726822759056728350, .residual 333397787280880⟩,
+    ⟨5675, 2862200060419630110, .residual 4308471733488275⟩
+  ],
+  [
+    ⟨44, 7185710678799494430, .residual 156055055194867⟩,
+    ⟨812, 3139951938278810910, .residual 119697331455858⟩,
+    ⟨1068, 5991979564789754910, .residual 2771134040222913⟩,
+    ⟨5420, 3293355667400352030, .residual 3302134262631682⟩,
+    ⟨5676, 6176836187159454750, .residual 935803625707443⟩
+  ],
+  [
+    ⟨45, 8189454433089957150, .residual 3919108499073156⟩,
+    ⟨813, 5996977927473358110, .residual 612398829144033⟩,
+    ⟨1069, 3145300087386762270, .residual 2286249345264866⟩,
+    ⟨5421, 4149308010581909790, .residual 2746007415644754⟩,
+    ⟨5677, 3857289827626705950, .residual 1006155204695987⟩
+  ],
+  [
+    ⟨46, 8410695252974972190, .hubPentagon 0 [0, 1, 2, 3, 4, 5, 7, 6] 2 0 1 5 7 4⟩,
+    ⟨814, 6453036656276563230, .residual 4409615268393216⟩,
+    ⟨1070, 3136574496252718110, .residual 3606055243924117⟩,
+    ⟨5422, 3862203534337040670, .residual 4231442020591303⟩,
+    ⟨5678, 6022957767204725790, .residual 3915696147353088⟩
+  ],
+  [
+    ⟨47, 8697798634003180830, .residual 4411569478585478⟩,
+    ⟨815, 4155289489154008350, .residual 4348042613567744⟩,
+    ⟨1071, 2849470020007848990, .residual 3602702921417377⟩,
+    ⟨5423, 3285751578126639390, .residual 1479526919118418⟩,
+    ⟨5679, 6020705941856117790, .residual 2317464136286432⟩
+  ]
+]
+
+end Erdos97Octagon.RawIncidence
diff --git a/LeanPool/Erdos97ConvexOctagon/CoverageData06.lean b/LeanPool/Erdos97ConvexOctagon/CoverageData06.lean
new file mode 100644
index 00000000..7c804d87
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/CoverageData06.lean
@@ -0,0 +1,132 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.CoverageDataTypes
+
+/-! # Coverage certificate data, buckets 48–55 -/
+
+namespace Erdos97Octagon.RawIncidence
+
+/-- Generated monotone-obstruction entries for this hash-bucket group. -/
+def patternBuckets06 : Array (List PatternEntry) := #[
+  [
+    ⟨48, 3503292416, .sharedThree 2 3 4 6 7⟩,
+    ⟨304, 55918460956, .k4 0 [0, 3, 4] 0 2 3 4⟩,
+    ⟨560, 15763046177701888, .k4 3 [3, 4, 6] 3 4 5 6⟩,
+    ⟨816, 43234887962, .k4 0 [0, 1, 3, 4] 0 1 3 4⟩,
+    ⟨1072, 3377700832691200, .k4 1 [1, 2, 6, 3] 1 2 3 6⟩,
+    ⟨1584, 88115556541440, .k4 1 [1, 2, 4, 5] 1 2 5 6⟩,
+  ],
+  [
+    ⟨49, 3758153728, .sharedThree 1 3 5 6 7⟩,
+    ⟨305, 56170119196, .k4 0 [0, 4, 3] 0 2 3 4⟩,
+    ⟨1329, 12464064959610880, .k4 2 [2, 6, 3, 5] 2 3 5 6⟩,
+    ⟨4145, 2450104432336281862, .k4 0 [0, 1, 2, 7, 5] 0 1 2 5⟩,
+    ⟨4657, 81364951198732, .k4 0 [0, 2, 3, 1, 5] 1 3 5 6⟩
+  ],
+  [
+    ⟨50, 3772776448, .sharedThree 2 3 5 6 7⟩,
+    ⟨562, 15842210209595392, .k4 4 [4, 6, 5] 3 4 5 6⟩,
+    ⟨818, 43251665178, .k4 0 [0, 1, 3, 4] 0 1 3 4⟩,
+    ⟨4146, 2450104432336282630, .k4 0 [0, 2, 1, 7, 5] 0 1 2 5⟩,
+  ],
+  [
+    ⟨51, 60129542158, .sharedThree 0 4 1 2 3⟩,
+    ⟨563, 15850561505067008, .k4 3 [3, 6, 5] 3 4 5 6⟩,
+    ⟨3379, 9646015512667142, .k4 0 [0, 2, 5, 6, 1] 0 1 2 5⟩,
+    ⟨4147, 2450108830432928010, .k4 0 [0, 1, 3, 7, 5] 0 1 3 5⟩,
+  ],
+  [
+    ⟨52, 150326149120, .sharedThree 2 4 0 1 5⟩,
+    ⟨564, 36591746985149440, .k4 1 [1, 2, 6] 1 2 6 7⟩,
+    ⟨2612, 12095234516230, .k4 0 [0, 1, 5, 3, 2] 0 1 2 5⟩,
+  ],
+  [
+    ⟨53, 150911057920, .sharedThree 3 4 0 1 5⟩,
+    ⟨821, 51625066524, .k4 0 [0, 3, 2, 4] 0 2 3 4⟩,
+    ⟨1077, 3377993126248448, .k4 2 [2, 4, 6, 3] 2 3 4 6⟩,
+    ⟨1333, 13531010998231040, .k4 1 [1, 5, 4, 6] 1 4 5 6⟩,
+    ⟨2357, 21526744094, .k4 0 [0, 3, 4, 1, 2] 0 1 2 3⟩,
+    ⟨4149, 2450117639360520466, .k4 0 [0, 1, 4, 7, 5] 0 1 4 5⟩
+  ],
+  [
+    ⟨54, 158913799424, .sharedThree 1 4 0 2 5⟩,
+    ⟨822, 51825410076, .k4 0 [0, 2, 3, 4] 0 2 3 4⟩,
+    ⟨1078, 3377993189163008, .k4 2 [2, 3, 4, 6] 2 3 4 6⟩,
+    ⟨2870, 844446410359062, .k4 0 [0, 1, 4, 6, 2] 0 1 2 6⟩,
+    ⟨5686, 16116641725161754, .k4 0 [0, 1, 3, 5, 6] 0 3 4 6⟩
+  ],
+  [
+    ⟨567, 36805052228231168, .k4 1 [1, 5, 6] 1 5 6 7⟩,
+    ⟨823, 51826393116, .k4 0 [0, 3, 4, 2] 0 2 3 4⟩,
+    ⟨1079, 3378009299484672, .k4 2 [2, 3, 6, 4] 2 3 4 6⟩,
+    ⟨1591, 90447716311314, .k4 0 [0, 1, 4, 5] 1 4 5 6⟩,
+    ⟨2871, 844446410359830, .k4 0 [0, 4, 2, 1, 6] 0 1 2 6⟩,
+    ⟨7735, 92531064988938, .k4 0 [0, 1, 3, 2, 4, 5] 1 2 5 6⟩
+  ]
+]
+
+/-- Generated exact-table entries for this hash-bucket group. -/
+def hardBuckets06 : Array (List HardEntry) := #[
+  [
+    ⟨48, 8410690872108330270, .cycleStrip 0 [0, 1, 2, 3, 4, 5, 7, 6] 0 1 2 5 7 6 4⟩,
+    ⟨816, 4147062961727366430, .residual 4189975189770273⟩,
+    ⟨1072, 6452484158910458910, .residual 3652170878076454⟩,
+    ⟨5424, 3858839028756046110, .residual 2112538780167762⟩,
+    ⟨5680, 6019017117765657630, .residual 3512535048794918⟩
+  ],
+  [
+    ⟨49, 6176905457452657950, .hubPentagon 0 [0, 1, 2, 4, 3, 5, 7, 6] 0 1 2 7 4 3⟩,
+    ⟨817, 3714723994569565470, .residual 4193297348544533⟩,
+    ⟨1073, 6451358276183485470, .residual 2316368651169888⟩,
+    ⟨5425, 3284630076266307870, .residual 4350117082851468⟩,
+    ⟨5681, 5564709195337098270, .residual 3794595216460167⟩
+  ],
+  [
+    ⟨50, 6455288723430124830, .residual 3911410038171667⟩,
+    ⟨818, 3714161053206078750, .residual 118598088034162⟩,
+    ⟨1074, 5155452660235791390, .residual 2624568115565872⟩,
+    ⟨5426, 6428199790775558430, .residual 2965185039579842⟩,
+    ⟨5682, 3858839152773227550, .residual 2317464136286433⟩
+  ],
+  [
+    ⟨51, 6032793555060337950, .residual 709111550073811⟩,
+    ⟨819, 5420526133700486430, .residual 611299585722337⟩,
+    ⟨1075, 7180383273861934110, .residual 3300931671773572⟩,
+    ⟨5427, 6141095314530689310, .residual 2315359605441125⟩,
+    ⟨5683, 5564643482337469470, .residual 347259562000626⟩
+  ],
+  [
+    ⟨52, 6024064678276312350, .residual 3724737840579622⟩,
+    ⟨820, 6427636857809429790, .residual 4189839890960417⟩,
+    ⟨1076, 3145158248256138270, .residual 3361557312056833⟩,
+    ⟨5428, 5564643358320288030, .residual 3598608540748482⟩,
+    ⟨5684, 3726892852872668190, .residual 3361542279613952⟩
+  ],
+  [
+    ⟨53, 8256604219807837470, .residual 3911410038171668⟩,
+    ⟨821, 5996980143442126110, .residual 4194259424888853⟩,
+    ⟨1077, 5446477755433774110, .residual 316422467528948⟩,
+    ⟨5429, 6137730808949694750, .residual 4231665620502210⟩,
+    ⟨5685, 3726884031244723230, .residual 2317584399040736⟩
+  ],
+  [
+    ⟨54, 7685068156178607390, .residual 4411569478585475⟩,
+    ⟨822, 3139951963814257950, .residual 620078509885409⟩,
+    ⟨1078, 8190295425286302750, .residual 316422467528947⟩,
+    ⟨5430, 5563521856459956510, .residual 4038048494102341⟩,
+    ⟨5686, 3726877459944760350, .residual 2949722519647014⟩
+  ],
+  [
+    ⟨55, 8406750222435298590, .hubPentagon 0 [0, 1, 2, 3, 4, 5, 7, 6] 1 0 2 5 6 3⟩,
+    ⟨823, 5996977953008805150, .residual 127256749442930⟩,
+    ⟨1079, 6164258437479951390, .residual 4409479976808715⟩,
+    ⟨5431, 2852284537808544030, .residual 1995216640734242⟩,
+    ⟨5687, 3292511242470220830, .residual 3302014003546503⟩
+  ]
+]
+
+end Erdos97Octagon.RawIncidence
diff --git a/LeanPool/Erdos97ConvexOctagon/CoverageData07.lean b/LeanPool/Erdos97ConvexOctagon/CoverageData07.lean
new file mode 100644
index 00000000..8ea32081
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/CoverageData07.lean
@@ -0,0 +1,131 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.CoverageDataTypes
+
+/-! # Coverage certificate data, buckets 56–63 -/
+
+namespace Erdos97Octagon.RawIncidence
+
+/-- Generated monotone-obstruction entries for this hash-bucket group. -/
+def patternBuckets07 : Array (List PatternEntry) := #[
+  [
+    ⟨56, 176093669632, .sharedThree 1 4 0 3 5⟩,
+    ⟨312, 163212043264, .k4 1 [1, 2, 4] 1 2 4 5⟩,
+    ⟨568, 37154696938570752, .k4 1 [1, 2, 6] 1 2 6 7⟩,
+    ⟨824, 51875741724, .k4 0 [0, 2, 3, 4] 0 2 3 4⟩,
+    ⟨1336, 13533218616639488, .k4 2 [2, 4, 5, 6] 2 4 5 6⟩
+  ],
+  [
+    ⟨57, 176096346112, .sharedThree 2 4 0 3 5⟩,
+    ⟨569, 37154700227248128, .k4 2 [2, 3, 6] 2 3 6 7⟩,
+    ⟨825, 51876266012, .k4 0 [0, 2, 4, 3] 0 2 3 4⟩,
+    ⟨1337, 13533218617688064, .k4 2 [2, 5, 4, 6] 2 4 5 6⟩,
+    ⟨2361, 21559905310, .k4 0 [0, 3, 4, 2, 1] 0 1 2 3⟩,
+    ⟨8761, 5233258635471103246, .k4 0 [0, 1, 3, 7, 6, 5] 0 1 2 5⟩
+  ],
+  [
+    ⟨58, 287767199744, .sharedThree 2 4 0 1 6⟩,
+    ⟨570, 37155538753028096, .k4 2 [2, 4, 6] 2 4 6 7⟩,
+    ⟨826, 3298537055494, .k4 0 [0, 1, 2, 5] 0 1 2 5⟩,
+    ⟨1082, 3452467122012160, .k4 2 [2, 3, 5, 6] 2 3 5 6⟩,
+    ⟨1338, 13537498277871616, .k4 3 [3, 4, 5, 6] 3 4 5 6⟩,
+    ⟨5178, 5657434005766172, .k4 0 [0, 2, 6, 4, 5] 0 3 4 5⟩
+  ],
+  [
+    ⟨59, 288886882304, .sharedThree 3 4 0 1 6⟩,
+    ⟨571, 37370201219530752, .k4 2 [2, 5, 6] 2 5 6 7⟩,
+    ⟨827, 3298537121030, .k4 0 [0, 1, 2, 5] 0 1 2 5⟩,
+    ⟨2107, 1369094862247362582, .k4 0 [0, 2, 4, 7] 0 1 4 7⟩,
+  ],
+  [
+    ⟨60, 296352761088, .sharedThree 1 4 0 2 6⟩,
+    ⟨572, 37717646887797760, .k4 1 [1, 2, 6] 1 2 6 7⟩,
+    ⟨828, 3298537185542, .k4 0 [0, 1, 2, 5] 0 1 2 5⟩,
+    ⟨1340, 13537635179954176, .k4 3 [3, 4, 5, 6] 3 4 5 6⟩,
+    ⟨1596, 92513600955392, .k4 1 [1, 2, 4, 5] 1 2 5 6⟩,
+    ⟨2108, 1369094879711330330, .k4 0 [0, 3, 4, 7] 0 1 4 7⟩,
+    ⟨8764, 5234308669077873930, .k4 0 [0, 1, 3, 2, 7, 6] 1 2 5 6⟩
+  ],
+  [
+    ⟨829, 3298537186310, .k4 0 [0, 2, 1, 5] 0 1 2 5⟩,
+    ⟨1341, 13537635448389632, .k4 3 [3, 5, 4, 6] 3 4 5 6⟩,
+    ⟨1597, 92515279044608, .k4 2 [2, 3, 4, 5] 2 3 5 6⟩,
+    ⟨2365, 21577075742, .k4 0 [0, 4, 2, 3, 1] 0 1 2 3⟩,
+    ⟨2877, 844743042941210, .k4 0 [0, 1, 3, 6, 4] 0 1 4 6⟩,
+    ⟨8765, 5801199824058010654, .k4 0 [0, 2, 4, 7, 6, 1] 0 1 2 3⟩,
+    ⟨10045, 5233821585424540686, .k4 0 [0, 3, 7, 6, 1, 5] 0 1 2 5⟩
+  ],
+  [
+    ⟨318, 181227497472, .k4 1 [1, 3, 4] 1 3 4 5⟩,
+    ⟨830, 3299088541962, .k4 0 [0, 1, 3, 5] 0 1 3 5⟩,
+    ⟨1086, 3456865168523264, .k4 2 [2, 3, 6, 5] 2 3 5 6⟩,
+    ⟨1598, 92638157013012, .k4 0 [0, 2, 4, 5] 2 4 5 6⟩,
+    ⟨2110, 1441152443408842774, .k4 0 [0, 4, 7, 2] 0 1 2 4⟩,
+    ⟨4414, 6597408989470, .k4 0 [0, 1, 5, 2, 3] 0 2 3 4⟩,
+    ⟨8766, 5801199824141306910, .k4 0 [0, 3, 4, 7, 6, 1] 0 1 2 3⟩
+  ],
+  [
+    ⟨63, 313537396736, .sharedThree 2 4 0 3 6⟩,
+    ⟨575, 37717646891991040, .k4 1 [1, 6, 2] 1 2 6 7⟩,
+    ⟨831, 3299105319178, .k4 0 [0, 1, 3, 5] 0 1 3 5⟩,
+    ⟨2111, 1441152456292761622, .k4 0 [0, 2, 7, 4] 0 1 2 4⟩,
+  ]
+]
+
+/-- Generated exact-table entries for this hash-bucket group. -/
+def hardBuckets07 : Array (List HardEntry) := #[
+  [
+    ⟨56, 6020124028603280670, .residual 3919108499073152⟩,
+    ⟨1080, 6425463230137789470, .residual 2983815835859488⟩,
+    ⟨5432, 4157540745662357790, .residual 1007216833091504⟩,
+    ⟨5688, 3284630063381406750, .residual 347139299246322⟩
+  ],
+  [
+    ⟨57, 6027726611954085150, .residual 3919108499073153⟩,
+    ⟨1081, 8185652733411486750, .residual 1243633049837364⟩,
+    ⟨5433, 3284067126346440990, .residual 1378663402953762⟩,
+    ⟨5689, 6141095301645788190, .residual 2317584399040737⟩
+  ],
+  [
+    ⟨58, 8401969528966360350, .hubPentagon 0 [0, 1, 3, 4, 2, 5, 6, 7] 0 1 2 4 6 3⟩,
+    ⟨1082, 7176861810043284510, .residual 1487082567597761⟩,
+    ⟨5434, 6455288481650499870, .residual 935767886174128⟩,
+    ⟨5690, 5155451889234600990, .residual 4377603802688147⟩
+  ],
+  [
+    ⟨59, 6455284342312807710, .residual 4403871017683987⟩,
+    ⟨1083, 5132363918658923550, .residual 1261221073035057⟩,
+    ⟨5435, 6453036656301891870, .residual 4408532936632841⟩,
+    ⟨5691, 3281954555917624350, .residual 4325651870951828⟩
+  ],
+  [
+    ⟨60, 7173065174095637790, .residual 3911410038171664⟩,
+    ⟨1084, 3862340685314288670, .residual 2923477778371360⟩,
+    ⟨5436, 5591723227567284510, .residual 4408532936632840⟩,
+    ⟨5692, 5600379139785876510, .residual 4394921110841748⟩
+  ],
+  [
+    ⟨61, 7175740309239901470, .residual 3911410038171665⟩,
+    ⟨1085, 7148858078349388830, .residual 3300931671773569⟩,
+    ⟨5437, 6461693248786325790, .residual 278426265174512⟩,
+    ⟨5693, 2862190729553372190, .residual 4308334562798227⟩
+  ],
+  [
+    ⟨62, 8404783183248764190, .residual 226269360933619⟩,
+    ⟨1086, 7148789079699778590, .residual 3303111367862661⟩,
+    ⟨5438, 4155298310807281950, .residual 1006134501218224⟩,
+    ⟨5694, 5446497545397396510, .residual 1755613694320864⟩
+  ],
+  [
+    ⟨63, 7395988974230580510, .residual 4348042613567750⟩,
+    ⟨1087, 6460844003279662110, .residual 752132264057780⟩,
+    ⟨5439, 4146632896694903070, .residual 279508604273136⟩,
+    ⟨5695, 5444245720048788510, .residual 3915711179795968⟩
+  ]
+]
+
+end Erdos97Octagon.RawIncidence
diff --git a/LeanPool/Erdos97ConvexOctagon/CoverageData08.lean b/LeanPool/Erdos97ConvexOctagon/CoverageData08.lean
new file mode 100644
index 00000000..513e27e8
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/CoverageData08.lean
@@ -0,0 +1,119 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.CoverageDataTypes
+
+/-! # Coverage certificate data, buckets 64–71 -/
+
+namespace Erdos97Octagon.RawIncidence
+
+/-- Generated monotone-obstruction entries for this hash-bucket group. -/
+def patternBuckets08 : Array (List PatternEntry) := #[
+  [
+    ⟨64, 416611852544, .sharedThree 1 4 0 5 6⟩,
+    ⟨832, 3299122094346, .k4 0 [0, 1, 3, 5] 0 1 3 5⟩,
+    ⟨1088, 3456866238070784, .k4 2 [2, 3, 5, 6] 2 3 5 6⟩,
+    ⟨6464, 2834705594477568, .k4 1 [1, 5, 6, 4, 3] 1 2 3 4⟩,
+  ],
+  [
+    ⟨577, 38280600134090752, .k4 2 [2, 3, 6] 2 3 6 7⟩,
+    ⟨833, 3299122096138, .k4 0 [0, 3, 1, 5] 0 1 3 5⟩,
+    ⟨1345, 13583787556364288, .k4 1 [1, 5, 6, 4] 1 4 5 6⟩,
+    ⟨7233, 13593708930801946, .k4 0 [0, 1, 5, 6, 4] 0 3 4 5⟩,
+    ⟨7745, 97049658853638, .k4 0 [0, 1, 2, 3, 4, 5] 2 4 5 6⟩,
+  ],
+  [
+    ⟨578, 38281459315769344, .k4 3 [3, 4, 6] 3 4 6 7⟩,
+    ⟨1602, 92775593869332, .k4 0 [0, 2, 4, 5] 2 4 5 6⟩,
+    ⟨2114, 1441152469179039772, .k4 0 [0, 4, 7, 2] 0 2 3 4⟩
+  ],
+  [
+    ⟨67, 420913217536, .sharedThree 2 4 1 5 6⟩,
+    ⟨579, 38500502916300800, .k4 3 [3, 5, 6] 3 5 6 7⟩,
+    ⟨1091, 3659174785843212, .k4 0 [0, 3, 2, 6] 0 2 3 6⟩,
+    ⟨5187, 6755679788338206, .k4 0 [0, 4, 6, 3, 1] 0 1 2 3⟩,
+    ⟨5699, 37154697022980362, .k4 0 [0, 1, 3, 2, 6] 1 2 6 7⟩,
+    ⟨8771, 5801762812669790494, .k4 0 [0, 1, 2, 6, 7, 4] 0 1 3 4⟩
+  ],
+  [
+    ⟨68, 422550962176, .sharedThree 3 4 1 5 6⟩,
+    ⟨836, 3448858747154, .k4 0 [0, 1, 4, 5] 0 1 4 5⟩,
+    ⟨2884, 1407376011905038, .k4 0 [0, 2, 3, 6, 1] 0 1 3 6⟩,
+    ⟨4164, 2594218521479752704, .k4 1 [1, 2, 3, 7, 5] 1 2 3 5⟩
+  ],
+  [
+    ⟨69, 429496755200, .sharedThree 1 4 2 5 6⟩,
+    ⟨1093, 3659175792476172, .k4 0 [0, 3, 6, 2] 0 2 3 6⟩,
+    ⟨1605, 96930238038016, .k4 2 [2, 3, 4, 5] 2 3 5 6⟩,
+    ⟨6469, 3096246224437534, .k4 0 [0, 1, 4, 6, 2] 0 2 3 6⟩,
+  ],
+  [
+    ⟨838, 5497560311046, .k4 0 [0, 1, 2, 5] 0 1 2 5⟩,
+    ⟨1606, 97038091943960, .k4 0 [0, 3, 4, 5] 3 4 5 6⟩,
+    ⟨5702, 37154718414455058, .k4 0 [0, 1, 4, 2, 6] 1 2 6 7⟩
+  ],
+  [
+    ⟨71, 446676625408, .sharedThree 1 4 3 5 6⟩,
+    ⟨327, 293472829440, .k4 2 [2, 3, 4] 2 3 4 6⟩,
+    ⟨583, 38843550040899584, .k4 1 [1, 6, 3] 1 3 6 7⟩,
+    ⟨839, 5497560376582, .k4 0 [0, 1, 2, 5] 0 1 2 5⟩,
+    ⟨8775, 5802888696483022110, .k4 0 [0, 1, 3, 6, 7, 4] 0 1 2 4⟩
+  ]
+]
+
+/-- Generated exact-table entries for this hash-bucket group. -/
+def hardBuckets08 : Array (List HardEntry) := #[
+  [
+    ⟨64, 8400275203023187230, .residual 779325855812563⟩,
+    ⟨1088, 6459722501419330590, .residual 933047028627393⟩,
+    ⟨5440, 4155289489179336990, .residual 4346960281807369⟩,
+    ⟨5696, 5442556895958328350, .residual 3512536927900454⟩
+  ],
+  [
+    ⟨65, 6166495397074709790, .residual 4277794395533350⟩,
+    ⟨1089, 4145503412625239070, .residual 760926224276401⟩,
+    ⟨5441, 3290611554863735070, .residual 4346960281807368⟩,
+    ⟨5697, 3150432631065338910, .residual 1755733957075168⟩
+  ],
+  [
+    ⟨66, 5157689080778599710, .residual 4411569478585472⟩,
+    ⟨1090, 3145018612410117150, .residual 3363706943147269⟩,
+    ⟨5442, 6141164599685341470, .residual 3795812839861506⟩,
+    ⟨5698, 3150423809437393950, .residual 3361557312056832⟩
+  ],
+  [
+    ⟨67, 5162203559574908190, .residual 4403871017683984⟩,
+    ⟨1091, 3136574491957816350, .residual 1231190103736098⟩,
+    ⟨5443, 3867564906395132190, .residual 3303231626947842⟩,
+    ⟨5699, 3150417238137431070, .residual 2949724398752550⟩
+  ],
+  [
+    ⟨68, 5442550540468235550, .residual 3919108499073160⟩,
+    ⟨1092, 6163132298061573150, .residual 2053936852036272⟩,
+    ⟨5444, 5417224136780079390, .residual 271808235357680⟩,
+    ⟨5700, 6141161301150458910, .residual 3795692580776327⟩
+  ],
+  [
+    ⟨69, 5155446064223366430, .residual 3919108499073161⟩,
+    ⟨1093, 5131176447107558430, .residual 746442617330594⟩,
+    ⟨5445, 3150353454651859230, .residual 263029311194608⟩,
+    ⟨5701, 3866720481465000990, .residual 3303111367862663⟩
+  ],
+  [
+    ⟨70, 5442549445251575070, .residual 3919108499073162⟩,
+    ⟨1094, 2852407912913464350, .residual 4317250646643985⟩,
+    ⟨5446, 3858978275153076510, .residual 4347907321983234⟩,
+    ⟨5702, 3858839182586864670, .residual 277870066581746⟩
+  ],
+  [
+    ⟨71, 5155444969006705950, .residual 3124964257345960⟩,
+    ⟨1095, 5446477729664363550, .residual 316422467528945⟩,
+    ⟨5447, 3862203688218190110, .residual 1479389748428370⟩,
+    ⟨5703, 5564643512151106590, .residual 1755733957075169⟩
+  ]
+]
+
+end Erdos97Octagon.RawIncidence
diff --git a/LeanPool/Erdos97ConvexOctagon/CoverageData09.lean b/LeanPool/Erdos97ConvexOctagon/CoverageData09.lean
new file mode 100644
index 00000000..180314c6
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/CoverageData09.lean
@@ -0,0 +1,125 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.CoverageDataTypes
+
+/-! # Coverage certificate data, buckets 72–79 -/
+
+namespace Erdos97Octagon.RawIncidence
+
+/-- Generated monotone-obstruction entries for this hash-bucket group. -/
+def patternBuckets09 : Array (List PatternEntry) := #[
+  [
+    ⟨584, 39406498967191552, .k4 2 [2, 3, 6] 2 3 6 7⟩,
+    ⟨840, 5497560441094, .k4 0 [0, 1, 2, 5] 0 1 2 5⟩,
+    ⟨1864, 10696049117193478, .k4 0 [0, 1, 2, 6] 1 2 5 6⟩,
+    ⟨2120, 1729382822000459802, .k4 0 [0, 4, 7, 3] 0 1 3 4⟩
+  ],
+  [
+    ⟨73, 562649300992, .sharedThree 2 4 0 1 7⟩,
+    ⟨585, 39406499973824512, .k4 2 [2, 6, 3] 2 3 6 7⟩,
+    ⟨841, 5497560441862, .k4 0 [0, 2, 1, 5] 0 1 2 5⟩,
+    ⟨1097, 4785353782263828, .k4 0 [0, 2, 4, 6] 0 2 4 6⟩,
+    ⟨1609, 97084253405184, .k4 2 [2, 4, 3, 5] 2 4 5 6⟩,
+    ⟨1865, 10696049117323526, .k4 0 [0, 1, 2, 6] 1 2 5 6⟩,
+    ⟨3145, 5066850228715798, .k4 0 [0, 1, 2, 6, 4] 0 1 2 4⟩,
+    ⟨6217, 92513601020166, .k4 0 [0, 1, 2, 4, 5] 1 2 5 6⟩
+  ],
+  [
+    ⟨74, 564838531072, .sharedThree 3 4 0 1 7⟩,
+    ⟨586, 39406500036739072, .k4 2 [2, 3, 6] 2 3 6 7⟩,
+    ⟨842, 5498114473996, .k4 0 [0, 2, 3, 5] 0 2 3 5⟩,
+    ⟨1610, 97174994026520, .k4 0 [0, 3, 4, 5] 3 4 5 6⟩,
+    ⟨1866, 10696049121371398, .k4 0 [0, 1, 2, 6] 1 2 5 6⟩,
+    ⟨2122, 1729382830623948828, .k4 0 [0, 4, 7, 3] 0 2 3 4⟩,
+    ⟨6218, 92515228778508, .k4 0 [0, 2, 3, 4, 5] 2 3 5 6⟩,
+  ],
+  [
+    ⟨587, 39406500040409088, .k4 2 [2, 6, 3] 2 3 6 7⟩,
+    ⟨2123, 1729382851813572634, .k4 0 [0, 3, 7, 4] 0 1 3 4⟩,
+    ⟨2635, 13216423346204, .k4 0 [0, 4, 2, 5, 3] 0 2 3 4⟩
+  ],
+  [
+    ⟨76, 573462020096, .sharedThree 3 4 0 2 7⟩,
+    ⟨1100, 4785362366906642, .k4 0 [0, 1, 4, 6] 0 1 4 6⟩,
+    ⟨6220, 92532676034572, .k4 0 [0, 2, 3, 4, 5] 2 3 5 6⟩,
+    ⟨6476, 3096551162462494, .k4 0 [0, 1, 2, 6, 4] 0 3 4 6⟩,
+    ⟨6732, 9654812157174798, .k4 0 [0, 3, 5, 6, 1] 0 1 2 5⟩,
+    ⟨8780, 5810207023318574354, .k4 0 [0, 1, 4, 2, 7, 6] 1 2 5 6⟩,
+  ],
+  [
+    ⟨589, 40533238473555968, .k4 2 [2, 4, 6] 2 4 6 7⟩,
+    ⟨8781, 5810769973267817746, .k4 0 [0, 1, 4, 2, 7, 6] 1 2 5 6⟩,
+    ⟨9805, 2460302402738880782, .k4 0 [0, 1, 3, 7, 5, 6, 2] 0 1 2 3⟩
+  ],
+  [
+    ⟨78, 588419497984, .sharedThree 2 4 0 3 7⟩,
+    ⟨590, 40533259129454592, .k4 3 [3, 4, 6] 3 4 6 7⟩,
+    ⟨846, 5639295270932, .k4 0 [0, 2, 4, 5] 0 2 4 5⟩,
+    ⟨1102, 4785366667165716, .k4 0 [0, 2, 4, 6] 0 2 4 6⟩,
+    ⟨1614, 143640897922048, .k4 1 [1, 2, 5, 4] 2 4 5 7⟩
+  ],
+  [
+    ⟨79, 691489775872, .sharedThree 1 4 0 5 7⟩,
+    ⟨591, 40762057137586176, .k4 4 [4, 5, 6] 4 5 6 7⟩,
+    ⟨847, 5652180172820, .k4 0 [0, 2, 4, 5] 0 2 4 5⟩,
+    ⟨1103, 4785370961084436, .k4 0 [0, 2, 4, 6] 0 2 4 6⟩,
+  ]
+]
+
+/-- Generated exact-table entries for this hash-bucket group. -/
+def hardBuckets09 : Array (List HardEntry) := #[
+  [
+    ⟨72, 7395849338384559390, .residual 1988157039375808⟩,
+    ⟨1096, 5450925404522572830, .residual 4346719763574277⟩,
+    ⟨5448, 4147065160742396190, .residual 2183194900947538⟩,
+    ⟨5704, 3280828673173939230, .residual 1007254448117683⟩
+  ],
+  [
+    ⟨73, 7389091843033017630, .residual 129319945053040⟩,
+    ⟨1097, 5162695045550730270, .residual 2508035153971762⟩,
+    ⟨5449, 3285751732007788830, .residual 4161210715195079⟩,
+    ⟨5705, 3284630093195043870, .residual 1755613694320865⟩
+  ],
+  [
+    ⟨74, 6166494858022759710, .residual 2059470678193712⟩,
+    ⟨1098, 5131229325436677150, .residual 3262818903856402⟩,
+    ⟨5450, 3858839182637195550, .residual 4349155010119820⟩,
+    ⟨5706, 6141095331459425310, .residual 277990329336050⟩
+  ],
+  [
+    ⟨75, 6164251841467526430, .residual 620939081163744⟩,
+    ⟨1099, 5131238018718919710, .residual 837909096354738⟩,
+    ⟨5451, 3284630230147457310, .residual 2675488465555026⟩,
+    ⟨5707, 5600374758902522910, .residual 936902869129139⟩
+  ],
+  [
+    ⟨76, 6461140884774923550, .residual 1202434926124884⟩,
+    ⟨1100, 8181864353213475870, .residual 1346467693059776⟩,
+    ⟨5452, 6141095468411838750, .residual 3668975137729218⟩,
+    ⟨5708, 6172627260742886430, .residual 4403716935715217⟩
+  ],
+  [
+    ⟨77, 6171789023942749470, .residual 2077096158814771⟩,
+    ⟨1101, 8184107220032056350, .residual 3902339872237968⟩,
+    ⟨5453, 6425956940936044830, .residual 2965170007136962⟩,
+    ⟨5709, 5164104614118220830, .residual 2468796906851412⟩
+  ],
+  [
+    ⟨78, 7681264814949346590, .residual 1202449987870548⟩,
+    ⟨1102, 7148782482630405150, .residual 1394214353296690⟩,
+    ⟨5454, 5564643512201437470, .residual 1752426831602277⟩,
+    ⟨5710, 3860651038767375390, .residual 4334447695825297⟩
+  ],
+  [
+    ⟨79, 7391912954117172510, .residual 2077111220560435⟩,
+    ⟨1103, 5995852285009751070, .residual 1835341575158225⟩,
+    ⟨5455, 6137730962830844190, .residual 4046707148285765⟩,
+    ⟨5711, 2852408767607792670, .residual 2469879245950036⟩
+  ]
+]
+
+end Erdos97Octagon.RawIncidence
diff --git a/LeanPool/Erdos97ConvexOctagon/CoverageData10.lean b/LeanPool/Erdos97ConvexOctagon/CoverageData10.lean
new file mode 100644
index 00000000..cfd4b47c
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/CoverageData10.lean
@@ -0,0 +1,127 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.CoverageDataTypes
+
+/-! # Coverage certificate data, buckets 80–87 -/
+
+namespace Erdos97Octagon.RawIncidence
+
+/-- Generated monotone-obstruction entries for this hash-bucket group. -/
+def patternBuckets10 : Array (List PatternEntry) := #[
+  [
+    ⟨80, 691500285952, .sharedThree 2 4 0 5 7⟩,
+    ⟨1104, 4785370962067476, .k4 0 [0, 4, 2, 6] 0 2 4 6⟩,
+    ⟨1616, 143661052471296, .k4 1 [1, 3, 5, 4] 3 4 5 7⟩,
+  ],
+  [
+    ⟨81, 694190866432, .sharedThree 3 4 0 5 7⟩,
+    ⟨1105, 4785385200680984, .k4 0 [0, 3, 4, 6] 0 3 4 6⟩,
+    ⟨1361, 13601104864501760, .k4 1 [1, 5, 4, 6] 1 4 5 6⟩,
+    ⟨2385, 38957286686, .k4 0 [0, 1, 2, 4, 3] 0 1 2 3⟩,
+    ⟨4177, 2594224018553307148, .k4 0 [0, 3, 2, 7, 5] 0 2 3 5⟩,
+    ⟨6225, 92646741796114, .k4 0 [0, 1, 4, 2, 5] 1 4 5 6⟩,
+    ⟨9809, 2460302415573975318, .k4 0 [0, 1, 4, 7, 5, 6, 2] 0 1 2 4⟩
+  ],
+  [
+    ⟨82, 695795318784, .sharedThree 2 4 1 5 7⟩,
+    ⟨1106, 4785389227212824, .k4 0 [0, 3, 4, 6] 0 3 4 6⟩,
+    ⟨3154, 5066867693602842, .k4 0 [0, 3, 4, 6, 1] 0 1 3 4⟩,
+    ⟨4178, 2594232836036821012, .k4 0 [0, 2, 4, 7, 5] 0 2 4 5⟩,
+    ⟨6226, 92663922581778, .k4 0 [0, 1, 4, 2, 5] 1 4 5 6⟩,
+  ],
+  [
+    ⟨83, 698502610944, .sharedThree 3 4 1 5 7⟩,
+    ⟨595, 41096179823460352, .k4 1 [1, 6, 4] 1 4 6 7⟩,
+    ⟨851, 6597642824704, .k4 1 [1, 3, 5, 2] 1 2 3 5⟩,
+    ⟨1107, 4785389478871064, .k4 0 [0, 4, 3, 6] 0 3 4 6⟩,
+    ⟨1363, 13601242303455232, .k4 1 [1, 5, 6, 4] 1 4 5 6⟩,
+    ⟨4179, 2594232836037804052, .k4 0 [0, 4, 2, 7, 5] 0 2 4 5⟩,
+  ],
+  [
+    ⟨84, 704374678528, .sharedThree 1 4 2 5 7⟩,
+    ⟨596, 41658863502491648, .k4 2 [2, 4, 6] 2 4 6 7⟩,
+    ⟨2388, 38957354014, .k4 0 [0, 4, 3, 1, 2] 0 1 2 3⟩,
+    ⟨3412, 9650414110664714, .k4 0 [0, 3, 5, 6, 1] 0 1 3 5⟩,
+    ⟨4180, 2595975540491969536, .k4 1 [1, 5, 6, 7, 2] 1 2 5 6⟩,
+    ⟨4692, 88102670591250, .k4 0 [0, 1, 4, 2, 5] 1 2 5 6⟩,
+  ],
+  [
+    ⟨85, 707126099968, .sharedThree 3 4 2 5 7⟩,
+    ⟨597, 41659121200529408, .k4 2 [2, 6, 4] 2 4 6 7⟩,
+    ⟨1365, 13603312483958784, .k4 2 [2, 5, 4, 6] 2 4 5 6⟩,
+    ⟨2133, 2450169303528563712, .k4 1 [1, 2, 7, 5] 1 2 5 6⟩,
+    ⟨6485, 3377726586094878, .k4 0 [0, 1, 3, 6, 2, 4] 0 1 2 4⟩,
+    ⟨8533, 14637008314066186, .k4 0 [0, 1, 3, 2, 4, 6] 1 2 5 6⟩
+  ],
+  [
+    ⟨598, 41659138376204288, .k4 2 [2, 4, 6] 2 4 6 7⟩,
+    ⟨1622, 145860111892480, .k4 2 [2, 3, 5, 4] 3 4 5 7⟩,
+    ⟨2902, 1688849915331854, .k4 0 [0, 1, 3, 6, 2] 0 1 2 3⟩,
+    ⟨4182, 2603859038865220608, .k4 1 [1, 6, 5, 7, 2] 1 2 5 6⟩,
+    ⟨8790, 6954834357664164110, .k4 0 [0, 1, 2, 6, 7, 5] 0 1 3 5⟩
+  ],
+  [
+    ⟨87, 721565515776, .sharedThree 2 4 3 5 7⟩,
+    ⟨599, 41659138379350016, .k4 2 [2, 6, 4] 2 4 6 7⟩,
+    ⟨1623, 145877225177088, .k4 2 [2, 4, 5, 3] 3 4 5 7⟩,
+    ⟨2903, 1688849915333646, .k4 0 [0, 3, 1, 6, 2] 0 1 2 3⟩,
+  ]
+]
+
+/-- Generated exact-table entries for this hash-bucket group. -/
+def hardBuckets10 : Array (List HardEntry) := #[
+  [
+    ⟨80, 7181721629143215390, .residual 1434001270554048⟩,
+    ⟨1104, 3865150934157388830, .residual 2466098654466387⟩,
+    ⟨5456, 5563522010341105950, .residual 4161314055964354⟩,
+    ⟨5712, 6139472451290588190, .residual 3280015953037714⟩
+  ],
+  [
+    ⟨81, 7684084094901300510, .residual 1434003178962368⟩,
+    ⟨1105, 5131230155405552670, .residual 2277607609955554⟩,
+    ⟨5457, 3858276241273708830, .residual 1440236054166562⟩,
+    ⟨5713, 3866713884395627550, .residual 3772597165951378⟩
+  ],
+  [
+    ⟨82, 6459170576917474590, .residual 3911410038171666⟩,
+    ⟨1106, 3865016222508149790, .residual 2457440067492148⟩,
+    ⟨5458, 2850032866341085470, .residual 2487797850035234⟩,
+    ⟨5714, 3858832585517491230, .residual 3685168810169621⟩
+  ],
+  [
+    ⟨83, 7176861673663376670, .residual 4403991276775442⟩,
+    ⟨1107, 3721463984385715230, .residual 2762492304913601⟩,
+    ⟨5459, 6176842108091162910, .residual 4409479976808706⟩,
+    ⟨5715, 3284623633027752990, .residual 3678569492256289⟩
+  ],
+  [
+    ⟨84, 7688143357060066590, .residual 4411569478585476⟩,
+    ⟨1108, 7148773669558840350, .residual 2448646004513073⟩,
+    ⟨5460, 4149308027560976670, .residual 3527982536284866⟩,
+    ⟨5716, 2850165361737262110, .residual 1977298036649044⟩
+  ],
+  [
+    ⟨85, 7679699108262063390, .residual 4411569478585473⟩,
+    ⟨1109, 5419387134861143070, .residual 2969521916484257⟩,
+    ⟨5461, 3862203551316107550, .residual 4046724067059525⟩,
+    ⟨5717, 2850026269221381150, .residual 1977298036649041⟩
+  ],
+  [
+    ⟨86, 5164102519270944030, .residual 138097067231088⟩,
+    ⟨1110, 5131161156755942430, .residual 2972874238990997⟩,
+    ⟨5462, 3285751595105706270, .residual 4161451237492418⟩,
+    ⟨5718, 3281946859336688670, .residual 4325651870951825⟩
+  ],
+  [
+    ⟨87, 8190575916684422430, .residual 3918988239981700⟩,
+    ⟨1111, 6171492125234457630, .residual 822483828394929⟩,
+    ⟨5463, 3858839045735112990, .residual 3106025427053250⟩,
+    ⟨5719, 5560768545664066590, .residual 3271220128164242⟩
+  ]
+]
+
+end Erdos97Octagon.RawIncidence
diff --git a/LeanPool/Erdos97ConvexOctagon/CoverageData11.lean b/LeanPool/Erdos97ConvexOctagon/CoverageData11.lean
new file mode 100644
index 00000000..bdf7754b
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/CoverageData11.lean
@@ -0,0 +1,122 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.CoverageDataTypes
+
+/-! # Coverage certificate data, buckets 88–95 -/
+
+namespace Erdos97Octagon.RawIncidence
+
+/-- Generated monotone-obstruction entries for this hash-bucket group. -/
+def patternBuckets11 : Array (List PatternEntry) := #[
+  [
+    ⟨88, 828928737536, .sharedThree 1 4 0 6 7⟩,
+    ⟨600, 42784784065232896, .k4 3 [3, 4, 6] 3 4 6 7⟩,
+    ⟨1368, 13607729046224896, .k4 3 [3, 4, 5, 6] 3 4 5 6⟩,
+    ⟨2136, 2450173701575073792, .k4 1 [1, 7, 5, 2] 1 2 5 6⟩,
+  ],
+  [
+    ⟨89, 828941336576, .sharedThree 2 4 0 6 7⟩,
+    ⟨601, 42785024583401472, .k4 3 [3, 6, 4] 3 4 6 7⟩,
+    ⟨1369, 13607729314660352, .k4 3 [3, 5, 4, 6] 3 4 5 6⟩,
+    ⟨1625, 147334566748422, .k4 0 [0, 1, 2, 5] 1 2 5 7⟩,
+    ⟨2137, 2450178101259329536, .k4 1 [1, 7, 5, 3] 1 3 5 6⟩,
+    ⟨4441, 10995990274334, .k4 0 [0, 1, 5, 3, 2] 0 2 3 4⟩
+  ],
+  [
+    ⟨602, 42785057869398016, .k4 3 [3, 4, 6] 3 4 6 7⟩,
+    ⟨2138, 2450187316614979584, .k4 1 [1, 7, 5, 4] 1 4 5 6⟩,
+    ⟨9818, 2461428303765143822, .k4 0 [0, 1, 2, 7, 5, 6, 3] 0 1 2 3⟩
+  ],
+  [
+    ⟨91, 833236369408, .sharedThree 2 4 1 6 7⟩,
+    ⟨603, 42785058674704384, .k4 3 [3, 6, 4] 3 4 6 7⟩,
+    ⟨1115, 5066850233762816, .k4 1 [1, 6, 4, 2] 1 2 4 6⟩,
+    ⟨1371, 13607866753613824, .k4 3 [3, 5, 6, 4] 3 4 5 6⟩,
+    ⟨2907, 1688849948429326, .k4 0 [0, 2, 3, 6, 1] 0 1 2 3⟩,
+    ⟨10075, 5810282889614484502, .k4 0 [0, 4, 7, 6, 1, 5] 0 1 2 5⟩,
+    ⟨10587, 3468546323312626718, .k4 0 [0, 2, 4, 7, 5, 6, 1] 0 1 2 3⟩
+  ],
+  [
+    ⟨92, 836478435328, .sharedThree 3 4 1 6 7⟩,
+    ⟨604, 45249301529550848, .k4 1 [1, 5, 6] 1 5 6 7⟩,
+    ⟨8796, 6955955860610753806, .k4 0 [0, 1, 3, 6, 7, 5] 0 1 2 5⟩,
+    ⟨9820, 2461428316851175706, .k4 0 [0, 1, 4, 7, 5, 6, 3] 0 1 3 4⟩
+  ],
+  [
+    ⟨93, 841813640192, .sharedThree 1 4 2 6 7⟩,
+    ⟨605, 45251500567429120, .k4 2 [2, 5, 6] 2 5 6 7⟩,
+    ⟨1629, 147337318638592, .k4 1 [1, 2, 5, 3] 2 3 5 7⟩
+  ],
+  [
+    ⟨94, 845101924352, .sharedThree 3 4 2 6 7⟩,
+    ⟨606, 45255902357356544, .k4 3 [3, 5, 6] 3 5 6 7⟩,
+    ⟨862, 7696581599494, .k4 0 [0, 1, 2, 5] 0 1 2 5⟩,
+    ⟨2654, 14294207046670, .k4 0 [0, 3, 5, 2, 1] 0 1 2 5⟩,
+  ],
+  [
+    ⟨607, 45265656764956672, .k4 4 [4, 5, 6] 4 5 6 7⟩,
+    ⟨863, 7696581600262, .k4 0 [0, 2, 1, 5] 0 1 2 5⟩,
+    ⟨1119, 5066868750567424, .k4 1 [1, 6, 4, 3] 1 3 4 6⟩,
+    ⟨1375, 14161855794667520, .k4 1 [1, 6, 5, 4] 1 4 5 6⟩,
+    ⟨1631, 148038942336000, .k4 1 [1, 2, 5, 4] 2 4 5 7⟩,
+    ⟨6239, 96912807100428, .k4 0 [0, 2, 3, 4, 5] 2 3 5 6⟩
+  ]
+]
+
+/-- Generated exact-table entries for this hash-bucket group. -/
+def hardBuckets11 : Array (List HardEntry) := #[
+  [
+    ⟨88, 6028848096049900830, .residual 3918988239981697⟩,
+    ⟨1112, 3858394538300697630, .residual 831277788613556⟩,
+    ⟨5464, 3284630093245374750, .residual 1752291532792421⟩,
+    ⟨5720, 6137154788874839070, .residual 3045388487022113⟩
+  ],
+  [
+    ⟨89, 7676196318743112990, .residual 129318065997680⟩,
+    ⟨1113, 3857273036440366110, .residual 1012192553183169⟩,
+    ⟨5465, 6428199807754625310, .residual 2183179864891986⟩,
+    ⟨5721, 5560702832664437790, .residual 3051987804935445⟩
+  ],
+  [
+    ⟨90, 6027669437570100510, .residual 4411569478585474⟩,
+    ⟨1114, 5131229055910702110, .residual 3916898738204933⟩,
+    ⟨5466, 6141095331509756190, .residual 4410727664945292⟩,
+    ⟨5722, 5128357294206673950, .residual 2468796906851409⟩
+  ],
+  [
+    ⟨91, 7391345605866958110, .residual 3918988239981698⟩,
+    ⟨1115, 5131161152477752350, .residual 1785208665339682⟩,
+    ⟨5467, 5564643375299354910, .residual 2605136886566482⟩,
+    ⟨5723, 6139406481599554590, .residual 3122356281021717⟩
+  ],
+  [
+    ⟨92, 6026825012690300190, .residual 4411689737676935⟩,
+    ⟨1116, 5131238848687795230, .residual 3793512884687234⟩,
+    ⟨5468, 6137730825928761630, .residual 1549756363472466⟩,
+    ⟨5724, 5562954525389153310, .residual 3115756963108385⟩
+  ],
+  [
+    ⟨93, 7175172823803505950, .residual 3919108499073159⟩,
+    ⟨1117, 5419400209010027550, .residual 1422509054762658⟩,
+    ⟨5469, 5563521873439023390, .residual 4161193796421319⟩,
+    ⟨5725, 5166346941884851230, .residual 1976215697550420⟩
+  ],
+  [
+    ⟨94, 6024064411992403230, .residual 1505314909371952⟩,
+    ⟨1118, 3716956004160138270, .residual 4249375660746946⟩,
+    ⟨5470, 6141093141076435230, .residual 1441333429320738⟩,
+    ⟨5726, 5130600165303444510, .residual 1976215697550417⟩
+  ],
+  [
+    ⟨95, 6454720852555541790, .residual 1505316817780272⟩,
+    ⟨1119, 3857143736701578270, .residual 3475218863138626⟩,
+    ⟨5471, 5132289015213646110, .residual 2486835773690914⟩,
+    ⟨5727, 5598408814949360670, .residual 4394921110841745⟩
+  ]
+]
+
+end Erdos97Octagon.RawIncidence
diff --git a/LeanPool/Erdos97ConvexOctagon/CoverageData12.lean b/LeanPool/Erdos97ConvexOctagon/CoverageData12.lean
new file mode 100644
index 00000000..2cc9640b
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/CoverageData12.lean
@@ -0,0 +1,127 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.CoverageDataTypes
+
+/-! # Coverage certificate data, buckets 96–103 -/
+
+namespace Erdos97Octagon.RawIncidence
+
+/-- Generated monotone-obstruction entries for this hash-bucket group. -/
+def patternBuckets12 : Array (List PatternEntry) := #[
+  [
+    ⟨96, 859006566400, .sharedThree 2 4 3 6 7⟩,
+    ⟨608, 45741882738794496, .k4 1 [1, 5, 6] 1 5 6 7⟩,
+    ⟨2912, 1688862750426390, .k4 0 [0, 1, 4, 6, 2] 0 1 2 4⟩,
+    ⟨6240, 96930214469898, .k4 0 [0, 1, 3, 4, 5] 1 3 5 6⟩,
+    ⟨9824, 2463680403052134678, .k4 0 [0, 1, 2, 7, 5, 6, 4] 0 1 2 4⟩,
+    ⟨10080, 7099229921754530830, .k4 0 [0, 3, 5, 7, 1, 6] 0 1 2 6⟩
+  ],
+  [
+    ⟨97, 962072731648, .sharedThree 1 4 5 6 7⟩,
+    ⟨609, 45810052459716608, .k4 1 [1, 6, 5] 1 5 6 7⟩,
+    ⟨865, 7696583566342, .k4 0 [0, 2, 5, 1] 0 1 2 5⟩,
+    ⟨1377, 14161993233620992, .k4 1 [1, 6, 4, 5] 1 4 5 6⟩,
+    ⟨4961, 162872166973464, .k4 0 [0, 3, 4, 5, 2] 2 3 5 7⟩,
+    ⟨6241, 96930254356492, .k4 0 [0, 2, 3, 4, 5] 2 3 5 6⟩,
+    ⟨10081, 7099238859027825686, .k4 0 [0, 4, 5, 7, 1, 6] 0 1 2 6⟩
+  ],
+  [
+    ⟨98, 962087354368, .sharedThree 2 4 5 6 7⟩,
+    ⟨9826, 2463680420282138906, .k4 0 [0, 1, 3, 7, 5, 6, 4] 0 1 3 4⟩
+  ],
+  [
+    ⟨99, 965830770688, .sharedThree 3 4 5 6 7⟩,
+    ⟨867, 7696583631110, .k4 0 [0, 1, 5, 2] 0 1 2 5⟩,
+    ⟨10083, 7100071048686642190, .k4 0 [0, 3, 6, 7, 1, 5] 0 1 2 5⟩
+  ],
+  [
+    ⟨100, 15393162788878, .sharedThree 0 5 1 2 3⟩,
+    ⟨612, 46307031730094080, .k4 2 [2, 5, 6] 2 5 6 7⟩,
+    ⟨868, 9896158308618, .k4 0 [0, 1, 3, 5] 0 1 3 5⟩,
+    ⟨1380, 14711877901746176, .k4 2 [2, 6, 4, 5] 2 4 5 6⟩,
+    ⟨5220, 7047871413100826, .k4 0 [0, 1, 5, 3, 6] 0 3 4 6⟩,
+    ⟨8804, 6958485835781054742, .k4 0 [0, 1, 2, 5, 7, 6] 0 2 4 6⟩
+  ],
+  [
+    ⟨101, 24189255811094, .sharedThree 0 5 1 2 4⟩,
+    ⟨613, 46373002427760640, .k4 2 [2, 6, 5] 2 5 6 7⟩,
+    ⟨3941, 216172782206746894, .k4 0 [0, 1, 3, 7, 2] 0 1 2 7⟩,
+    ⟨4197, 2882453297348881408, .k4 1 [1, 2, 3, 7, 5] 1 2 3 5⟩
+  ],
+  [
+    ⟨102, 28587302322202, .sharedThree 0 5 1 3 4⟩,
+    ⟨614, 46377400470077440, .k4 2 [2, 5, 6] 2 5 6 7⟩,
+    ⟨870, 9896175085834, .k4 0 [0, 1, 3, 5] 0 1 3 5⟩,
+    ⟨3942, 216172784362553614, .k4 0 [0, 1, 2, 7, 3] 0 1 3 7⟩
+  ],
+  [
+    ⟨103, 30786325577756, .sharedThree 0 5 2 3 4⟩,
+    ⟨359, 603787886592, .k4 2 [2, 4, 3] 2 3 4 7⟩,
+    ⟨615, 46377400472174592, .k4 2 [2, 6, 5] 2 5 6 7⟩,
+    ⟨871, 9896191861002, .k4 0 [0, 1, 3, 5] 0 1 3 5⟩,
+    ⟨1127, 5154931417833472, .k4 1 [1, 6, 4, 5] 1 4 5 6⟩,
+    ⟨1383, 14724951783243776, .k4 2 [2, 6, 4, 5] 2 4 5 6⟩,
+    ⟨3943, 216172803598221590, .k4 0 [0, 1, 4, 7, 2] 0 1 2 7⟩,
+    ⟨4967, 163281783358738, .k4 0 [0, 1, 4, 2, 5] 2 4 5 7⟩,
+    ⟨7271, 14434390528508186, .k4 0 [0, 1, 6, 5, 3] 0 3 4 6⟩,
+    ⟨10087, 7102323126582682646, .k4 0 [0, 4, 6, 7, 1, 5] 0 1 2 5⟩
+  ]
+]
+
+/-- Generated exact-table entries for this hash-bucket group. -/
+def hardBuckets12 : Array (List HardEntry) := #[
+  [
+    ⟨96, 6028799718126071070, .residual 4411689737676930⟩,
+    ⟨1120, 2852278069844536350, .residual 4170004660737221⟩,
+    ⟨5472, 6164806280117018910, .residual 953327621082032⟩,
+    ⟨5728, 3292495849308349470, .residual 3763801341077906⟩
+  ],
+  [
+    ⟨97, 7679580362667797790, .residual 3919108499073154⟩,
+    ⟨1121, 3713030747648977950, .residual 2317405881600101⟩,
+    ⟨5473, 3867059112994464030, .residual 1023696118844336⟩,
+    ⟨5729, 3858823622709273630, .residual 3608201016170017⟩
+  ],
+  [
+    ⟨98, 6463393094542306590, .residual 4403871017683988⟩,
+    ⟨1122, 2851717318914370590, .residual 2982865092065602⟩,
+    ⟨5474, 5590605597368705310, .residual 945631039630256⟩,
+    ⟨5730, 3284614670219535390, .residual 3614800334083349⟩
+  ],
+  [
+    ⟨99, 6459170970143304990, .residual 4403871017683985⟩,
+    ⟨1123, 5995847784353786910, .residual 1481298832039378⟩,
+    ⟨5475, 3858832585567822110, .residual 1873304089393186⟩,
+    ⟨5731, 2852269131761771550, .residual 2469879245950033⟩
+  ],
+  [
+    ⟨100, 5159386447612488990, .residual 629716203341792⟩,
+    ⟨1124, 6136035516895226910, .residual 2748053695466578⟩,
+    ⟨5476, 5560702845549338910, .residual 2427322651097122⟩,
+    ⟨5732, 7148705516495692830, .residual 4049790669524776⟩
+  ],
+  [
+    ⟨101, 8257725703402302750, .residual 3911289779080212⟩,
+    ⟨1125, 5131169850038184990, .residual 4411539413806348⟩,
+    ⟨5477, 3292858430246150430, .residual 1015999537392560⟩,
+    ⟨5733, 7146462512775029790, .residual 3792821395080714⟩
+  ],
+  [
+    ⟨102, 7176861793085041950, .residual 3911289779080209⟩,
+    ⟨1126, 5991922527842626590, .residual 4248877701442759⟩,
+    ⟨5478, 6139406481649885470, .residual 1873168790583330⟩,
+    ⟨5734, 7148705379593610270, .residual 3300240182167050⟩
+  ],
+  [
+    ⟨103, 6451356316910234910, .residual 620937202108384⟩,
+    ⟨1127, 5130609099108019230, .residual 989142335587282⟩,
+    ⟨5479, 3284614683104436510, .residual 2427457949906978⟩,
+    ⟨5735, 7146462375872947230, .residual 4049788786806568⟩
+  ]
+]
+
+end Erdos97Octagon.RawIncidence
diff --git a/LeanPool/Erdos97ConvexOctagon/CoverageData13.lean b/LeanPool/Erdos97ConvexOctagon/CoverageData13.lean
new file mode 100644
index 00000000..df735beb
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/CoverageData13.lean
@@ -0,0 +1,130 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.CoverageDataTypes
+
+/-! # Coverage certificate data, buckets 104–111 -/
+
+namespace Erdos97Octagon.RawIncidence
+
+/-- Generated monotone-obstruction entries for this hash-bucket group. -/
+def patternBuckets13 : Array (List PatternEntry) := #[
+  [
+    ⟨104, 73667283451904, .sharedThree 2 5 0 1 6⟩,
+    ⟨616, 47437333426864128, .k4 3 [3, 5, 6] 3 5 6 7⟩,
+    ⟨872, 9896191862794, .k4 0 [0, 3, 1, 5] 0 1 3 5⟩,
+    ⟨1128, 5348037442421010, .k4 0 [0, 1, 4, 6] 0 1 4 6⟩,
+    ⟨1640, 151734802489610, .k4 0 [0, 1, 3, 5] 1 3 5 7⟩,
+    ⟨3944, 216172823217996058, .k4 0 [0, 1, 4, 7, 3] 0 1 3 7⟩,
+    ⟨4200, 2882453452204015616, .k4 2 [2, 3, 4, 7, 5] 2 3 4 5⟩,
+    ⟨4712, 88399018025222, .k4 0 [0, 1, 2, 4, 5] 1 4 5 6⟩,
+    ⟨6248, 97079951122706, .k4 0 [0, 1, 4, 3, 5] 1 4 5 6⟩,
+    ⟨6760, 9663749430469654, .k4 0 [0, 4, 5, 6, 1] 0 1 2 5⟩,
+  ],
+  [
+    ⟨105, 73668403134464, .sharedThree 3 5 0 1 6⟩,
+    ⟨617, 47498906078019584, .k4 3 [3, 6, 5] 3 5 6 7⟩,
+    ⟨1385, 15842176655163392, .k4 3 [3, 5, 6, 4] 3 4 5 6⟩,
+    ⟨2153, 2594284491612775424, .k4 1 [1, 2, 7, 5] 1 2 5 6⟩,
+    ⟨3945, 216173357640548630, .k4 0 [0, 1, 2, 7, 4] 0 1 4 7⟩,
+    ⟨7273, 14636849117094166, .k4 0 [0, 1, 2, 4, 6] 1 4 5 6⟩,
+  ],
+  [
+    ⟨106, 73955041869824, .sharedThree 4 5 0 1 6⟩,
+    ⟨618, 47507701097299968, .k4 3 [3, 5, 6] 3 5 6 7⟩,
+    ⟨1386, 15842177192034304, .k4 3 [3, 6, 4, 5] 3 4 5 6⟩,
+    ⟨3946, 216173375104516378, .k4 0 [0, 1, 3, 7, 4] 0 1 4 7⟩,
+    ⟨7274, 14636849117160722, .k4 0 [0, 1, 4, 2, 6] 1 4 5 6⟩
+  ],
+  [
+    ⟨107, 75866302334208, .sharedThree 1 5 0 2 6⟩,
+    ⟨619, 47507701634170880, .k4 3 [3, 6, 5] 3 5 6 7⟩,
+    ⟨875, 9896228028428, .k4 0 [0, 3, 2, 5] 0 2 3 5⟩,
+    ⟨1387, 15850733035323392, .k4 3 [3, 6, 5, 4] 3 4 5 6⟩,
+    ⟨5739, 1441152434818256158, .k4 0 [0, 1, 4, 7, 2] 0 1 2 3⟩,
+    ⟨7275, 14636866297946386, .k4 0 [0, 1, 4, 2, 6] 1 4 5 6⟩
+  ],
+  [
+    ⟨620, 49698887648149504, .k4 4 [4, 5, 6] 4 5 6 7⟩,
+    ⟨876, 10038160654360, .k4 0 [0, 3, 4, 5] 0 3 4 5⟩,
+    ⟨2156, 2594286690635899904, .k4 1 [1, 5, 7, 2] 1 2 5 6⟩,
+    ⟨4716, 88416481992970, .k4 0 [0, 1, 3, 4, 5] 1 4 5 6⟩,
+  ],
+  [
+    ⟨621, 49751664206282752, .k4 4 [4, 6, 5] 4 5 6 7⟩,
+    ⟨877, 10068225425432, .k4 0 [0, 3, 4, 5] 0 3 4 5⟩,
+    ⟨1133, 5348308025360658, .k4 0 [0, 1, 6, 4] 0 1 4 6⟩,
+    ⟨1389, 15850870474276864, .k4 3 [3, 6, 4, 5] 3 4 5 6⟩,
+  ],
+  [
+    ⟨366, 7696581403910, .k4 0 [0, 1, 5] 0 1 2 5⟩,
+    ⟨622, 49768981514420224, .k4 4 [4, 5, 6] 4 5 6 7⟩,
+    ⟨878, 10072251957272, .k4 0 [0, 3, 4, 5] 0 3 4 5⟩,
+    ⟨1390, 216172782122402054, .k4 0 [0, 1, 2, 7] 0 1 2 7⟩
+  ],
+  [
+    ⟨111, 80264353611776, .sharedThree 2 5 0 3 6⟩,
+    ⟨623, 49769118953373696, .k4 4 [4, 6, 5] 4 5 6 7⟩,
+    ⟨879, 10072503615512, .k4 0 [0, 4, 3, 5] 0 3 4 5⟩,
+    ⟨1391, 216172784311632138, .k4 0 [0, 1, 3, 7] 0 1 3 7⟩,
+    ⟨4207, 2882463232058982424, .k4 0 [0, 3, 4, 7, 5] 0 3 4 5⟩,
+    ⟨7279, 14636977964146966, .k4 0 [0, 1, 2, 4, 6] 1 2 5 6⟩,
+  ]
+]
+
+/-- Generated exact-table entries for this hash-bucket group. -/
+def hardBuckets13 : Array (List HardEntry) := #[
+  [
+    ⟨104, 6170944581331856670, .residual 3911289779080210⟩,
+    ⟨1128, 5131237749192944670, .residual 3793753402863879⟩,
+    ⟨5480, 6428269058399658270, .residual 3795948131345666⟩,
+    ⟨5736, 8688943183795184670, .residual 3911135697111444⟩
+  ],
+  [
+    ⟨105, 7175740154322627870, .residual 4403871017683986⟩,
+    ⟨1129, 3713030743370787870, .residual 2316368651169889⟩,
+    ⟨5481, 4155790866969780510, .residual 3303366918432002⟩,
+    ⟨5737, 6019017377682416670, .residual 3885159734774419⟩
+  ],
+  [
+    ⟨106, 6026829393289555230, .residual 4411569478585479⟩,
+    ⟨1130, 5131169845759994910, .residual 346164076884082⟩,
+    ⟨5482, 7364891501338026270, .residual 1084199734522800⟩,
+    ⟨5738, 5995936430967874590, .residual 3772597165951380⟩
+  ],
+  [
+    ⟨107, 7175177204402760990, .residual 3918988239981703⟩,
+    ⟨1131, 6460928950737792030, .residual 4386519886533904⟩,
+    ⟨5483, 7366012866296275230, .residual 1084201617241008⟩,
+    ⟨5739, 8657980938202506270, .residual 3746621203614355⟩
+  ],
+  [
+    ⟨108, 6461140884022897950, .residual 1514146473778739⟩,
+    ⟨1132, 6171858560587361310, .hubPentagon 0 [0, 2, 3, 4, 1, 6, 7, 5] 0 1 2 7 4 3⟩,
+    ⟨5484, 6426025797853896990, .residual 3794986058614018⟩,
+    ⟨5740, 8688929985562076190, .residual 935818687453107⟩
+  ],
+  [
+    ⟨109, 6171789023190723870, .residual 1765384611160916⟩,
+    ⟨1133, 3148396187577707550, .residual 768641746508722⟩,
+    ⟨5485, 7366004198549479710, .residual 1092980530566064⟩,
+    ⟨5741, 6166510004257612830, .residual 4408277385956864⟩
+  ],
+  [
+    ⟨110, 7681264814197320990, .residual 1514161535524403⟩,
+    ⟨1134, 3141636390559902750, .residual 1202449987870545⟩,
+    ⟨5486, 4158033476963262750, .residual 3302404845700354⟩,
+    ⟨5742, 5590049226419266590, .residual 2308685135053024⟩
+  ],
+  [
+    ⟨111, 7391912953365146910, .residual 1765399672906580⟩,
+    ⟨1135, 6032721106497530910, .residual 1342760365907412⟩,
+    ⟨5487, 7362639556066402590, .residual 1092978647847856⟩,
+    ⟨5743, 5157703687961502750, .residual 4066688967914278⟩
+  ]
+]
+
+end Erdos97Octagon.RawIncidence
diff --git a/LeanPool/Erdos97ConvexOctagon/CoverageData14.lean b/LeanPool/Erdos97ConvexOctagon/CoverageData14.lean
new file mode 100644
index 00000000..d756afd3
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/CoverageData14.lean
@@ -0,0 +1,130 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.CoverageDataTypes
+
+/-! # Coverage certificate data, buckets 112–119 -/
+
+namespace Erdos97Octagon.RawIncidence
+
+/-- Generated monotone-obstruction entries for this hash-bucket group. -/
+def patternBuckets14 : Array (List PatternEntry) := #[
+  [
+    ⟨112, 80577881440256, .sharedThree 4 5 0 3 6⟩,
+    ⟨1392, 216173344754532626, .k4 0 [0, 1, 4, 7] 0 1 4 7⟩,
+    ⟨1648, 153933869809676, .k4 0 [0, 2, 3, 5] 2 3 5 7⟩,
+    ⟨4720, 90301693781012, .k4 0 [0, 2, 4, 5, 1] 1 2 5 6⟩,
+  ],
+  [
+    ⟨625, 504403158274080774, .k4 0 [0, 2, 7] 0 1 2 7⟩,
+    ⟨881, 10995219573760, .k4 1 [1, 3, 5, 2] 1 2 3 5⟩,
+    ⟨1137, 5629552421765120, .k4 2 [2, 4, 6, 3] 2 3 4 6⟩,
+    ⟨1393, 360287972429463564, .k4 0 [0, 2, 3, 7] 0 2 3 7⟩,
+    ⟨2673, 18833433830678, .k4 0 [0, 1, 4, 2, 5] 0 1 2 5⟩,
+    ⟨3185, 5348303734719510, .k4 0 [0, 4, 6, 1, 2] 0 1 2 6⟩,
+    ⟨4209, 2885331819224393728, .k4 1 [1, 5, 6, 7, 3] 1 3 5 6⟩,
+    ⟨8561, 432345603193340190, .k4 0 [0, 1, 4, 7, 3, 2] 0 1 2 3⟩
+  ],
+  [
+    ⟨114, 89060447158272, .sharedThree 2 5 0 4 6⟩,
+    ⟨882, 10995722497024, .k4 1 [1, 2, 5, 3] 1 2 3 5⟩,
+    ⟨1138, 5629783007446016, .k4 1 [1, 2, 6, 4] 1 2 4 6⟩,
+    ⟨1394, 360288541428744212, .k4 0 [0, 2, 4, 7] 0 2 4 7⟩,
+    ⟨1906, 11821949609074954, .k4 0 [0, 1, 3, 6] 1 3 5 6⟩,
+    ⟨5746, 1729382817421525022, .k4 0 [0, 2, 3, 7, 4] 0 1 2 4⟩,
+    ⟨6514, 3399854544519168, .k4 2 [2, 5, 6, 4, 3] 1 2 3 4⟩,
+    ⟨7282, 14636990850097414, .k4 0 [0, 1, 2, 4, 6] 1 2 5 6⟩,
+    ⟨7794, 149555621569560, .k4 0 [0, 3, 4, 5, 2, 1] 1 2 5 7⟩
+  ],
+  [
+    ⟨115, 89061800804352, .sharedThree 3 5 0 4 6⟩,
+    ⟨371, 12094627916042, .k4 0 [0, 1, 5] 0 1 3 5⟩,
+    ⟨627, 792633536615022602, .k4 0 [0, 3, 7] 0 1 3 7⟩,
+    ⟨1139, 5629800183120896, .k4 1 [1, 2, 4, 6] 1 2 4 6⟩,
+    ⟨1395, 648518936916131864, .k4 0 [0, 3, 4, 7] 0 3 4 7⟩,
+    ⟨4211, 2892093816272087040, .k4 1 [1, 6, 5, 7, 3] 1 3 5 6⟩,
+    ⟨6515, 3399871523586048, .k4 2 [2, 5, 6, 4, 3] 1 2 3 4⟩,
+    ⟨7283, 14636992477855756, .k4 0 [0, 2, 3, 4, 6] 2 3 5 6⟩,
+    ⟨8563, 432345607472054558, .k4 0 [0, 1, 3, 7, 4, 2] 0 1 2 4⟩
+  ],
+  [
+    ⟨116, 144036031823872, .sharedThree 2 5 0 1 7⟩,
+    ⟨372, 12095215108106, .k4 0 [0, 3, 5] 0 1 3 5⟩,
+    ⟨628, 936748722502041612, .k4 0 [0, 2, 7] 0 2 3 7⟩,
+    ⟨5236, 9570149264878604, .k4 0 [0, 2, 3, 1, 6] 1 2 5 6⟩,
+    ⟨6516, 3404253125804032, .k4 2 [2, 6, 3, 5, 4] 1 2 3 4⟩,
+    ⟨7284, 14637009925111820, .k4 0 [0, 2, 3, 4, 6] 2 3 5 6⟩
+  ],
+  [
+    ⟨117, 144038221053952, .sharedThree 3 5 0 1 7⟩,
+    ⟨373, 14293653848076, .k4 0 [0, 2, 5] 0 2 3 5⟩,
+    ⟨629, 936748724724432908, .k4 0 [0, 3, 7] 0 2 3 7⟩,
+    ⟨1909, 11821950649248010, .k4 0 [0, 1, 3, 6] 1 3 5 6⟩,
+    ⟨2165, 2703779357062594560, .k4 2 [2, 6, 7, 5] 0 5 6 7⟩,
+    ⟨3445, 9659222534938898, .k4 0 [0, 1, 4, 6, 5] 0 1 4 5⟩,
+    ⟨4213, 2893714496444981248, .k4 1 [1, 5, 7, 3, 6] 1 3 5 6⟩,
+    ⟨4469, 13220466262046, .k4 0 [0, 3, 5, 2, 4] 0 1 2 4⟩,
+    ⟨6517, 3404270104870912, .k4 2 [2, 6, 3, 5, 4] 1 2 3 4⟩
+  ],
+  [
+    ⟨118, 144598663954432, .sharedThree 4 5 0 1 7⟩,
+    ⟨374, 14294271918092, .k4 0 [0, 3, 5] 0 2 3 5⟩,
+    ⟨1142, 5629809918476288, .k4 2 [2, 3, 6, 4] 2 3 4 6⟩,
+    ⟨3190, 5348304837691418, .k4 0 [0, 4, 6, 1, 3] 0 1 3 6⟩,
+    ⟨5238, 9570150835776524, .k4 0 [0, 2, 3, 1, 6] 1 3 5 6⟩
+  ],
+  [
+    ⟨631, 1369094849361346578, .k4 0 [0, 4, 7] 0 1 4 7⟩,
+    ⟨1143, 5629827094151168, .k4 2 [2, 3, 4, 6] 2 3 4 6⟩,
+    ⟨7799, 149573052113940, .k4 0 [0, 2, 4, 1, 3, 5] 1 2 5 7⟩
+  ]
+]
+
+/-- Generated exact-table entries for this hash-bucket group. -/
+def hardBuckets14 : Array (List HardEntry) := #[
+  [
+    ⟨1136, 3140087176546053150, .residual 1704648176168674⟩,
+    ⟨5488, 5128989379177079070, .residual 201441638627824⟩,
+    ⟨5744, 4147200936674780190, .residual 4348749135579527⟩
+  ],
+  [
+    ⟨1137, 3148743769030487070, .residual 235185532687729⟩,
+    ⟨5489, 2860997195188527390, .residual 192662714464752⟩,
+    ⟨5745, 4147065129808880670, .residual 338600849211634⟩
+  ],
+  [
+    ⟨1138, 8192828562639252510, .residual 3792565844454918⟩,
+    ⟨5490, 5131232109093576990, .residual 201443517733360⟩,
+    ⟨5746, 5563521979407590430, .residual 2308685135053025⟩
+  ],
+  [
+    ⟨1139, 8154843163203824670, .residual 1831596634339923⟩,
+    ⟨5491, 7364878298609475870, .residual 3792821395080713⟩,
+    ⟨5747, 5131245298419164190, .residual 1076521948190643⟩
+  ],
+  [
+    ⟨1140, 4149440763195386910, .residual 2924577021592352⟩,
+    ⟨5492, 7362635294888812830, .residual 3792821395080712⟩,
+    ⟨5748, 8661360575725102110, .residual 3299969599098368⟩
+  ],
+  [
+    ⟨1141, 7149979562712591390, .residual 3302014003546497⟩,
+    ⟨5493, 2858753780761616670, .residual 192664593570288⟩,
+    ⟨5749, 8661351754097157150, .residual 2308925686251744⟩
+  ],
+  [
+    ⟨1142, 7149910564062981150, .residual 3303126400255365⟩,
+    ⟨5494, 7364878161707393310, .residual 3300240182167048⟩,
+    ⟨5750, 8661345182797194270, .residual 2941063806858022⟩
+  ],
+  [
+    ⟨1143, 8184102838881315870, .residual 3893560959063440⟩,
+    ⟨5495, 7362635157986730270, .residual 3300240182167049⟩,
+    ⟨5751, 8155343033993978910, .residual 3363586684062087⟩
+  ]
+]
+
+end Erdos97Octagon.RawIncidence
diff --git a/LeanPool/Erdos97ConvexOctagon/CoverageData15.lean b/LeanPool/Erdos97ConvexOctagon/CoverageData15.lean
new file mode 100644
index 00000000..e63f5b5c
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/CoverageData15.lean
@@ -0,0 +1,117 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.CoverageDataTypes
+
+/-! # Coverage certificate data, buckets 120–127 -/
+
+namespace Erdos97Octagon.RawIncidence
+
+/-- Generated monotone-obstruction entries for this hash-bucket group. -/
+def patternBuckets15 : Array (List PatternEntry) := #[
+  [
+    ⟨120, 146237277863936, .sharedThree 3 5 0 2 7⟩,
+    ⟨632, 1513209474805989396, .k4 0 [0, 2, 7] 0 2 4 7⟩,
+    ⟨1144, 5629827295477760, .k4 2 [2, 4, 3, 6] 2 3 4 6⟩,
+    ⟨1656, 158484304929792, .k4 1 [1, 2, 4, 5] 1 2 5 7⟩,
+    ⟨6008, 20890808492318, .k4 0 [0, 1, 3, 5, 2] 0 2 4 5⟩
+  ],
+  [
+    ⟨121, 146806277144576, .sharedThree 4 5 0 2 7⟩,
+    ⟨633, 1513210046027137044, .k4 0 [0, 4, 7] 0 2 4 7⟩,
+    ⟨1145, 5629827298623488, .k4 2 [2, 6, 4, 3] 2 3 4 6⟩,
+    ⟨1401, 353502494, .k4 0 [0, 1, 3, 2] 0 2 3 4⟩,
+    ⟨6009, 20891593941278, .k4 0 [0, 1, 2, 5, 3] 0 3 4 5⟩
+  ],
+  [
+    ⟨634, 1801439853380894744, .k4 0 [0, 3, 7] 0 3 4 7⟩,
+    ⟨1146, 5704420951064576, .k4 2 [2, 4, 5, 6] 2 4 5 6⟩,
+    ⟨3962, 432351061796364550, .k4 0 [0, 1, 7, 2, 5] 0 1 2 5⟩,
+    ⟨4218, 2896034912622608384, .k4 3 [3, 7, 5, 6, 4] 3 4 5 6⟩,
+    ⟨5242, 9570170690494738, .k4 0 [0, 1, 4, 6, 2] 1 2 5 6⟩
+  ],
+  [
+    ⟨123, 150633101983744, .sharedThree 2 5 0 3 7⟩,
+    ⟨635, 1801440439358717976, .k4 0 [0, 4, 7] 0 3 4 7⟩,
+    ⟨3195, 5348316620539142, .k4 0 [0, 1, 6, 4, 2] 0 1 2 6⟩,
+    ⟨4219, 2898225002077749248, .k4 3 [3, 4, 7, 6, 5] 3 4 5 6⟩
+  ],
+  [
+    ⟨124, 151221503524864, .sharedThree 4 5 0 3 7⟩,
+    ⟨380, 23089747394580, .k4 0 [0, 2, 5] 0 2 4 5⟩,
+    ⟨636, 2423430280246198272, .k4 5 [5, 6, 7] 0 5 6 7⟩,
+    ⟨892, 12094678245642, .k4 0 [0, 1, 3, 5] 0 1 3 5⟩,
+    ⟨1404, 21476412702, .k4 0 [0, 1, 4, 2] 0 1 2 3⟩,
+  ],
+  [
+    ⟨381, 23248657973268, .k4 0 [0, 4, 5] 0 2 4 5⟩,
+    ⟨637, 2449958197300208640, .k4 1 [1, 2, 7] 1 2 5 7⟩,
+    ⟨893, 12094678247434, .k4 0 [0, 3, 1, 5] 0 1 3 5⟩,
+    ⟨1405, 21593456670, .k4 0 [0, 3, 4, 2] 0 1 2 3⟩
+  ],
+  [
+    ⟨126, 159429195530240, .sharedThree 2 5 0 4 7⟩,
+    ⟨382, 27488612778008, .k4 0 [0, 3, 5] 0 3 4 5⟩,
+    ⟨1150, 5717615090597888, .k4 2 [2, 4, 6, 5] 2 4 5 6⟩,
+    ⟨1406, 26089685022, .k4 0 [0, 2, 3, 4] 0 1 3 4⟩,
+    ⟨7038, 11350260412588314, .k4 0 [0, 1, 5, 6, 3] 0 3 4 5⟩
+  ],
+  [
+    ⟨127, 159431618723840, .sharedThree 3 5 0 4 7⟩,
+    ⟨383, 27663884353560, .k4 0 [0, 4, 5] 0 3 4 5⟩,
+    ⟨895, 12095181563914, .k4 0 [0, 3, 5, 1] 0 1 3 5⟩,
+    ⟨1663, 161091338412306, .k4 0 [0, 1, 4, 5] 1 4 5 7⟩,
+    ⟨2175, 2882466492194488320, .k4 2 [2, 5, 7, 3] 2 3 4 5⟩,
+    ⟨3199, 5629783007364374, .k4 0 [0, 1, 2, 6, 4] 0 1 2 4⟩,
+    ⟨4991, 167822105813258, .k4 0 [0, 1, 3, 5, 4] 1 4 5 7⟩,
+  ]
+]
+
+/-- Generated exact-table entries for this hash-bucket group. -/
+def hardBuckets15 : Array (List HardEntry) := #[
+  [
+    ⟨1144, 7149908365073280030, .residual 1886795562547506⟩,
+    ⟨5496, 8686693566026277150, .residual 3917034029789442⟩,
+    ⟨5752, 4149307722823296030, .residual 2308925686251745⟩
+  ],
+  [
+    ⟨1145, 5996973786585984030, .residual 1342760365907409⟩,
+    ⟨5497, 6455296733343310110, .residual 3915816406444552⟩,
+    ⟨5753, 6137730521191080990, .residual 338360298012914⟩
+  ],
+  [
+    ⟨1146, 4158097218777738270, .residual 4348869394664715⟩,
+    ⟨5498, 6168192257098440990, .residual 3915816406444553⟩,
+    ⟨5754, 5442556364409922590, .residual 3885022564084371⟩
+  ],
+  [
+    ⟨1147, 3870922648666598430, .residual 3608201016170016⟩,
+    ⟨5499, 3860667132533203230, .residual 349873322198512⟩,
+    ⟨5755, 5417224003053020190, .residual 3763801341077908⟩
+  ],
+  [
+    ⟨1148, 3148391789498035230, .residual 1823073397568305⟩,
+    ⟨5500, 5997058082598478110, .residual 342178590499312⟩,
+    ⟨5756, 8686681890678236190, .residual 3902339872237972⟩
+  ],
+  [
+    ⟨1149, 8154776094017940510, .residual 1814279334589236⟩,
+    ⟨5501, 4147204235209662750, .residual 4348869394664706⟩,
+    ⟨5757, 8657971881140413470, .residual 3746484032924307⟩
+  ],
+  [
+    ⟨1150, 7149910427160898590, .residual 2120263579856577⟩,
+    ⟨5502, 4149308146414444830, .residual 2042202262924882⟩,
+    ⟨5758, 6164258461135856670, .residual 1746834693087456⟩
+  ],
+  [
+    ⟨1151, 8192759294463667230, .residual 1839033866255040⟩,
+    ⟨5503, 4147065142693781790, .residual 3919108499073164⟩,
+    ⟨5759, 5587797683297510430, .residual 4408292418399744⟩
+  ]
+]
+
+end Erdos97Octagon.RawIncidence
diff --git a/LeanPool/Erdos97ConvexOctagon/CoverageData16.lean b/LeanPool/Erdos97ConvexOctagon/CoverageData16.lean
new file mode 100644
index 00000000..570de3b6
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/CoverageData16.lean
@@ -0,0 +1,125 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.CoverageDataTypes
+
+/-! # Coverage certificate data, buckets 128–135 -/
+
+namespace Erdos97Octagon.RawIncidence
+
+/-- Generated monotone-obstruction entries for this hash-bucket group. -/
+def patternBuckets16 : Array (List PatternEntry) := #[
+  [
+    ⟨128, 212205744210176, .sharedThree 1 5 0 6 7⟩,
+    ⟨384, 72567773881344, .k4 1 [1, 2, 5] 1 2 5 6⟩,
+    ⟨1152, 5717889964310528, .k4 2 [2, 4, 5, 6] 2 4 5 6⟩,
+    ⟨1408, 30115105822, .k4 0 [0, 3, 4, 1] 0 1 2 4⟩,
+    ⟨3968, 433752939123884294, .k4 0 [0, 1, 7, 2, 6] 0 1 2 6⟩,
+    ⟨4224, 3458915838688493592, .k4 0 [0, 3, 4, 7, 5] 0 3 4 5⟩,
+  ],
+  [
+    ⟨129, 212205756809216, .sharedThree 2 5 0 6 7⟩,
+    ⟨385, 72569411627008, .k4 1 [1, 3, 5] 1 3 5 6⟩,
+    ⟨897, 12095198339338, .k4 0 [0, 1, 5, 3] 0 1 3 5⟩,
+    ⟨1409, 30149312542, .k4 0 [0, 3, 4, 2] 0 1 2 4⟩,
+    ⟨2177, 2882514871541327872, .k4 1 [1, 3, 7, 5] 1 3 5 6⟩,
+  ],
+  [
+    ⟨130, 212208982163456, .sharedThree 3 5 0 6 7⟩,
+    ⟨642, 2450119421771907072, .k4 4 [4, 5, 7] 1 4 5 7⟩,
+    ⟨1410, 38957416478, .k4 0 [0, 2, 4, 3] 0 1 2 3⟩,
+    ⟨3202, 5629787302266134, .k4 0 [0, 1, 4, 6, 2] 0 1 2 4⟩,
+    ⟨6530, 5066828804670494, .k4 0 [0, 3, 4, 6, 1, 2] 0 1 2 3⟩,
+    ⟨8578, 720575964103475486, .k4 0 [0, 1, 4, 7, 2, 3] 0 1 2 3⟩
+  ],
+  [
+    ⟨131, 213034672848896, .sharedThree 4 5 0 6 7⟩,
+    ⟨387, 74766797136896, .k4 1 [1, 2, 5] 1 2 5 6⟩,
+    ⟨643, 2594073385376064512, .k4 1 [1, 2, 7] 1 2 5 7⟩,
+    ⟨1155, 5910995991003156, .k4 0 [0, 4, 2, 6] 0 2 4 6⟩,
+    ⟨1411, 38990253342, .k4 0 [0, 1, 4, 3] 0 1 2 3⟩,
+    ⟨4739, 92500715070484, .k4 0 [0, 2, 4, 1, 5] 1 2 5 6⟩,
+  ],
+  [
+    ⟨132, 213305268502528, .sharedThree 2 5 1 6 7⟩,
+    ⟨900, 13194712720384, .k4 1 [1, 2, 5, 3] 1 2 3 5⟩,
+    ⟨1156, 5911253684912148, .k4 0 [0, 2, 4, 6] 0 2 4 6⟩,
+    ⟨2180, 2882517070531028992, .k4 1 [1, 5, 7, 3] 1 3 5 6⟩,
+    ⟨4484, 19932943821854, .k4 0 [0, 2, 4, 5, 1] 0 1 2 3⟩,
+    ⟨7300, 14991020705997846, .k4 0 [0, 4, 6, 5, 1] 0 1 2 6⟩,
+    ⟨7812, 158471503389720, .k4 0 [0, 3, 4, 2, 5, 1] 1 2 5 7⟩
+  ],
+  [
+    ⟨133, 213308510568448, .sharedThree 3 5 1 6 7⟩,
+    ⟨1157, 5911253689040916, .k4 0 [0, 4, 6, 2] 0 2 4 6⟩,
+    ⟨1413, 43236130846, .k4 0 [0, 2, 3, 4] 0 1 2 4⟩,
+    ⟨1669, 162885101158400, .k4 2 [2, 3, 4, 5] 2 3 5 7⟩,
+    ⟨4485, 19932943887390, .k4 0 [0, 4, 5, 1, 2] 0 1 2 3⟩,
+    ⟨10117, 8108030482475655446, .k4 0 [0, 1, 5, 7, 4, 6] 0 2 4 6⟩
+  ],
+  [
+    ⟨134, 214138479443968, .sharedThree 4 5 1 6 7⟩,
+    ⟨390, 76965818295296, .k4 1 [1, 2, 5] 1 2 5 6⟩,
+    ⟨646, 2594220719923569664, .k4 1 [1, 5, 7] 1 2 5 7⟩,
+    ⟨1414, 47244839966, .k4 0 [0, 2, 4, 1] 0 1 3 4⟩,
+    ⟨1670, 163281783291924, .k4 0 [0, 2, 4, 5] 2 4 5 7⟩
+  ],
+  [
+    ⟨135, 215504279094272, .sharedThree 1 5 2 6 7⟩,
+    ⟨391, 76965820261376, .k4 1 [1, 5, 2] 1 2 5 6⟩,
+    ⟨647, 2594227319744757760, .k4 3 [3, 5, 7] 2 3 5 7⟩,
+    ⟨1159, 5911266572959764, .k4 0 [0, 2, 6, 4] 0 2 4 6⟩,
+    ⟨1671, 163298962112532, .k4 0 [0, 2, 4, 5] 2 4 5 7⟩,
+    ⟨4487, 19933027118110, .k4 0 [0, 3, 4, 5, 1] 0 1 2 3⟩,
+    ⟨10119, 8108384237456991506, .k4 0 [0, 1, 4, 7, 5, 6] 1 2 5 6⟩
+  ]
+]
+
+/-- Generated exact-table entries for this hash-bucket group. -/
+def hardBuckets16 : Array (List HardEntry) := #[
+  [
+    ⟨1152, 4158110292926622750, .residual 3363586684062080⟩,
+    ⟨5504, 3285751713959174430, .residual 2675625636094546⟩,
+    ⟨5760, 5155452144839746590, .residual 4066690847019814⟩
+  ],
+  [
+    ⟨1153, 3140508291630197790, .residual 2924577021592353⟩,
+    ⟨5505, 3858839164588581150, .residual 1620245215911506⟩,
+    ⟨5761, 4149444089998402590, .residual 4349846499895687⟩
+  ],
+  [
+    ⟨1154, 3139947540700032030, .residual 2927914223747861⟩,
+    ⟨5506, 3284630212098842910, .residual 3668475211310791⟩,
+    ⟨5762, 7581134641813447710, .residual 3364684048378247⟩
+  ],
+  [
+    ⟨1155, 2851717181728189470, .residual 195669169027698⟩,
+    ⟨5507, 6428199926608093470, .residual 3668990170121922⟩,
+    ⟨5763, 4147065159622517790, .residual 1747075244286177⟩
+  ],
+  [
+    ⟨1156, 5995847647167605790, .residual 1180591036317281⟩,
+    ⟨5508, 6425956922887430430, .residual 3475132492523333⟩,
+    ⟨5764, 5563522009221227550, .residual 269091065348338⟩
+  ],
+  [
+    ⟨1157, 2862200039420881950, .residual 712148126415824⟩,
+    ⟨5509, 5564643494152823070, .residual 4090947459234498⟩,
+    ⟨5765, 5128993644064465950, .residual 1077621191612339⟩
+  ],
+  [
+    ⟨1158, 3870992742516157470, .residual 1202805157281616⟩,
+    ⟨5510, 6137730944782229790, .residual 3035521571474114⟩,
+    ⟨5766, 8659109032603345950, .residual 1747075244286176⟩
+  ],
+  [
+    ⟨1159, 6175166435649285150, .residual 349065324160112⟩,
+    ⟨5511, 5563521992292491550, .residual 2306430243652197⟩,
+    ⟨5767, 8659100210975400990, .residual 3299984631541248⟩
+  ]
+]
+
+end Erdos97Octagon.RawIncidence
diff --git a/LeanPool/Erdos97ConvexOctagon/CoverageData17.lean b/LeanPool/Erdos97ConvexOctagon/CoverageData17.lean
new file mode 100644
index 00000000..5dda5991
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/CoverageData17.lean
@@ -0,0 +1,120 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.CoverageDataTypes
+
+/-! # Coverage certificate data, buckets 136–143 -/
+
+namespace Erdos97Octagon.RawIncidence
+
+/-- Generated monotone-obstruction entries for this hash-bucket group. -/
+def patternBuckets17 : Array (List PatternEntry) := #[
+  [
+    ⟨136, 215507567378432, .sharedThree 3 5 2 6 7⟩,
+    ⟨648, 2594236817460953088, .k4 4 [4, 5, 7] 2 4 5 7⟩,
+    ⟨2440, 3298621531150, .k4 0 [0, 3, 2, 1, 5] 0 1 2 5⟩,
+    ⟨4488, 19933043895326, .k4 0 [0, 4, 5, 1, 3] 0 1 2 3⟩,
+    ⟨5000, 1688850201592094, .k4 0 [0, 1, 6, 2, 3] 0 2 3 4⟩,
+    ⟨6024, 21062857924870, .k4 0 [0, 1, 5, 4, 3, 2] 0 1 2 5⟩
+  ],
+  [
+    ⟨137, 216346092634112, .sharedThree 4 5 2 6 7⟩,
+    ⟨393, 76965820391424, .k4 1 [1, 5, 2] 1 2 5 6⟩,
+    ⟨649, 2738188573443531776, .k4 1 [1, 2, 7] 1 2 5 7⟩,
+  ],
+  [
+    ⟨394, 79166481393664, .k4 1 [1, 3, 5] 1 3 5 6⟩,
+    ⟨650, 2738188573451789312, .k4 1 [1, 7, 2] 1 2 5 7⟩,
+    ⟨906, 13349632344064, .k4 2 [2, 3, 4, 5] 2 3 4 5⟩,
+    ⟨1418, 55835231518, .k4 0 [0, 1, 4, 2] 0 2 3 4⟩,
+  ],
+  [
+    ⟨139, 219902338662400, .sharedThree 2 5 3 6 7⟩,
+    ⟨651, 2738188573451887616, .k4 1 [1, 2, 7] 1 2 5 7⟩,
+    ⟨907, 13366277439488, .k4 2 [2, 3, 5, 4] 2 3 4 5⟩,
+    ⟨1163, 6755452395192320, .k4 2 [2, 4, 3, 6] 2 3 4 6⟩,
+    ⟨2443, 3299158270222, .k4 0 [0, 1, 3, 5, 2] 0 2 3 5⟩,
+    ⟨4747, 92638157079826, .k4 0 [0, 1, 4, 2, 5] 2 4 5 6⟩,
+    ⟨7307, 15762784721592594, .k4 0 [0, 1, 4, 3, 6] 1 4 5 6⟩,
+  ],
+  [
+    ⟨140, 220761319014400, .sharedThree 4 5 3 6 7⟩,
+    ⟨396, 79613392846848, .k4 3 [3, 4, 5] 3 4 5 6⟩,
+    ⟨652, 2738188573451919360, .k4 1 [1, 7, 2] 1 2 5 7⟩,
+    ⟨1164, 6755684284647424, .k4 1 [1, 3, 6, 4] 1 3 4 6⟩,
+    ⟨2188, 2898295061584281600, .k4 3 [3, 7, 5, 6] 3 4 5 6⟩,
+    ⟨4236, 3458923445398011904, .k4 2 [2, 3, 4, 7, 5] 2 3 4 5⟩,
+    ⟨7308, 15762793317859348, .k4 0 [0, 2, 4, 3, 6] 2 4 5 6⟩
+  ],
+  [
+    ⟨397, 81364967778304, .k4 1 [1, 3, 5] 1 3 5 6⟩,
+    ⟨2189, 2993135636329791488, .k4 3 [3, 6, 7, 5] 0 5 6 7⟩,
+    ⟨4493, 19963009638686, .k4 0 [0, 1, 2, 5, 4] 0 2 3 4⟩,
+    ⟨8333, 11331568246268190, .k4 0 [0, 1, 2, 5, 6, 3] 0 2 3 4⟩
+  ],
+  [
+    ⟨142, 228698432208896, .sharedThree 2 5 4 6 7⟩,
+    ⟨398, 81365471094784, .k4 1 [1, 5, 3] 1 3 5 6⟩,
+    ⟨654, 2738333708976169984, .k4 1 [1, 7, 5] 1 2 5 7⟩,
+    ⟨1166, 6755717570643968, .k4 1 [1, 3, 4, 6] 1 3 4 6⟩,
+    ⟨1422, 6597072399630, .k4 0 [0, 1, 5, 2] 0 1 2 3⟩,
+    ⟨1678, 167682787770392, .k4 0 [0, 3, 4, 5] 3 4 5 7⟩,
+    ⟨2190, 2999759093838643200, .k4 3 [3, 5, 7, 6] 0 5 6 7⟩,
+  ],
+  [
+    ⟨143, 228701908238336, .sharedThree 3 5 4 6 7⟩,
+    ⟨911, 14293737668620, .k4 0 [0, 3, 2, 5] 0 2 3 5⟩,
+    ⟨1423, 6597072464910, .k4 0 [0, 2, 5, 1] 0 1 2 3⟩,
+    ⟨1679, 167716879073304, .k4 0 [0, 3, 4, 5] 3 4 5 7⟩,
+    ⟨5263, 9649314666138638, .k4 0 [0, 3, 5, 6, 1] 0 1 2 3⟩,
+  ]
+]
+
+/-- Generated exact-table entries for this hash-bucket group. -/
+def hardBuckets17 : Array (List HardEntry) := #[
+  [
+    ⟨1160, 3871005816665041950, .residual 4348869394664713⟩,
+    ⟨5512, 4145376318603321630, .residual 1994389914580002⟩,
+    ⟨5768, 8659093639675438110, .residual 2941065685963558⟩
+  ],
+  [
+    ⟨1161, 3726892827612441630, .residual 4348869394664712⟩,
+    ⟨5513, 5591731479260094750, .residual 936852126455728⟩,
+    ⟨5769, 4149307752636933150, .residual 269331616547058⟩
+  ],
+  [
+    ⟨1162, 4158040199043640350, .residual 333670249292016⟩,
+    ⟨5514, 4147062943704080670, .residual 1380722880142370⟩,
+    ⟨5770, 6137730551004718110, .residual 1746834693087457⟩
+  ],
+  [
+    ⟨1163, 3866783692266040350, .residual 3608063844275752⟩,
+    ⟨5515, 6137799802251567390, .residual 3793888694448386⟩,
+    ⟨5771, 8686677509794882590, .residual 936917930874803⟩
+  ],
+  [
+    ⟨1164, 3722670703213440030, .residual 4348869394664714⟩,
+    ⟨5516, 8401838035908092190, .residual 340013860921840⟩,
+    ⟨5772, 7608079273227248670, .residual 3911135697111441⟩
+  ],
+  [
+    ⟨1165, 4153385690690841630, .residual 2396829421902163⟩,
+    ⟨5517, 8661430669641703710, .residual 332315396802032⟩,
+    ⟨5773, 7676198412520842270, .residual 2468811968597076⟩
+  ],
+  [
+    ⟨1166, 5420582032932695070, .residual 2286266264038626⟩,
+    ⟨5518, 8230703861408129310, .residual 3792671071103497⟩,
+    ⟨5774, 3717098525771228190, .residual 3349285244307858⟩
+  ],
+  [
+    ⟨1167, 4153242217308318750, .residual 2526709300056372⟩,
+    ⟨5519, 8229582359547797790, .residual 3792671071103496⟩,
+    ⟨5775, 7581128044744074270, .residual 4334447695825298⟩
+  ]
+]
+
+end Erdos97Octagon.RawIncidence
diff --git a/LeanPool/Erdos97ConvexOctagon/CoverageData18.lean b/LeanPool/Erdos97ConvexOctagon/CoverageData18.lean
new file mode 100644
index 00000000..2f91131c
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/CoverageData18.lean
@@ -0,0 +1,120 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.CoverageDataTypes
+
+/-! # Coverage certificate data, buckets 144–151 -/
+
+namespace Erdos97Octagon.RawIncidence
+
+/-- Generated monotone-obstruction entries for this hash-bucket group. -/
+def patternBuckets18 : Array (List PatternEntry) := #[
+  [
+    ⟨144, 3940649673949198, .sharedThree 0 6 1 2 3⟩,
+    ⟨400, 81365504647168, .k4 1 [1, 5, 3] 1 3 5 6⟩,
+    ⟨656, 2882303764279590912, .k4 2 [2, 3, 7] 2 3 5 7⟩,
+    ⟨4496, 19980188459294, .k4 0 [0, 1, 2, 5, 4] 0 2 3 4⟩,
+    ⟨7056, 11821950135512326, .k4 0 [0, 1, 2, 3, 6] 1 2 5 6⟩,
+    ⟨7312, 15762891381735436, .k4 0 [0, 2, 3, 4, 6] 2 3 5 6⟩
+  ],
+  [
+    ⟨145, 6192449487634454, .sharedThree 0 6 1 2 4⟩,
+    ⟨401, 83564031377408, .k4 2 [2, 3, 5] 2 3 5 6⟩,
+    ⟨657, 2882304486024413184, .k4 3 [3, 4, 7] 3 4 5 7⟩,
+    ⟨913, 14294207430668, .k4 0 [0, 3, 5, 2] 0 2 3 5⟩,
+    ⟨1169, 6755726198833152, .k4 2 [2, 3, 4, 6] 2 3 4 6⟩,
+    ⟨1681, 167727879684096, .k4 2 [2, 4, 3, 5] 2 4 5 7⟩,
+    ⟨2193, 3026577977501548544, .k4 3 [3, 7, 5, 4] 1 3 4 7⟩,
+    ⟨7313, 15762908789104906, .k4 0 [0, 1, 3, 4, 6] 1 3 5 6⟩
+  ],
+  [
+    ⟨146, 7318349394477082, .sharedThree 0 6 1 3 4⟩,
+    ⟨914, 14294255730700, .k4 0 [0, 2, 3, 5] 0 2 3 5⟩,
+    ⟨1682, 167819689852952, .k4 0 [0, 3, 4, 5] 3 4 5 7⟩,
+    ⟨4242, 3470253037820313600, .k4 3 [3, 6, 5, 7, 4] 3 4 5 6⟩,
+    ⟨7314, 15762908828991500, .k4 0 [0, 2, 3, 4, 6] 2 3 5 6⟩
+  ],
+  [
+    ⟨147, 7881299347898396, .sharedThree 0 6 2 3 4⟩,
+    ⟨403, 83564566151168, .k4 2 [2, 3, 5] 2 3 5 6⟩,
+    ⟨659, 2882457693156016128, .k4 2 [2, 5, 7] 2 3 5 7⟩,
+    ⟨1171, 6755727004663808, .k4 2 [2, 4, 6, 3] 2 3 4 6⟩,
+    ⟨2451, 3320013005078, .k4 0 [0, 1, 4, 5, 2] 0 1 2 5⟩,
+    ⟨4243, 3472436674623987712, .k4 1 [1, 5, 7, 4, 6] 1 4 5 6⟩,
+    ⟨4499, 19980523413790, .k4 0 [0, 1, 5, 4, 3] 0 2 3 4⟩,
+  ],
+  [
+    ⟨148, 9851624187166720, .sharedThree 2 6 0 1 5⟩,
+    ⟨660, 2882471608839045120, .k4 4 [4, 5, 7] 3 4 5 7⟩,
+    ⟨1172, 6834737955995648, .k4 3 [3, 4, 5, 6] 3 4 5 6⟩,
+    ⟨2452, 3320013005846, .k4 0 [0, 4, 2, 1, 5] 0 1 2 5⟩,
+    ⟨2964, 2533275881131022, .k4 0 [0, 2, 3, 1, 6] 0 1 3 6⟩
+  ],
+  [
+    ⟨149, 9851624772075520, .sharedThree 3 6 0 1 5⟩,
+    ⟨917, 18833434804244, .k4 0 [0, 2, 4, 5] 0 2 4 5⟩,
+  ],
+  [
+    ⟨150, 9851774508728320, .sharedThree 4 6 0 1 5⟩,
+    ⟨406, 88390434291712, .k4 2 [2, 4, 5] 2 4 5 6⟩,
+    ⟨918, 18834253676568, .k4 0 [0, 3, 4, 5] 0 3 4 5⟩,
+    ⟨1174, 6835011760160768, .k4 3 [3, 4, 5, 6] 3 4 5 6⟩,
+    ⟨1430, 7696631737358, .k4 0 [0, 3, 1, 5] 0 1 2 5⟩,
+  ],
+  [
+    ⟨151, 10414574138303744, .sharedThree 1 6 0 2 5⟩,
+    ⟨407, 88409485869056, .k4 3 [3, 4, 5] 3 4 5 6⟩,
+    ⟨663, 3026418952310892544, .k4 1 [1, 3, 7] 1 3 5 7⟩,
+    ⟨3735, 11348099792371736, .k4 0 [0, 3, 4, 6, 5] 0 3 4 5⟩,
+    ⟨6551, 5073464481836032, .k4 1 [1, 5, 6, 2, 4] 1 2 3 4⟩
+  ]
+]
+
+/-- Generated exact-table entries for this hash-bucket group. -/
+def hardBuckets18 : Array (List HardEntry) := #[
+  [
+    ⟨1168, 3722585502941015070, .residual 2771150958996673⟩,
+    ⟨5520, 8371515816107761950, .residual 3363706943147266⟩,
+    ⟨5776, 6137724364641592350, .residual 4241517474354721⟩
+  ],
+  [
+    ⟨1169, 7149895188114140190, .residual 2517915237077297⟩,
+    ⟨5521, 4149307735708197150, .residual 2306700892652133⟩,
+    ⟨5777, 5563515412151854110, .residual 4247019340043541⟩
+  ],
+  [
+    ⟨1170, 5420513034283084830, .residual 3043242714776213⟩,
+    ⟨5522, 3862203259463328030, .residual 2965322298178242⟩,
+    ⟨5778, 5559643761362396190, .residual 1978395488873556⟩
+  ],
+  [
+    ⟨1171, 5132287056177884190, .residual 3039890392269473⟩,
+    ⟨5523, 4147064731987534110, .residual 4161421172656834⟩,
+    ⟨5779, 5559574762712785950, .residual 1978395488873553⟩
+  ],
+  [
+    ⟨1172, 4158101616623447070, .residual 1765752963262288⟩,
+    ⟨5524, 3858838753882333470, .residual 3475098603595589⟩,
+    ⟨5780, 3138394620144706590, .residual 3340489419434386⟩
+  ],
+  [
+    ⟨1173, 4158101496834124830, .residual 3089358348928550⟩,
+    ⟨5525, 3284629801392595230, .residual 3668715729995458⟩,
+    ⟨5781, 5417216306472084510, .residual 3763801341077905⟩
+  ],
+  [
+    ⟨1174, 4158097115967482910, .residual 2316488913924192⟩,
+    ⟨5526, 6428199515901845790, .residual 3668509100238535⟩,
+    ⟨5782, 3140501816999470110, .residual 3045523837212193⟩
+  ],
+  [
+    ⟨1175, 7185710407163735070, .residual 3793512884687236⟩,
+    ⟨5527, 6141095039656976670, .residual 2675655733895762⟩,
+    ⟨5783, 3138258813278807070, .residual 3051025702901013⟩
+  ]
+]
+
+end Erdos97Octagon.RawIncidence
diff --git a/LeanPool/Erdos97ConvexOctagon/CoverageData19.lean b/LeanPool/Erdos97ConvexOctagon/CoverageData19.lean
new file mode 100644
index 00000000..99f89c0a
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/CoverageData19.lean
@@ -0,0 +1,117 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.CoverageDataTypes
+
+/-! # Coverage certificate data, buckets 152–159 -/
+
+namespace Erdos97Octagon.RawIncidence
+
+/-- Generated monotone-obstruction entries for this hash-bucket group. -/
+def patternBuckets19 : Array (List PatternEntry) := #[
+  [
+    ⟨664, 3026418952310923264, .k4 1 [1, 7, 3] 1 3 5 7⟩,
+    ⟨920, 18842021536018, .k4 0 [0, 1, 4, 5] 0 1 4 5⟩,
+    ⟨1176, 6843534049017856, .k4 3 [3, 4, 6, 5] 3 4 5 6⟩,
+    ⟨1688, 1688849865067534, .k4 0 [0, 2, 6, 1] 0 1 2 3⟩,
+    ⟨4248, 3474677368994398208, .k4 3 [3, 4, 6, 7, 5] 3 4 5 6⟩
+  ],
+  [
+    ⟨665, 3026561888822493184, .k4 3 [3, 7, 5] 1 3 5 7⟩,
+    ⟨1433, 7697202159886, .k4 0 [0, 1, 3, 5] 0 2 3 5⟩,
+  ],
+  [
+    ⟨154, 11540474045147392, .sharedThree 1 6 0 3 5⟩,
+    ⟨922, 18846319706132, .k4 0 [0, 2, 4, 5] 0 2 4 5⟩,
+    ⟨1178, 6843807853182976, .k4 3 [3, 4, 5, 6] 3 4 5 6⟩,
+  ],
+  [
+    ⟨155, 11540474047823872, .sharedThree 2 6 0 3 5⟩,
+    ⟨411, 90580860297216, .k4 1 [1, 5, 4] 1 4 5 6⟩,
+    ⟨667, 3170534138283819008, .k4 2 [2, 3, 7] 2 3 5 7⟩,
+    ⟨923, 18850613624852, .k4 0 [0, 2, 4, 5] 0 2 4 5⟩,
+    ⟨4251, 4792392955699284992, .k4 1 [1, 2, 6, 3, 7] 1 2 3 7⟩,
+    ⟨6555, 5077846217223168, .k4 1 [1, 5, 6, 3, 4] 1 2 3 4⟩,
+    ⟨8603, 1297037268292895006, .k4 0 [0, 1, 3, 7, 2, 4] 0 1 2 4⟩
+  ],
+  [
+    ⟨156, 11540650138796032, .sharedThree 4 6 0 3 5⟩,
+    ⟨412, 92651041849344, .k4 2 [2, 4, 5] 2 4 5 6⟩,
+    ⟨924, 18850614607892, .k4 0 [0, 4, 2, 5] 0 2 4 5⟩,
+    ⟨2204, 3458919167006605312, .k4 2 [2, 5, 7, 4] 2 3 4 5⟩,
+    ⟨4252, 4792392955732708352, .k4 1 [1, 3, 6, 2, 7] 1 2 3 7⟩,
+  ],
+  [
+    ⟨413, 92771300933632, .k4 2 [2, 5, 4] 2 4 5 6⟩,
+    ⟨669, 3170534140422914048, .k4 2 [2, 3, 7] 2 3 5 7⟩,
+    ⟨925, 18864318447640, .k4 0 [0, 3, 4, 5] 0 3 4 5⟩,
+    ⟨1181, 7036914414649368, .k4 0 [0, 4, 3, 6] 0 3 4 6⟩,
+    ⟨1437, 7855495192854, .k4 0 [0, 1, 4, 5] 0 2 4 5⟩,
+    ⟨3997, 720585838701879562, .k4 0 [0, 1, 7, 3, 5] 0 1 3 5⟩,
+    ⟨9885, 2892085019122682894, .k4 0 [0, 2, 3, 7, 5, 6, 1] 0 1 2 3⟩
+  ],
+  [
+    ⟨158, 13792273862033408, .sharedThree 2 6 0 4 5⟩,
+    ⟨414, 92788478705664, .k4 2 [2, 4, 5] 2 4 5 6⟩,
+    ⟨926, 18868344979480, .k4 0 [0, 3, 4, 5] 0 3 4 5⟩,
+    ⟨1182, 7037153875853336, .k4 0 [0, 3, 4, 6] 0 3 4 6⟩,
+    ⟨2718, 19937239311638, .k4 0 [0, 1, 2, 5, 4] 0 1 2 4⟩,
+  ],
+  [
+    ⟨159, 13792274680905728, .sharedThree 3 6 0 4 5⟩,
+    ⟨415, 92788479754240, .k4 2 [2, 5, 4] 2 4 5 6⟩,
+    ⟨671, 3170679275955159040, .k4 3 [3, 7, 5] 2 3 5 7⟩,
+    ⟨927, 18868596637720, .k4 0 [0, 4, 3, 5] 0 3 4 5⟩,
+    ⟨1183, 7037154932817944, .k4 0 [0, 4, 6, 3] 0 3 4 6⟩,
+    ⟨1695, 1970324887325710, .k4 0 [0, 3, 1, 6] 0 1 2 6⟩,
+  ]
+]
+
+/-- Generated exact-table entries for this hash-bucket group. -/
+def hardBuckets19 : Array (List HardEntry) := #[
+  [
+    ⟨1176, 5456328253332679710, .residual 3915711179795969⟩,
+    ⟨5528, 6425956512181182750, .residual 1479511857372754⟩,
+    ⟨5784, 3136569989188346910, .residual 2468811968597073⟩
+  ],
+  [
+    ⟨1177, 2862191363117706270, .residual 2694936613328176⟩,
+    ⟨5529, 6137730534075982110, .residual 3795963163732108⟩,
+    ⟨5785, 5995919938294440990, .residual 3772597165951377⟩
+  ],
+  [
+    ⟨1178, 3145366082195450910, .residual 316285286000884⟩,
+    ⟨5530, 5563521581586243870, .residual 2182905523662418⟩,
+    ⟨5786, 6136095572114334750, .residual 2470976698174548⟩
+  ],
+  [
+    ⟨1179, 8189454161454197790, .residual 316285286000883⟩,
+    ⟨5531, 6136041709985521950, .residual 1996314092958754⟩,
+    ⟨5787, 3716962188409758750, .residual 3121394178987285⟩
+  ],
+  [
+    ⟨1180, 6172914892527528990, .residual 3486425606329120⟩,
+    ⟨5532, 5993615346033680670, .residual 1378528052763682⟩,
+    ⟨5788, 3714719184689095710, .residual 3115892313298465⟩
+  ],
+  [
+    ⟨1181, 7185587263740472350, .residual 3793512884687233⟩,
+    ⟨5533, 8230695039780184350, .residual 1077585484994480⟩,
+    ⟨5789, 8252649692777210910, .residual 1976230759296084⟩
+  ],
+  [
+    ⟨1182, 7176861672606428190, .residual 3795692580776325⟩,
+    ⟨5534, 6168183730531918110, .residual 935769794582448⟩,
+    ⟨5790, 3713021538970690590, .residual 1976230759296081⟩
+  ],
+  [
+    ⟨1183, 6460844002744888350, .residual 752132264057777⟩,
+    ⟨5535, 6453036381428179230, .residual 3915951698029064⟩,
+    ⟨5791, 8182278732413199390, .residual 3902339872237969⟩
+  ]
+]
+
+end Erdos97Octagon.RawIncidence
diff --git a/LeanPool/Erdos97ConvexOctagon/CoverageData20.lean b/LeanPool/Erdos97ConvexOctagon/CoverageData20.lean
new file mode 100644
index 00000000..278bf032
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/CoverageData20.lean
@@ -0,0 +1,126 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.CoverageDataTypes
+
+/-! # Coverage certificate data, buckets 160–167 -/
+
+namespace Erdos97Octagon.RawIncidence
+
+/-- Generated monotone-obstruction entries for this hash-bucket group. -/
+def patternBuckets20 : Array (List PatternEntry) := #[
+  [
+    ⟨160, 36873221957681152, .sharedThree 2 6 0 1 7⟩,
+    ⟨416, 97068139937792, .k4 3 [3, 4, 5] 3 4 5 6⟩,
+    ⟨672, 3170683671261216768, .k4 2 [2, 7, 5] 2 3 5 7⟩,
+    ⟨1184, 7037183940624408, .k4 0 [0, 3, 4, 6] 0 3 4 6⟩,
+    ⟨8096, 9570170740698136, .k4 0 [0, 3, 4, 1, 2, 6] 1 2 5 6⟩
+  ],
+  [
+    ⟨161, 36873224146911232, .sharedThree 3 6 0 1 7⟩,
+    ⟨417, 97171219152896, .k4 3 [3, 5, 4] 3 4 5 6⟩,
+    ⟨1185, 7037184745930776, .k4 0 [0, 3, 6, 4] 0 3 4 6⟩,
+    ⟨8097, 9570189742140436, .k4 0 [0, 2, 4, 1, 3, 6] 1 3 5 6⟩
+  ],
+  [
+    ⟨162, 36873784589811712, .sharedThree 4 6 0 1 7⟩,
+    ⟨418, 97205042020352, .k4 3 [3, 4, 5] 3 4 5 6⟩,
+    ⟨674, 3458765218206711808, .k4 2 [2, 4, 7] 2 4 5 7⟩,
+    ⟨1186, 9576746282279936, .k4 1 [1, 2, 5, 6] 1 2 5 6⟩,
+    ⟨1442, 10995720269070, .k4 0 [0, 1, 5, 3] 0 1 2 3⟩,
+    ⟨2466, 5497610644494, .k4 0 [0, 2, 3, 5, 1] 0 1 2 5⟩
+  ],
+  [
+    ⟨163, 37017257972334592, .sharedThree 5 6 0 1 7⟩,
+    ⟨419, 97205310455808, .k4 3 [3, 5, 4] 3 4 5 6⟩,
+    ⟨675, 3458765238327836672, .k4 3 [3, 4, 7] 3 4 5 7⟩,
+    ⟨1187, 9576746284246016, .k4 1 [1, 5, 6, 2] 1 2 5 6⟩,
+    ⟨1443, 10995737046030, .k4 0 [0, 3, 5, 1] 0 1 2 3⟩,
+    ⟨1955, 14073899159413010, .k4 0 [0, 1, 4, 6] 1 4 5 6⟩,
+    ⟨2467, 5497610710030, .k4 0 [0, 3, 1, 2, 5] 0 1 2 5⟩,
+    ⟨4003, 723109218424504586, .k4 0 [0, 1, 7, 3, 6] 0 1 3 6⟩,
+    ⟨4771, 97178483712266, .k4 0 [0, 1, 3, 5, 4] 1 4 5 6⟩
+  ],
+  [
+    ⟨420, 142936522269696, .k4 1 [1, 2, 5] 1 2 5 7⟩,
+    ⟨1444, 10995753821454, .k4 0 [0, 1, 5, 3] 0 1 2 3⟩,
+  ],
+  [
+    ⟨165, 37436174133886976, .sharedThree 3 6 0 2 7⟩,
+    ⟨677, 3458927241552986112, .k4 2 [2, 5, 7] 2 4 5 7⟩,
+    ⟨8613, 1441172359171615758, .k4 0 [0, 2, 7, 4, 5, 1] 0 1 2 3⟩
+  ],
+  [
+    ⟨166, 37436743133167616, .sharedThree 4 6 0 2 7⟩,
+    ⟨678, 3458931642540752896, .k4 3 [3, 5, 7] 3 4 5 7⟩,
+    ⟨1190, 9581145431762944, .k4 1 [1, 3, 5, 6] 1 3 5 6⟩,
+    ⟨1702, 1970621189734678, .k4 0 [0, 1, 4, 6] 0 2 4 6⟩,
+    ⟨2470, 5497644786702, .k4 0 [0, 3, 2, 1, 5] 0 1 2 5⟩,
+    ⟨4262, 4793237378406007046, .k4 0 [0, 1, 2, 7, 6] 0 1 2 6⟩,
+    ⟨6566, 5348024647172382, .k4 0 [0, 1, 3, 6, 2] 0 2 4 6⟩
+  ],
+  [
+    ⟨167, 37582406949011456, .sharedThree 5 6 0 2 7⟩,
+    ⟨423, 145135545525248, .k4 1 [1, 2, 5] 1 2 5 7⟩,
+    ⟨935, 19954421212160, .k4 1 [1, 5, 4, 2] 1 2 4 5⟩,
+    ⟨5031, 2814751177523486, .k4 0 [0, 1, 2, 6, 3] 0 2 3 4⟩,
+    ⟨6567, 5348025967395102, .k4 0 [0, 1, 2, 6, 3] 0 3 4 6⟩,
+  ]
+]
+
+/-- Generated exact-table entries for this hash-bucket group. -/
+def hardBuckets20 : Array (List HardEntry) := #[
+  [
+    ⟨672, 8697238970799187230, .hubPentagon 0 [0, 1, 2, 3, 4, 6, 5, 7] 1 0 2 5 6 4⟩,
+    ⟨1184, 4146624913950796830, .residual 1003398607615937⟩,
+    ⟨5536, 5591722952693571870, .residual 3915951698029065⟩,
+    ⟨5792, 8155327640832107550, .residual 4325651870951826⟩
+  ],
+  [
+    ⟨673, 8266578970781902110, .residual 3918852948510086⟩,
+    ⟨1185, 4145503412090465310, .residual 760926224276404⟩,
+    ⟨5537, 7825369142209470750, .residual 269647263941104⟩,
+    ⟨5793, 6137715128029209630, .residual 4176650863957269⟩
+  ],
+  [
+    ⟨674, 8697232399499224350, .cycleStrip 0 [0, 1, 2, 3, 4, 5, 6, 7] 0 2 1 5 6 7 4⟩,
+    ⟨1186, 5420580933421132830, .residual 3917860810886405⟩,
+    ⟨5538, 4149447388533285150, .residual 4349966758980866⟩,
+    ⟨5794, 5563506175539471390, .residual 4171148998268449⟩
+  ],
+  [
+    ⟨675, 8689072911311136030, .residual 1201555500719955⟩,
+    ⟨1187, 5420513029988183070, .residual 1231054804926242⟩,
+    ⟨5539, 7797307423927230750, .residual 3364804307463426⟩,
+    ⟨5795, 6136026303938749470, .residual 2470976698174545⟩
+  ],
+  [
+    ⟨676, 6455284343629374750, .residual 4278889880649894⟩,
+    ⟨1188, 3870997140361866270, .residual 4347907321983243⟩,
+    ⟨5540, 3281954687505588510, .residual 279504846112240⟩,
+    ⟨5796, 8661431066944988190, .residual 3349285244307860⟩
+  ],
+  [
+    ⟨677, 8688506675741287710, .hubPentagon 0 [0, 1, 2, 4, 5, 6, 3, 7] 0 1 2 3 4 6⟩,
+    ⟨1189, 4158031522740464670, .residual 3546628365007392⟩,
+    ⟨5541, 8659170591530737950, .residual 261946920715760⟩,
+    ⟨5797, 3726877582424663070, .residual 3323309281970835⟩
+  ],
+  [
+    ⟨678, 6024071250642167070, .residual 4403974365339923⟩,
+    ⟨1190, 2860165828355189790, .residual 1261222955753265⟩,
+    ⟨5542, 5563591007921168670, .residual 3793753402863874⟩,
+    ⟨5798, 3726822607682135070, .residual 3280015953037716⟩
+  ],
+  [
+    ⟨679, 6031614906202809630, .residual 4403974365339924⟩,
+    ⟨1191, 8153654609119964190, .residual 1252428892774196⟩,
+    ⟨5543, 4149308163393511710, .residual 4231787769637570⟩,
+    ⟨5799, 8661345306346644510, .residual 3254039990700691⟩
+  ]
+]
+
+end Erdos97Octagon.RawIncidence
diff --git a/LeanPool/Erdos97ConvexOctagon/CoverageData21.lean b/LeanPool/Erdos97ConvexOctagon/CoverageData21.lean
new file mode 100644
index 00000000..b5d4e7cd
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/CoverageData21.lean
@@ -0,0 +1,126 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.CoverageDataTypes
+
+/-! # Coverage certificate data, buckets 168–175 -/
+
+namespace Erdos97Octagon.RawIncidence
+
+/-- Generated monotone-obstruction entries for this hash-bucket group. -/
+def patternBuckets21 : Array (List PatternEntry) := #[
+  [
+    ⟨424, 145138297339904, .k4 2 [2, 3, 5] 2 3 5 7⟩,
+    ⟨2216, 3474747736396398592, .k4 4 [4, 7, 5, 6] 3 4 5 6⟩,
+    ⟨5032, 2814751177982238, .k4 0 [0, 1, 6, 3, 2] 0 2 3 4⟩
+  ],
+  [
+    ⟨169, 38562071818338304, .sharedThree 2 6 0 3 7⟩,
+    ⟨425, 145839921037312, .k4 2 [2, 4, 5] 2 4 5 7⟩,
+    ⟨2217, 3571849009859395584, .k4 4 [4, 6, 7, 5] 0 5 6 7⟩,
+    ⟨3753, 11613042903115786, .k4 0 [0, 3, 6, 5, 1] 0 1 3 6⟩,
+    ⟨4009, 731914107002871808, .k4 1 [1, 7, 3, 5, 6] 1 3 5 6⟩,
+    ⟨7081, 12191831605395738, .k4 0 [0, 1, 6, 5, 4] 0 3 4 6⟩
+  ],
+  [
+    ⟨170, 38562660219879424, .sharedThree 4 6 0 3 7⟩,
+    ⟨426, 147334566683648, .k4 1 [1, 2, 5] 1 2 5 7⟩,
+    ⟨682, 3602880397681139712, .k4 1 [1, 7, 4] 1 4 5 7⟩,
+    ⟨1450, 12094628113422, .k4 0 [0, 2, 1, 5] 0 1 3 5⟩,
+    ⟨2218, 3576229326745501696, .k4 4 [4, 5, 7, 6] 0 5 6 7⟩,
+    ⟨4010, 731914107539742720, .k4 1 [1, 7, 3, 6, 5] 1 3 5 6⟩,
+    ⟨4266, 4794363278362984714, .k4 0 [0, 1, 3, 7, 6] 0 1 3 6⟩,
+  ],
+  [
+    ⟨171, 38712704902365184, .sharedThree 5 6 0 3 7⟩,
+    ⟨683, 3603023334192709632, .k4 4 [4, 7, 5] 1 4 5 7⟩,
+    ⟨939, 19972403243008, .k4 1 [1, 5, 4, 3] 1 3 4 5⟩,
+    ⟨1451, 12094630600974, .k4 0 [0, 1, 2, 5] 0 2 3 5⟩,
+    ⟨5291, 9663629171376406, .k4 0 [0, 1, 4, 6, 5] 0 2 4 5⟩,
+    ⟨7083, 12384899566822666, .k4 0 [0, 1, 3, 2, 6] 1 3 5 6⟩,
+    ⟨9899, 2892931643075486734, .k4 0 [0, 3, 7, 5, 1, 6] 0 1 2 6⟩,
+  ],
+  [
+    ⟨940, 20903605838098, .k4 0 [0, 1, 4, 5] 0 1 4 5⟩,
+    ⟨7084, 12384899634323722, .k4 0 [0, 1, 3, 2, 6] 1 3 5 6⟩,
+    ⟨10924, 2885263662928446486, .k4 0 [0, 2, 4, 5, 7, 3, 6, 1] 0 1 2 4⟩
+  ],
+  [
+    ⟨173, 40813871632547840, .sharedThree 2 6 0 4 7⟩,
+    ⟨429, 147334568779776, .k4 1 [1, 5, 2] 1 2 5 7⟩,
+    ⟨685, 3746995044602609664, .k4 2 [2, 4, 7] 2 4 5 7⟩,
+    ⟨1709, 2814750924753934, .k4 0 [0, 3, 6, 1] 0 1 2 3⟩,
+  ],
+  [
+    ⟨174, 40813874055741440, .sharedThree 3 6 0 4 7⟩,
+    ⟨686, 3746995577178554368, .k4 2 [2, 7, 4] 2 4 5 7⟩,
+    ⟨1198, 9642716982027264, .k4 1 [1, 2, 5, 6] 1 2 5 6⟩,
+    ⟨2222, 3603029830901170176, .k4 3 [3, 5, 7, 4] 1 3 4 7⟩,
+    ⟨4270, 4796615091011240210, .k4 0 [0, 1, 4, 7, 6] 0 1 4 6⟩,
+    ⟨6062, 23231528447006, .k4 0 [0, 3, 4, 1, 5] 0 1 2 5⟩,
+    ⟨8622, 2450103333113331998, .k4 0 [0, 1, 3, 7, 5, 2] 0 2 3 4⟩
+  ],
+  [
+    ⟨175, 40973300809072640, .sharedThree 5 6 0 4 7⟩,
+    ⟨431, 149536343851008, .k4 2 [2, 3, 5] 2 3 5 7⟩,
+    ⟨687, 3746995594350034944, .k4 2 [2, 4, 7] 2 4 5 7⟩,
+    ⟨7087, 12384900118962438, .k4 0 [0, 1, 2, 3, 6] 1 2 5 6⟩
+  ]
+]
+
+/-- Generated exact-table entries for this hash-bucket group. -/
+def hardBuckets21 : Array (List HardEntry) := #[
+  [
+    ⟨680, 8694995735922566430, .hubPentagon 0 [0, 1, 2, 3, 4, 6, 5, 7] 1 0 2 5 6 3⟩,
+    ⟨1192, 7148788942262922270, .residual 1557451065360065⟩,
+    ⟨5544, 4147065159672848670, .residual 1743768118813285⟩,
+    ⟨5800, 8658053363130885150, .residual 1006185302497203⟩
+  ],
+  [
+    ⟨681, 7690126770580972830, .residual 3917770616636806⟩,
+    ⟨1193, 3870992639705902110, .residual 2124303467080368⟩,
+    ⟨5545, 3285751730938241310, .residual 2965307265735362⟩,
+    ⟨5801, 3871005840320947230, .residual 4346704731131392⟩
+  ],
+  [
+    ⟨682, 8686829787667457310, .residual 1200473168846675⟩,
+    ⟨1194, 2853406031337384990, .residual 745345242176418⟩,
+    ⟨5546, 3858839181567648030, .residual 3598364165457602⟩,
+    ⟨5802, 3294545062482600990, .residual 2300026473644256⟩
+  ],
+  [
+    ⟨683, 8694980342994658590, .cycleStrip 0 [0, 1, 2, 3, 4, 5, 6, 7] 0 2 1 5 6 7 3⟩,
+    ⟨1195, 5163823246521953310, .residual 4386519886533905⟩,
+    ⟨5547, 3284630229077909790, .residual 3483757257779013⟩,
+    ⟨5803, 2862199524024837150, .residual 4058030306505510⟩
+  ],
+  [
+    ⟨684, 8686254751860614430, .hubPentagon 0 [0, 1, 2, 3, 5, 6, 4, 7] 0 1 2 4 3 6⟩,
+    ⟨1196, 3140070683872619550, .residual 4408292418399749⟩,
+    ⟨5548, 6428199943587160350, .residual 1479374686682706⟩,
+    ⟨5804, 6463102140822512670, .residual 4410321790404999⟩
+  ],
+  [
+    ⟨685, 5452902448340624670, .residual 4395315711156500⟩,
+    ⟨1197, 2851840324900776990, .residual 2516829114190386⟩,
+    ⟨5549, 6425956939866497310, .residual 3598277794842311⟩,
+    ⟨5805, 3285751563637416990, .residual 2300026473644257⟩
+  ],
+  [
+    ⟨686, 5447619063275808030, .residual 4395315711156499⟩,
+    ⟨1198, 3145366056426040350, .residual 316285286000881⟩,
+    ⟨5550, 5564643511131889950, .residual 2112843219198546⟩,
+    ⟨5806, 6428199776286336030, .residual 329821925048562⟩
+  ],
+  [
+    ⟨687, 6453032278568428830, .residual 4209620647985318⟩,
+    ⟨1199, 2857909870174694430, .residual 3755400116770066⟩,
+    ⟨5551, 6137730961761296670, .residual 2745855209049682⟩,
+    ⟨5807, 2862131475133424670, .residual 1076536984246195⟩
+  ]
+]
+
+end Erdos97Octagon.RawIncidence
diff --git a/LeanPool/Erdos97ConvexOctagon/CoverageData22.lean b/LeanPool/Erdos97ConvexOctagon/CoverageData22.lean
new file mode 100644
index 00000000..9fc7e269
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/CoverageData22.lean
@@ -0,0 +1,127 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.CoverageDataTypes
+
+/-! # Coverage certificate data, buckets 176–183 -/
+
+namespace Erdos97Octagon.RawIncidence
+
+/-- Generated monotone-obstruction entries for this hash-bucket group. -/
+def patternBuckets22 : Array (List PatternEntry) := #[
+  [
+    ⟨176, 45317471250456832, .sharedThree 1 6 0 5 7⟩,
+    ⟨432, 150258088673280, .k4 3 [3, 4, 5] 3 4 5 7⟩,
+    ⟨3248, 5911253688140822, .k4 0 [0, 4, 6, 2, 1] 0 1 2 6⟩,
+  ],
+  [
+    ⟨177, 45317471260966912, .sharedThree 2 6 0 5 7⟩,
+    ⟨689, 3747140729881755648, .k4 4 [4, 7, 5] 2 4 5 7⟩,
+    ⟨945, 21036749824274, .k4 0 [0, 1, 5, 4] 0 1 4 5⟩,
+  ],
+  [
+    ⟨178, 45317473951547392, .sharedThree 3 6 0 5 7⟩,
+    ⟨690, 3747153219658186752, .k4 2 [2, 7, 5] 2 4 5 7⟩,
+    ⟨1458, 12270721573146, .k4 0 [0, 1, 4, 5] 0 3 4 5⟩,
+    ⟨2994, 2814750941724942, .k4 0 [0, 1, 2, 6, 3] 0 1 2 3⟩,
+    ⟨10674, 4945031569138122782, .k4 0 [0, 3, 4, 5, 6, 7, 2] 0 1 2 4⟩
+  ],
+  [
+    ⟨179, 45318162740150272, .sharedThree 4 6 0 5 7⟩,
+    ⟨691, 4035225440875446272, .k4 3 [3, 4, 7] 3 4 5 7⟩,
+    ⟨10931, 2892085062324536598, .k4 0 [0, 1, 2, 6, 5, 7, 3, 4] 0 1 2 4⟩
+  ],
+  [
+    ⟨180, 45598946237743104, .sharedThree 2 6 1 5 7⟩,
+    ⟨436, 151735322583040, .k4 1 [1, 5, 3] 1 3 5 7⟩,
+    ⟨692, 4035225956271521792, .k4 3 [3, 7, 4] 3 4 5 7⟩,
+    ⟨948, 22042379812864, .k4 2 [2, 3, 4, 5] 2 3 4 5⟩,
+    ⟨1204, 9644916003202048, .k4 1 [1, 2, 6, 5] 1 2 5 6⟩,
+    ⟨1716, 3096224744033294, .k4 0 [0, 2, 1, 6] 0 1 3 6⟩,
+    ⟨1972, 14637115403993108, .k4 0 [0, 2, 4, 6] 2 4 5 6⟩,
+    ⟨10932, 2892647981982485526, .k4 0 [0, 2, 4, 6, 5, 7, 3, 1] 0 1 2 4⟩
+  ],
+  [
+    ⟨181, 45598948945035264, .sharedThree 3 6 1 5 7⟩,
+    ⟨437, 153933853491200, .k4 2 [2, 3, 5] 2 3 5 7⟩,
+    ⟨693, 4035225988483776512, .k4 3 [3, 4, 7] 3 4 5 7⟩,
+    ⟨949, 22042581139456, .k4 2 [2, 4, 5, 3] 2 3 4 5⟩,
+    ⟨1205, 9644916005168128, .k4 1 [1, 6, 5, 2] 1 2 5 6⟩,
+    ⟨1717, 3096224748617998, .k4 0 [0, 1, 2, 6] 0 2 3 6⟩,
+    ⟨5301, 10133099218299916, .k4 0 [0, 2, 3, 6, 1] 1 2 5 6⟩
+  ],
+  [
+    ⟨182, 45599642011828224, .sharedThree 4 6 1 5 7⟩,
+    ⟨438, 153934323253248, .k4 2 [2, 5, 3] 2 3 5 7⟩,
+    ⟨950, 22136264729600, .k4 1 [1, 2, 5, 4] 1 2 4 5⟩,
+    ⟨1974, 14709567204123648, .k4 1 [1, 5, 6, 4] 1 2 4 6⟩,
+  ],
+  [
+    ⟨183, 46161896180589568, .sharedThree 1 6 2 5 7⟩,
+    ⟨439, 153934388264960, .k4 2 [2, 3, 5] 2 3 5 7⟩,
+    ⟨695, 4035375521259847680, .k4 4 [4, 7, 5] 3 4 5 7⟩,
+    ⟨951, 22153442501632, .k4 1 [1, 2, 4, 5] 1 2 4 5⟩,
+    ⟨1207, 9644916005298176, .k4 1 [1, 6, 5, 2] 1 2 5 6⟩,
+    ⟨1463, 13194948575260, .k4 0 [0, 2, 5, 3] 0 2 3 4⟩,
+    ⟨2231, 4793032869243053056, .k4 1 [1, 5, 7, 6] 1 2 5 6⟩,
+    ⟨4279, 4936789616540845318, .k4 0 [0, 1, 2, 7, 6] 0 1 2 6⟩,
+    ⟨10935, 3463977023622956046, .k4 0 [0, 2, 3, 5, 7, 4, 6, 1] 0 1 2 3⟩
+  ]
+]
+
+/-- Generated exact-table entries for this hash-bucket group. -/
+def hardBuckets22 : Array (List HardEntry) := #[
+  [
+    ⟨688, 5446478027099301150, .residual 1180592915422816⟩,
+    ⟨1200, 8190520808261053470, .residual 3340489419434384⟩,
+    ⟨5552, 5563522009271558430, .residual 3795001091000460⟩,
+    ⟨5808, 8661921326120494110, .residual 3792550812012032⟩
+  ],
+  [
+    ⟨689, 6020686714341254430, .residual 1180591036317280⟩,
+    ⟨1201, 7175172822746557470, .residual 1385418510359858⟩,
+    ⟨5553, 5419406829785637150, .residual 1440100703976482⟩,
+    ⟨5809, 8659669500771886110, .residual 2300146762088672⟩
+  ],
+  [
+    ⟨690, 8695556580571833630, .hubPentagon 0 [0, 1, 2, 3, 4, 5, 6, 7] 1 0 2 6 5 4⟩,
+    ⟨1202, 3714156749630499870, .residual 1836423914256849⟩,
+    ⟨5554, 5559581359832490270, .residual 2488895302259746⟩,
+    ⟨5810, 8657980676681425950, .residual 3495217674597158⟩
+  ],
+  [
+    ⟨691, 8262373201368802590, .residual 3364699080770950⟩,
+    ⟨1203, 6171834931792604190, .residual 2466096771748179⟩,
+    ⟨5555, 7654243378631205150, .residual 1076503153121200⟩,
+    ⟨5811, 8185658630621291550, .residual 3917740551801223⟩
+  ],
+  [
+    ⟨692, 8693867756481373470, .cycleStrip 0 [0, 1, 2, 3, 4, 5, 6, 7] 0 2 1 6 5 7 4⟩,
+    ⟨1204, 7172921005954329630, .residual 2439850161576241⟩,
+    ⟨5556, 5420588367487361310, .residual 271811993518576⟩,
+    ⟨5812, 3862203246043653150, .residual 329701636604146⟩
+  ],
+  [
+    ⟨693, 8694645099340719390, .residual 1201420201910099⟩,
+    ⟨1205, 6137214037938170910, .residual 2457438184773940⟩,
+    ⟨5557, 7654234557003260190, .residual 3792806362688009⟩,
+    ⟨5813, 6425956498761507870, .residual 2300146762088673⟩
+  ],
+  [
+    ⟨694, 4154172533488968990, .residual 4270231219241126⟩,
+    ⟨1206, 5993101048885570590, .residual 2762475386139841⟩,
+    ⟨5558, 7650870051422265630, .residual 3792806362688008⟩,
+    ⟨5814, 3150416706054251550, .residual 3323172111280787⟩
+  ],
+  [
+    ⟨695, 8693798488305788190, .hubPentagon 0 [0, 1, 2, 4, 5, 6, 3, 7] 0 1 2 3 4 5⟩,
+    ⟨1207, 2858191212510735390, .residual 2277590691181794⟩,
+    ⟨5559, 8688935906493784350, .residual 3916898738204930⟩,
+    ⟨5815, 3150353183487943710, .residual 3271220128164244⟩
+  ]
+]
+
+end Erdos97Octagon.RawIncidence
diff --git a/LeanPool/Erdos97ConvexOctagon/CoverageData23.lean b/LeanPool/Erdos97ConvexOctagon/CoverageData23.lean
new file mode 100644
index 00000000..90c3cbdd
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/CoverageData23.lean
@@ -0,0 +1,116 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.CoverageDataTypes
+
+/-! # Coverage certificate data, buckets 184–191 -/
+
+namespace Erdos97Octagon.RawIncidence
+
+/-- Generated monotone-obstruction entries for this hash-bucket group. -/
+def patternBuckets23 : Array (List PatternEntry) := #[
+  [
+    ⟨440, 153934389837824, .k4 2 [2, 5, 3] 2 3 5 7⟩,
+    ⟨696, 4035383598751154176, .k4 3 [3, 7, 5] 3 4 5 7⟩,
+    ⟨1208, 9647115026441216, .k4 1 [1, 2, 5, 6] 1 2 5 6⟩,
+    ⟨1464, 13194965286940, .k4 0 [0, 3, 5, 2] 0 2 3 4⟩,
+    ⟨2744, 21032457085974, .k4 0 [0, 4, 5, 1, 2] 0 1 2 5⟩,
+    ⟨4280, 4936789616540910854, .k4 0 [0, 1, 2, 7, 6] 0 1 2 6⟩,
+  ],
+  [
+    ⟨697, 4729273289459892224, .k4 5 [5, 6, 7] 0 5 6 7⟩,
+    ⟨4281, 4937071092621265920, .k4 1 [1, 2, 3, 7, 6] 1 2 3 6⟩,
+  ],
+  [
+    ⟨442, 159034060570624, .k4 2 [2, 4, 5] 2 4 5 7⟩,
+    ⟨698, 4755801206516007936, .k4 1 [1, 2, 7] 1 2 6 7⟩,
+    ⟨4794, 143640897855750, .k4 0 [0, 1, 2, 5, 4] 2 4 5 7⟩,
+  ],
+  [
+    ⟨187, 47287796098400256, .sharedThree 2 6 3 5 7⟩,
+    ⟨443, 159054181695488, .k4 3 [3, 4, 5] 3 4 5 7⟩,
+    ⟨8891, 83602348138774, .k4 0 [0, 1, 2, 4, 3, 5] 1 2 5 6⟩
+  ],
+  [
+    ⟨188, 47288517641895936, .sharedThree 4 6 3 5 7⟩,
+    ⟨1212, 9649315152685056, .k4 1 [1, 3, 6, 5] 1 3 5 6⟩,
+    ⟨1724, 3096538276446490, .k4 0 [0, 1, 4, 6] 0 3 4 6⟩
+  ],
+  [
+    ⟨701, 4793518853395185664, .k4 2 [2, 6, 7] 1 2 6 7⟩,
+    ⟨1213, 9649315656001536, .k4 1 [1, 6, 5, 3] 1 3 5 6⟩,
+    ⟨2749, 21033025284122, .k4 0 [0, 4, 5, 1, 3] 0 1 3 5⟩,
+  ],
+  [
+    ⟨190, 49539595912609792, .sharedThree 2 6 4 5 7⟩,
+    ⟨702, 4794644756544094208, .k4 3 [3, 6, 7] 1 3 6 7⟩,
+    ⟨958, 23111221182484, .k4 0 [0, 2, 4, 5] 0 2 4 5⟩,
+    ⟨1214, 9649315689539584, .k4 1 [1, 3, 5, 6] 1 3 5 6⟩,
+    ⟨1470, 14294204818702, .k4 0 [0, 1, 3, 5] 0 1 2 5⟩,
+  ],
+  [
+    ⟨191, 49539598853865472, .sharedThree 3 6 4 5 7⟩,
+    ⟨447, 161224482398208, .k4 1 [1, 5, 4] 1 4 5 7⟩,
+    ⟨703, 4796897386326654976, .k4 4 [4, 6, 7] 1 4 6 7⟩,
+    ⟨959, 23111222165524, .k4 0 [0, 4, 2, 5] 0 2 4 5⟩,
+    ⟨1215, 9649315689553920, .k4 1 [1, 6, 5, 3] 1 3 5 6⟩,
+    ⟨1983, 15762908812673024, .k4 2 [2, 3, 4, 6] 2 3 5 6⟩
+  ]
+]
+
+/-- Generated exact-table entries for this hash-bucket group. -/
+def hardBuckets23 : Array (List HardEntry) := #[
+  [
+    ⟨696, 3723520191431927070, .residual 4334705125450003⟩,
+    ⟨1208, 3136570097621560350, .residual 3532334445632161⟩,
+    ⟨5560, 4149307752687264030, .residual 3918146426341516⟩,
+    ⟨5816, 8659170047632204830, .residual 3340489419434388⟩
+  ],
+  [
+    ⟨697, 3718236806367110430, .residual 4334705125450004⟩,
+    ⟨1209, 2849465621376691230, .residual 3535686768138901⟩,
+    ⟨5561, 3862203276442394910, .residual 2112813121397330⟩,
+    ⟨5817, 8659093382465971230, .residual 3253902820010643⟩
+  ],
+  [
+    ⟨698, 8697799490038621470, .hubPentagon 0 [0, 1, 2, 3, 4, 5, 6, 7] 1 0 2 6 5 3⟩,
+    ⟨1210, 6172613626560015390, .residual 941840974194625⟩,
+    ⟨5562, 4147064748966600990, .residual 2605151948312146⟩,
+    ⟨5818, 6460859423606891550, .residual 4411419154721159⟩
+  ],
+  [
+    ⟨699, 7688164141790618910, .residual 3363616748897670⟩,
+    ⟨1211, 6171492124699683870, .residual 822483828394932⟩,
+    ⟨5563, 3858838770861400350, .residual 3598243905914567⟩,
+    ⟨5819, 7609207234720097310, .residual 3918837916117383⟩
+  ],
+  [
+    ⟨700, 8696888256942531870, .residual 1200337870036819⟩,
+    ⟨1212, 3858394537765923870, .residual 831277788613553⟩,
+    ⟨5564, 3284629818371662110, .residual 1620108045221458⟩,
+    ⟨5820, 3870997164017771550, .residual 1738176031678688⟩
+  ],
+  [
+    ⟨701, 8693858840599553310, .cycleStrip 0 [0, 1, 2, 3, 4, 5, 6, 7] 0 2 1 6 5 7 3⟩,
+    ⟨1213, 2857909737550801950, .residual 3362744870465797⟩,
+    ⟨5565, 6428199532880912670, .residual 3483791146706757⟩,
+    ⟨5821, 3294536386179425310, .residual 4346719763574272⟩
+  ],
+  [
+    ⟨702, 8693789841949943070, .hubPentagon 0 [0, 1, 2, 3, 5, 6, 4, 7] 0 1 2 4 3 5⟩,
+    ⟨1214, 2849465617098501150, .residual 1785343964149538⟩,
+    ⟨5566, 6141095056636043550, .residual 4090932426791618⟩,
+    ⟨5822, 2862190847721661470, .residual 4058032185611046⟩
+  ],
+  [
+    ⟨703, 3141767489127671070, .residual 4326046471266580⟩,
+    ⟨1215, 2860161430275517470, .residual 837910979072946⟩,
+    ⟨5567, 6425956529160249630, .residual 3598638605584066⟩,
+    ⟨5823, 3285751593451054110, .residual 260432403939570⟩
+  ]
+]
+
+end Erdos97Octagon.RawIncidence
diff --git a/LeanPool/Erdos97ConvexOctagon/CoverageData24.lean b/LeanPool/Erdos97ConvexOctagon/CoverageData24.lean
new file mode 100644
index 00000000..11236754
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/CoverageData24.lean
@@ -0,0 +1,132 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.CoverageDataTypes
+
+/-! # Coverage certificate data, buckets 192–199 -/
+
+namespace Erdos97Octagon.RawIncidence
+
+/-- Generated monotone-obstruction entries for this hash-bucket group. -/
+def patternBuckets24 : Array (List PatternEntry) := #[
+  [
+    ⟨192, 1008806316530991118, .sharedThree 0 7 1 2 3⟩,
+    ⟨448, 163294668128256, .k4 2 [2, 4, 5] 2 4 5 7⟩,
+    ⟨704, 4899916394591863808, .k4 1 [1, 2, 7] 1 2 6 7⟩,
+    ⟨960, 23231479218196, .k4 0 [0, 2, 4, 5] 0 2 4 5⟩,
+    ⟨1984, 15763016129708056, .k4 0 [0, 3, 4, 6] 3 4 5 6⟩,
+    ⟨2240, 4800837202783429632, .k4 1 [1, 2, 7, 6] 1 2 5 6⟩,
+    ⟨10944, 3468546353679385870, .k4 0 [0, 1, 2, 6, 5, 7, 4, 3] 0 1 2 3⟩
+  ],
+  [
+    ⟨193, 1585267068834414614, .sharedThree 0 7 1 2 4⟩,
+    ⟨449, 163414927212544, .k4 2 [2, 5, 4] 2 4 5 7⟩,
+    ⟨705, 4899916397880541184, .k4 2 [2, 3, 7] 2 3 6 7⟩,
+    ⟨961, 23231481249812, .k4 0 [0, 4, 5, 2] 0 2 4 5⟩,
+    ⟨1473, 14315129667612, .k4 0 [0, 4, 2, 5] 0 2 3 5⟩,
+    ⟨1729, 3377701068537884, .k4 0 [0, 2, 6, 3] 0 2 3 4⟩,
+  ],
+  [
+    ⟨194, 1873497444986126362, .sharedThree 0 7 1 3 4⟩,
+    ⟨450, 163432104984576, .k4 2 [2, 4, 5] 2 4 5 7⟩,
+    ⟨706, 4899917236406321152, .k4 2 [2, 4, 7] 2 4 6 7⟩,
+    ⟨962, 23244364120084, .k4 0 [0, 2, 4, 5] 0 2 4 5⟩,
+    ⟨1474, 14333178282012, .k4 0 [0, 4, 3, 5] 0 2 3 5⟩,
+    ⟨1730, 3377701085249564, .k4 0 [0, 3, 6, 2] 0 2 3 4⟩,
+    ⟨1986, 15835484290836480, .k4 1 [1, 5, 6, 4] 1 3 4 6⟩
+  ],
+  [
+    ⟨195, 2017612633061982236, .sharedThree 0 7 2 3 4⟩,
+    ⟨451, 163432106033152, .k4 2 [2, 5, 4] 2 4 5 7⟩,
+    ⟨707, 4937634041458377728, .k4 1 [1, 6, 7] 1 2 6 7⟩,
+    ⟨963, 23244365168660, .k4 0 [0, 2, 5, 4] 0 2 4 5⟩,
+    ⟨1731, 3377701135122460, .k4 0 [0, 2, 6, 3] 0 2 3 4⟩,
+    ⟨2243, 4801963102690271232, .k4 1 [1, 7, 6, 2] 1 2 5 6⟩,
+    ⟨5315, 10205666933812238, .k4 0 [0, 2, 6, 5, 1] 0 1 2 3⟩,
+  ],
+  [
+    ⟨196, 2522015791329771520, .sharedThree 2 7 0 1 5⟩,
+    ⟨452, 167712835764224, .k4 3 [3, 4, 5] 3 4 5 7⟩,
+    ⟨708, 4939322894606925824, .k4 3 [3, 6, 7] 2 3 6 7⟩,
+    ⟨1732, 3377701151834140, .k4 0 [0, 3, 6, 2] 0 2 3 4⟩,
+    ⟨2756, 21045342905606, .k4 0 [0, 1, 5, 4, 2] 0 1 2 5⟩,
+  ],
+  [
+    ⟨197, 2522015791914680320, .sharedThree 3 7 0 1 5⟩,
+    ⟨453, 167815914979328, .k4 3 [3, 5, 4] 3 4 5 7⟩,
+    ⟨709, 4941575532945866752, .k4 4 [4, 6, 7] 2 4 6 7⟩,
+    ⟨2245, 4803089004234858496, .k4 1 [1, 7, 6, 3] 1 3 5 6⟩,
+  ],
+  [
+    ⟨198, 2522015941651333120, .sharedThree 4 7 0 1 5⟩,
+    ⟨454, 167849737846784, .k4 3 [3, 4, 5] 3 4 5 7⟩,
+    ⟨710, 5044031582659331072, .k4 1 [1, 2, 7] 1 2 6 7⟩,
+    ⟨2502, 6597122729230, .k4 0 [0, 1, 3, 5, 2] 0 1 2 3⟩,
+    ⟨7110, 12738942809957390, .k4 0 [0, 3, 6, 5, 1] 0 1 2 6⟩,
+  ],
+  [
+    ⟨199, 2531867415512350720, .sharedThree 6 7 0 1 5⟩,
+    ⟨455, 167850006282240, .k4 3 [3, 5, 4] 3 4 5 7⟩,
+    ⟨1223, 9658531045203968, .k4 1 [1, 6, 5, 4] 1 4 5 6⟩,
+    ⟨2247, 4805341223311171584, .k4 1 [1, 7, 6, 4] 1 4 5 6⟩,
+    ⟨2503, 6597122731022, .k4 0 [0, 3, 1, 5, 2] 0 1 2 3⟩,
+    ⟨10439, 1441159062240111630, .k4 0 [0, 3, 4, 7, 2, 5, 1] 0 1 2 3⟩
+  ]
+]
+
+/-- Generated exact-table entries for this hash-bucket group. -/
+def hardBuckets24 : Array (List HardEntry) := #[
+  [
+    ⟨704, 3149311144688313630, .residual 4326046471266579⟩,
+    ⟨1216, 8192763675079633950, .residual 1346452657004224⟩,
+    ⟨5568, 6137730551055048990, .residual 1743497469813349⟩,
+    ⟨5824, 6428199806099973150, .residual 1738296320123105⟩
+  ],
+  [
+    ⟨705, 4154163609050768670, .residual 4200961986576550⟩,
+    ⟨1217, 2860442772611558430, .residual 3300931671773570⟩,
+    ⟨5569, 5563521598565310750, .residual 3105888168454850⟩,
+    ⟨5825, 2862122824499389470, .residual 1077636227667891⟩
+  ],
+  [
+    ⟨706, 3145366216958895390, .residual 1171934254014048⟩,
+    ⟨1218, 3139947540449356830, .residual 1423471131106978⟩,
+    ⟨5570, 4149305562253943070, .residual 1442295531355170⟩,
+    ⟨5826, 8661912649817318430, .residual 1738296320123104⟩
+  ],
+  [
+    ⟨707, 3721818044823594270, .residual 1171932374908512⟩,
+    ⟨1219, 3860508104845716510, .residual 2748068731522130⟩,
+    ⟨5571, 4145367103248195870, .residual 2486971123880994⟩,
+    ⟨5827, 8659660824468710430, .residual 3792565844454912⟩
+  ],
+  [
+    ⟨708, 6028587786195068190, .residual 1231998015078208⟩,
+    ⟨1220, 3716955866723281950, .residual 4248894620216519⟩,
+    ⟨5572, 5590597052753568030, .residual 953325712673712⟩,
+    ⟨5828, 8657972000378250270, .residual 3495219553702694⟩
+  ],
+  [
+    ⟨709, 3726950546396570910, .residual 1231999897796416⟩,
+    ⟨1221, 2852277932407680030, .residual 918775720543186⟩,
+    ⟨5573, 6164814548788896030, .residual 945629131221936⟩,
+    ⟨5829, 3862203275857290270, .residual 1738176031678689⟩
+  ],
+  [
+    ⟨710, 5454378726616884510, .residual 1223339360894784⟩,
+    ⟨1222, 3713030610212121630, .residual 1551650411027922⟩,
+    ⟨5574, 5563515412202184990, .residual 1872341987358754⟩,
+    ⟨5830, 6425956528575144990, .residual 260552692383986⟩
+  ],
+  [
+    ⟨711, 3150498346195641630, .residual 1223341243612992⟩,
+    ⟨1223, 2851717181477514270, .residual 4349966758980876⟩,
+    ⟨5575, 3138258826163708190, .residual 2426225198872610⟩,
+    ⟨5831, 8658044164888519710, .residual 1007284545918899⟩
+  ]
+]
+
+end Erdos97Octagon.RawIncidence
diff --git a/LeanPool/Erdos97ConvexOctagon/CoverageData25.lean b/LeanPool/Erdos97ConvexOctagon/CoverageData25.lean
new file mode 100644
index 00000000..a3292fc8
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/CoverageData25.lean
@@ -0,0 +1,123 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.CoverageDataTypes
+
+/-! # Coverage certificate data, buckets 200–207 -/
+
+namespace Erdos97Octagon.RawIncidence
+
+/-- Generated monotone-obstruction entries for this hash-bucket group. -/
+def patternBuckets25 : Array (List PatternEntry) := #[
+  [
+    ⟨200, 2666130979403343104, .sharedThree 1 7 0 2 5⟩,
+    ⟨712, 5044031582667686912, .k4 1 [1, 2, 7] 1 2 6 7⟩,
+    ⟨968, 26535146825728, .k4 1 [1, 3, 5, 4] 1 3 4 5⟩,
+    ⟨1736, 3659175787775246, .k4 0 [0, 1, 3, 6] 0 1 2 6⟩,
+    ⟨1992, 36592588799755264, .k4 1 [1, 2, 6, 4] 2 4 6 7⟩,
+    ⟨4296, 4938478466485452812, .k4 0 [0, 3, 2, 7, 6] 0 2 3 6⟩,
+  ],
+  [
+    ⟨713, 5044031582667718656, .k4 1 [1, 7, 2] 1 2 6 7⟩,
+    ⟨4041, 936748724665877518, .k4 0 [0, 3, 7, 2, 1] 0 1 2 7⟩,
+  ],
+  [
+    ⟨714, 5080623329640054784, .k4 2 [2, 7, 6] 1 2 6 7⟩,
+    ⟨970, 26568969693184, .k4 1 [1, 3, 4, 5] 1 3 4 5⟩,
+    ⟨2762, 22136264656150, .k4 0 [0, 1, 2, 5, 4] 0 1 2 4⟩,
+    ⟨4554, 27642410641678, .k4 0 [0, 1, 2, 4, 5] 0 1 3 5⟩
+  ],
+  [
+    ⟨459, 918092209217792, .k4 1 [1, 5, 6] 0 1 5 6⟩,
+    ⟨715, 5081186279580812288, .k4 1 [1, 7, 6] 1 2 6 7⟩,
+    ⟨1739, 3659196177842204, .k4 0 [0, 4, 2, 6] 0 2 3 6⟩,
+    ⟨4299, 4940730287689629716, .k4 0 [0, 2, 4, 7, 6] 0 2 4 6⟩,
+    ⟨4555, 72567824149516, .k4 0 [0, 2, 3, 1, 5] 1 2 5 6⟩
+  ],
+  [
+    ⟨204, 2954361355555055872, .sharedThree 1 7 0 3 5⟩,
+    ⟨1228, 10139696235701248, .k4 1 [1, 2, 5, 6] 1 2 5 6⟩,
+    ⟨1740, 3659214761230364, .k4 0 [0, 4, 3, 6] 0 2 3 6⟩,
+    ⟨9932, 3469392947265430550, .k4 0 [0, 4, 7, 5, 1, 6] 0 1 2 6⟩,
+    ⟨10444, 1442841315032714254, .k4 0 [0, 3, 4, 7, 2, 6, 1] 0 1 2 3⟩
+  ],
+  [
+    ⟨205, 2954361355557732352, .sharedThree 2 7 0 3 5⟩,
+    ⟨717, 5188146774032252928, .k4 2 [2, 3, 7] 2 3 6 7⟩,
+    ⟨973, 26577595793408, .k4 2 [2, 3, 4, 5] 2 3 4 5⟩,
+    ⟨1485, 19954418066710, .k4 0 [0, 1, 5, 4] 0 1 2 4⟩,
+    ⟨2253, 4938759941378296832, .k4 1 [1, 6, 7, 2] 1 2 3 6⟩,
+    ⟨6605, 5642995167264768, .k4 2 [2, 5, 6, 3, 4] 1 2 3 4⟩,
+  ],
+  [
+    ⟨206, 2954361531648704512, .sharedThree 4 7 0 3 5⟩,
+    ⟨718, 5188147633213931520, .k4 3 [3, 4, 7] 3 4 6 7⟩,
+    ⟨4558, 72569395047436, .k4 0 [0, 2, 3, 1, 5] 1 3 5 6⟩,
+    ⟨6606, 5643012146331648, .k4 2 [2, 5, 6, 3, 4] 1 2 3 4⟩,
+    ⟨8654, 2603854640815098894, .k4 0 [0, 2, 7, 5, 6, 1] 0 1 2 3⟩,
+    ⟨10702, 5228698273575021824, .k4 1 [1, 2, 3, 7, 6, 4, 5] 0 1 2 5⟩
+  ],
+  [
+    ⟨207, 2965901829600182272, .sharedThree 6 7 0 3 5⟩,
+    ⟨463, 1483241192226816, .k4 2 [2, 5, 6] 0 2 5 6⟩,
+    ⟨4303, 4946150858537591808, .k4 1 [1, 5, 6, 7, 2] 1 2 5 6⟩,
+    ⟨10959, 5224741857310893078, .k4 0 [0, 2, 4, 3, 7, 6, 1, 5] 0 1 2 5⟩
+  ]
+]
+
+/-- Generated exact-table entries for this hash-bucket group. -/
+def hardBuckets25 : Array (List HardEntry) := #[
+  [
+    ⟨712, 6022942919503668510, .residual 2400121526892880⟩,
+    ⟨1224, 6139399885039365150, .residual 2912406333990722⟩,
+    ⟨5576, 7653108657063256350, .residual 1094062862338992⟩,
+    ⟨5832, 6028513859379717150, .residual 3911135697111442⟩
+  ],
+  [
+    ⟨713, 5446490950458696990, .residual 4410727664945291⟩,
+    ⟨1225, 5995847646916930590, .residual 2317541180409957⟩,
+    ⟨5577, 3716962188460089630, .residual 1872071338358818⟩,
+    ⟨5833, 7607518384860226590, .residual 4403716935715218⟩
+  ],
+  [
+    ⟨714, 3140087327753790750, .residual 2968558023252640⟩,
+    ⟨1226, 5131169712601328670, .residual 3545814802741570⟩,
+    ⟨5578, 8227326153098584350, .residual 1086366280887216⟩,
+    ⟨5834, 7580567156377052190, .residual 3349285244307857⟩
+  ],
+  [
+    ⟨715, 6030757277541623070, .residual 1382169606544948⟩,
+    ⟨1227, 5991922390405770270, .residual 4249238479218882⟩,
+    ⟨5579, 6137715140914110750, .residual 2426495847872546⟩,
+    ⟨5835, 7653172303111971870, .residual 2469909343751252⟩
+  ],
+  [
+    ⟨716, 6028514273820960030, .residual 1504382905597377⟩,
+    ⟨1228, 5130608961671162910, .residual 4169987741963461⟩,
+    ⟨5580, 8661985203826909470, .residual 3362880162050306⟩,
+    ⟨5836, 3860514699801584670, .residual 4241652773164577⟩
+  ],
+  [
+    ⟨717, 3714855935957034270, .residual 1390963566763569⟩,
+    ⟨1229, 2860161297651624990, .residual 3301172189950215⟩,
+    ⟨5581, 6176848712146018590, .residual 348790983099888⟩,
+    ⟨5837, 3284062743591183390, .residual 4246057263699221⟩
+  ],
+  [
+    ⟨718, 6020691094155060510, .residual 4411689737676939⟩,
+    ⟨1230, 2851717177199324190, .residual 346043814129778⟩,
+    ⟨5582, 4157549565685981470, .residual 3361662538705416⟩,
+    ⟨5838, 3292772941797319710, .residual 1978410524929108⟩
+  ],
+  [
+    ⟨719, 6029347686639494430, .residual 3532605094632096⟩,
+    ⟨1231, 5995847642638740510, .residual 2316488913924193⟩,
+    ⟨5583, 3869323587580780830, .residual 3361662538705417⟩,
+    ⟨5839, 3284047350663275550, .residual 1978410524929105⟩
+  ]
+]
+
+end Erdos97Octagon.RawIncidence
diff --git a/LeanPool/Erdos97ConvexOctagon/CoverageData26.lean b/LeanPool/Erdos97ConvexOctagon/CoverageData26.lean
new file mode 100644
index 00000000..d22141fa
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/CoverageData26.lean
@@ -0,0 +1,137 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.CoverageDataTypes
+
+/-! # Coverage certificate data, buckets 208–215 -/
+
+namespace Erdos97Octagon.RawIncidence
+
+/-- Generated monotone-obstruction entries for this hash-bucket group. -/
+def patternBuckets26 : Array (List PatternEntry) := #[
+  [
+    ⟨464, 1970324836992262, .k4 0 [0, 1, 6] 0 1 2 6⟩,
+    ⟨720, 5227553267483410432, .k4 2 [2, 6, 7] 2 3 6 7⟩,
+    ⟨1232, 10146294448783360, .k4 2 [2, 3, 5, 6] 2 3 5 6⟩,
+    ⟨2000, 37155559480754176, .k4 2 [2, 3, 6, 4] 3 4 6 7⟩,
+    ⟨2512, 6609957823766, .k4 0 [0, 1, 4, 5, 2] 0 1 2 4⟩,
+    ⟨7376, 2450103332877533454, .k4 0 [0, 1, 3, 7, 5, 2] 0 1 2 3⟩
+  ],
+  [
+    ⟨209, 3530822107861680128, .sharedThree 2 7 0 4 5⟩,
+    ⟨721, 5230931826184290304, .k4 4 [4, 6, 7] 3 4 6 7⟩,
+    ⟨977, 27527250706456, .k4 0 [0, 4, 3, 5] 0 3 4 5⟩,
+    ⟨1489, 19971597936922, .k4 0 [0, 1, 5, 4] 0 1 3 4⟩,
+    ⟨2001, 37155576594038784, .k4 2 [2, 4, 6, 3] 3 4 6 7⟩,
+  ],
+  [
+    ⟨210, 3530822108680552448, .sharedThree 3 7 0 4 5⟩,
+    ⟨978, 27629809827864, .k4 0 [0, 3, 4, 5] 0 3 4 5⟩,
+    ⟨7378, 2450103345712627990, .k4 0 [0, 1, 4, 7, 5, 2] 0 1 2 4⟩
+  ],
+  [
+    ⟨211, 3544614381717291008, .sharedThree 6 7 0 4 5⟩,
+    ⟨979, 27630329921560, .k4 0 [0, 4, 5, 3] 0 3 4 5⟩,
+    ⟨2003, 37717646887862534, .k4 0 [0, 1, 2, 6] 1 2 6 7⟩,
+    ⟨6611, 5656326743654400, .k4 2 [2, 6, 4, 5, 3] 1 2 3 4⟩
+  ],
+  [
+    ⟨212, 4827858800545562624, .sharedThree 2 7 0 1 6⟩,
+    ⟨724, 5332261962061465600, .k4 1 [1, 3, 7] 1 3 6 7⟩,
+    ⟨1236, 10155381459255296, .k4 2 [2, 4, 5, 6] 2 4 5 6⟩,
+    ⟨1492, 20890724147478, .k4 0 [0, 1, 2, 5] 0 2 4 5⟩,
+    ⟨4308, 5225019995917912330, .k4 0 [0, 1, 3, 7, 6] 0 1 3 6⟩,
+    ⟨6612, 5656343722721280, .k4 2 [2, 6, 4, 5, 3] 1 2 3 4⟩
+  ],
+  [
+    ⟨213, 4827858801665245184, .sharedThree 3 7 0 1 6⟩,
+    ⟨469, 2613540766613504, .k4 3 [3, 5, 6] 0 3 5 6⟩,
+    ⟨725, 5332261962061496320, .k4 1 [1, 7, 3] 1 3 6 7⟩,
+    ⟨981, 27660143034392, .k4 0 [0, 3, 5, 4] 0 3 4 5⟩,
+    ⟨4309, 5225019995934689546, .k4 0 [0, 1, 3, 7, 6] 0 1 3 6⟩
+  ],
+  [
+    ⟨214, 4827859088303980544, .sharedThree 4 7 0 1 6⟩,
+    ⟨726, 5368853709033832448, .k4 3 [3, 7, 6] 1 3 6 7⟩,
+    ⟨982, 844424934409478, .k4 0 [0, 1, 2, 6] 0 1 2 6⟩,
+    ⟨1494, 20891543019802, .k4 0 [0, 1, 3, 5] 0 3 4 5⟩,
+    ⟨2774, 22162118803484, .k4 0 [0, 3, 2, 5, 4] 0 2 3 4⟩,
+    ⟨8662, 2882446700512878878, .k4 0 [0, 1, 2, 5, 7, 3] 0 2 3 4⟩
+  ],
+  [
+    ⟨215, 4827932467820232704, .sharedThree 5 7 0 1 6⟩,
+    ⟨471, 3096225867890698, .k4 0 [0, 3, 6] 0 1 3 6⟩,
+    ⟨983, 844424934475014, .k4 0 [0, 1, 2, 6] 0 1 2 6⟩,
+    ⟨1751, 5066850228520214, .k4 0 [0, 1, 6, 4] 0 1 2 4⟩,
+    ⟨2007, 37717650176623616, .k4 1 [1, 2, 6, 3] 2 3 6 7⟩,
+    ⟨2263, 4945515340820931584, .k4 1 [1, 6, 7, 2] 1 2 5 6⟩,
+    ⟨5079, 3377744050192414, .k4 0 [0, 2, 6, 3, 4] 0 1 3 4⟩,
+    ⟨5847, 7736108523806, .k4 0 [0, 1, 4, 5, 3] 0 2 3 5⟩,
+    ⟨6615, 5910975890917662, .k4 0 [0, 1, 2, 3, 6] 0 3 4 6⟩
+  ]
+]
+
+/-- Generated exact-table entries for this hash-bucket group. -/
+def hardBuckets26 : Array (List HardEntry) := #[
+  [
+    ⟨720, 5452053504538993950, .residual 1452521171082801⟩,
+    ⟨976, 6461210423826017310, .hubPentagon 0 [0, 2, 3, 4, 1, 5, 6, 7] 0 1 2 4 7 3⟩,
+    ⟨1232, 5456273428076129310, .residual 4408532936632834⟩,
+    ⟨5584, 3725701255592075550, .residual 333399666336240⟩,
+    ⟨5840, 5454295824292439070, .residual 3902339872237970⟩
+  ],
+  [
+    ⟨721, 3140638170395731230, .residual 1461315131301428⟩,
+    ⟨977, 6171577092312099870, .residual 4395315711156496⟩,
+    ⟨1233, 3140091574124375070, .residual 4346960281807362⟩,
+    ⟨5585, 6463946565752643870, .residual 4410442049490178⟩,
+    ⟨5841, 3148382858651427870, .residual 3271220128164241⟩
+  ],
+  [
+    ⟨722, 3138395166675068190, .residual 1583528430353857⟩,
+    ⟨978, 5450932123503651870, .residual 4395315711156497⟩,
+    ⟨1234, 6454735974900526110, .residual 4409479976808713⟩,
+    ⟨5586, 4149308008977588510, .residual 2912182781847365⟩,
+    ⟨5842, 5419393459756262430, .residual 3612876155704597⟩
+  ],
+  [
+    ⟨723, 5444239125110088990, .residual 1837173720611152⟩,
+    ⟨979, 5447603640283130910, .residual 3902373695234451⟩,
+    ⟨1235, 6024079260533222430, .residual 4409479976808712⟩,
+    ⟨5587, 3862203532732719390, .residual 3598334100622018⟩,
+    ⟨5843, 5417150456035599390, .residual 3608471665169953⟩
+  ],
+  [
+    ⟨724, 3722952748660450590, .residual 2399022269020496⟩,
+    ⟨980, 5442552740523371550, .residual 2632264696967472⟩,
+    ⟨1236, 4149453854055951390, .residual 350012371774576⟩,
+    ⟨5588, 4147065005256925470, .residual 3106040459445954⟩,
+    ⟨5844, 5419386888456299550, .residual 2469909343751249⟩
+  ],
+  [
+    ⟨725, 5455147406041048350, .residual 3531505851210400⟩,
+    ⟨981, 6031599607043681310, .residual 1835341575158228⟩,
+    ⟨1237, 6139488811347962910, .residual 342312002915568⟩,
+    ⟨5589, 3285751576522318110, .residual 2297771582243429⟩,
+    ⟨5845, 3722600483032458270, .residual 3280015953037713⟩
+  ],
+  [
+    ⟨726, 6030757140639540510, .residual 1382169606544945⟩,
+    ⟨982, 7184588890747530270, .residual 3794595216460164⟩,
+    ⟨1238, 6452484158108298270, .residual 1491004078448304⟩,
+    ⟨5590, 3284630074661986590, .residual 4091084640762562⟩,
+    ⟨5846, 3866981748828595230, .residual 2470991734230100⟩
+  ],
+  [
+    ⟨727, 3717098802775614750, .residual 1574734484585921⟩,
+    ⟨983, 5166976377944632350, .residual 3915846471280129⟩,
+    ⟨1239, 5420528307154283550, .residual 816811093115810⟩,
+    ⟨5591, 6428199789171237150, .residual 3364954631334028⟩,
+    ⟨5847, 5995853968068633630, .residual 3678840141256225⟩
+  ]
+]
+
+end Erdos97Octagon.RawIncidence
diff --git a/LeanPool/Erdos97ConvexOctagon/CoverageData27.lean b/LeanPool/Erdos97ConvexOctagon/CoverageData27.lean
new file mode 100644
index 00000000..e2307555
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/CoverageData27.lean
@@ -0,0 +1,136 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.CoverageDataTypes
+
+/-! # Coverage certificate data, buckets 216–223 -/
+
+namespace Erdos97Octagon.RawIncidence
+
+/-- Generated monotone-obstruction entries for this hash-bucket group. -/
+def patternBuckets27 : Array (List PatternEntry) := #[
+  [
+    ⟨216, 4971973988617045248, .sharedThree 1 7 0 2 6⟩,
+    ⟨472, 3659174702022668, .k4 0 [0, 2, 6] 0 2 3 6⟩,
+    ⟨728, 5476377148036481024, .k4 2 [2, 3, 7] 2 3 6 7⟩,
+    ⟨984, 844424934539526, .k4 0 [0, 1, 2, 6] 0 1 2 6⟩,
+    ⟨1240, 10205666931270656, .k4 1 [1, 2, 5, 6] 1 2 5 6⟩,
+    ⟨6616, 5911253734149150, .k4 0 [0, 3, 4, 1, 6] 0 1 2 6⟩,
+    ⟨10968, 5233255380138665238, .k4 0 [0, 1, 2, 5, 6, 7, 3, 4] 0 1 2 4⟩
+  ],
+  [
+    ⟨217, 4971973989774655488, .sharedThree 3 7 0 2 6⟩,
+    ⟨473, 3659175854866444, .k4 0 [0, 3, 6] 0 2 3 6⟩,
+    ⟨985, 844424934540294, .k4 0 [0, 2, 1, 6] 0 1 2 6⟩,
+    ⟨1241, 10205666935333888, .k4 1 [1, 5, 6, 2] 1 2 5 6⟩,
+    ⟨2009, 37718488702403584, .k4 1 [1, 2, 6, 4] 2 4 6 7⟩,
+    ⟨5593, 13591342403823898, .k4 0 [0, 1, 4, 6, 5] 0 1 3 5⟩,
+    ⟨7385, 2450107731508691214, .k4 0 [0, 1, 2, 7, 5, 3] 0 1 2 3⟩,
+    ⟨10969, 5233257548864359446, .k4 0 [0, 2, 4, 5, 6, 7, 3, 1] 0 1 2 4⟩
+  ],
+  [
+    ⟨730, 5476377150175576064, .k4 2 [2, 3, 7] 2 3 6 7⟩,
+    ⟨7386, 2450107744594723098, .k4 0 [0, 1, 4, 7, 5, 3] 0 1 3 4⟩
+  ],
+  [
+    ⟨219, 4972049854919344128, .sharedThree 5 7 0 2 6⟩,
+    ⟨2011, 38280597986788352, .k4 1 [1, 2, 3, 6] 1 2 6 7⟩,
+    ⟨2267, 4949456419991584768, .k4 2 [2, 7, 6, 4] 2 4 5 6⟩,
+    ⟨4315, 5226427369815952384, .k4 1 [1, 2, 3, 7, 6] 1 2 3 6⟩,
+    ⟨4827, 145864339292180, .k4 0 [0, 2, 4, 5, 3] 3 4 5 7⟩
+  ],
+  [
+    ⟨732, 5513531847096664064, .k4 3 [3, 7, 6] 2 3 6 7⟩,
+    ⟨988, 844426054222090, .k4 0 [0, 1, 3, 6] 0 1 3 6⟩,
+    ⟨1756, 5066871703357466, .k4 0 [0, 4, 6, 1] 0 1 3 4⟩,
+    ⟨2268, 4949548349470539776, .k4 2 [2, 7, 6, 5] 2 4 5 6⟩,
+    ⟨4060, 1297056080165118226, .k4 0 [0, 1, 7, 4, 5] 0 1 4 5⟩,
+    ⟨8156, 9649314918908190, .k4 0 [0, 1, 2, 6, 5, 3] 0 2 3 4⟩,
+    ⟨10716, 5233270876129132574, .k4 0 [0, 2, 3, 7, 6, 5, 4] 0 1 2 4⟩
+  ],
+  [
+    ⟨221, 5260204364773523456, .sharedThree 2 7 0 3 6⟩,
+    ⟨477, 4874551657758720, .k4 4 [4, 5, 6] 0 4 5 6⟩,
+    ⟨733, 5514657743728279552, .k4 2 [2, 7, 6] 2 3 6 7⟩,
+    ⟨989, 844426054223882, .k4 0 [0, 3, 1, 6] 0 1 3 6⟩,
+    ⟨1245, 10207865956623360, .k4 1 [1, 2, 6, 5] 1 2 5 6⟩,
+    ⟨8669, 2882452236657501206, .k4 0 [0, 4, 3, 7, 5, 1] 0 1 2 5⟩,
+    ⟨10973, 5801203152944456718, .k4 0 [0, 2, 3, 4, 7, 6, 1, 5] 0 1 2 5⟩
+  ],
+  [
+    ⟨222, 5260204678301351936, .sharedThree 4 7 0 3 6⟩,
+    ⟨1758, 5348024562827542, .k4 0 [0, 1, 2, 6] 0 2 4 6⟩,
+    ⟨2270, 5017437694924423168, .k4 2 [2, 5, 7, 6] 0 5 6 7⟩,
+    ⟨4318, 5226427662110031872, .k4 2 [2, 3, 4, 7, 6] 2 3 4 6⟩,
+  ],
+  [
+    ⟨223, 5260284629117566976, .sharedThree 5 7 0 3 6⟩,
+    ⟨479, 5348312320311314, .k4 0 [0, 4, 6] 0 1 4 6⟩,
+    ⟨735, 5764608364861456384, .k4 2 [2, 4, 7] 2 4 6 7⟩,
+  ]
+]
+
+/-- Generated exact-table entries for this hash-bucket group. -/
+def hardBuckets27 : Array (List HardEntry) := #[
+  [
+    ⟨728, 3714855799054951710, .residual 1390963566763572⟩,
+    ⟨984, 5166917172072115230, .residual 4408547969025538⟩,
+    ⟨1240, 5420595106814192670, .residual 3794595216460162⟩,
+    ⟨5592, 6141095312926368030, .residual 1620230179855954⟩,
+    ⟨5848, 5993610964347970590, .residual 3683244631790869⟩
+  ],
+  [
+    ⟨729, 3148743783336142110, .residual 4349155010119819⟩,
+    ⟨985, 6031599482976168990, .residual 2051807927923379⟩,
+    ⟨1241, 3718086284181335070, .residual 4240596747572418⟩,
+    ⟨5593, 6425956785450574110, .residual 2112568877968978⟩,
+    ⟨5849, 8227380853451842590, .residual 1977328134450260⟩
+  ],
+  [
+    ⟨730, 3714287334548071710, .residual 2969657266674336⟩,
+    ⟨986, 5450925406644956190, .residual 3885056387080850⟩,
+    ⟨1242, 4146499994827975710, .residual 3466424917571394⟩,
+    ⟨5594, 5564643356715966750, .residual 3105542419408583⟩,
+    ⟨5850, 5993595571420062750, .residual 1977328134450257⟩
+  ],
+  [
+    ⟨731, 3722943927032505630, .residual 4350117082851467⟩,
+    ⟨987, 5162695047673113630, .residual 4408427709883911⟩,
+    ⟨1243, 3141634327970933790, .residual 4108432009574597⟩,
+    ⟨5595, 5563521854855635230, .residual 2605274057106002⟩,
+    ⟨5851, 8181717980948259870, .residual 4394921110841746⟩
+  ],
+  [
+    ⟨732, 5454296371357574430, .residual 1513176851365313⟩,
+    ⟨988, 4158171306167331870, .hubPentagon 0 [0, 2, 3, 4, 1, 6, 5, 7] 0 1 2 4 7 3⟩,
+    ⟨1244, 3714161027670174750, .residual 2316323549827173⟩,
+    ⟨5596, 6428193217871274270, .residual 1995487289734178⟩,
+    ⟨5852, 8154766889367168030, .residual 3340489419434385⟩
+  ],
+  [
+    ⟨733, 5452053367636911390, .residual 1452521171082804⟩,
+    ⟨989, 3871061353839160350, .residual 4326046471266576⟩,
+    ⟨1245, 3139952075180436510, .residual 3044437743228226⟩,
+    ⟨5597, 3292862809742434590, .residual 1007220624218032⟩,
+    ⟨5853, 3858262596370621470, .residual 4175688787612949⟩
+  ],
+  [
+    ⟨734, 3140638033493648670, .residual 1461315131301425⟩,
+    ⟨990, 3141759792546278430, .residual 4326046471266577⟩,
+    ⟨1246, 5996978064374983710, .residual 2043149273854418⟩,
+    ⟨5598, 6427636839251370270, .residual 1380587581332514⟩,
+    ⟨5854, 3281810640160220190, .residual 4171284297078305⟩
+  ],
+  [
+    ⟨735, 3148734961708197150, .residual 1836074462738768⟩,
+    ⟨991, 3145370465184476190, .residual 3340523242430867⟩,
+    ⟨1247, 6425391775021624350, .residual 2747091622785106⟩,
+    ⟨5599, 3870928982686490910, .residual 3301307481534722⟩,
+    ⟨5855, 3858256025070658590, .residual 2470991734230097⟩
+  ]
+]
+
+end Erdos97Octagon.RawIncidence
diff --git a/LeanPool/Erdos97ConvexOctagon/CoverageData28.lean b/LeanPool/Erdos97ConvexOctagon/CoverageData28.lean
new file mode 100644
index 00000000..f67d8f15
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/CoverageData28.lean
@@ -0,0 +1,136 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.CoverageDataTypes
+
+/-! # Coverage certificate data, buckets 224–231 -/
+
+namespace Erdos97Octagon.RawIncidence
+
+/-- Generated monotone-obstruction entries for this hash-bucket group. -/
+def patternBuckets28 : Array (List PatternEntry) := #[
+  [
+    ⟨480, 5910974516232212, .k4 0 [0, 2, 6] 0 2 4 6⟩,
+    ⟨736, 5764608385517355008, .k4 3 [3, 4, 7] 3 4 6 7⟩,
+    ⟨992, 844712692957458, .k4 0 [0, 1, 4, 6] 0 1 4 6⟩,
+    ⟨1760, 5348025916473626, .k4 0 [0, 1, 3, 6] 0 3 4 6⟩,
+    ⟨3040, 3096225889404166, .k4 0 [0, 1, 6, 3, 2] 0 1 2 6⟩,
+    ⟨5856, 7885845176606, .k4 0 [0, 1, 3, 5, 4] 0 2 4 5⟩,
+    ⟨7392, 2450116690172936470, .k4 0 [0, 1, 2, 7, 5, 4] 0 1 2 4⟩
+  ],
+  [
+    ⟨225, 5836665117077471232, .sharedThree 2 7 0 4 6⟩,
+    ⟨481, 5911270863667220, .k4 0 [0, 4, 6] 0 2 4 6⟩,
+    ⟨1505, 22162034982940, .k4 0 [0, 2, 5, 4] 0 2 3 4⟩,
+    ⟨6369, 167300076470284, .k4 0 [0, 2, 3, 4, 5] 2 3 5 7⟩,
+    ⟨7393, 2450116707402940698, .k4 0 [0, 1, 3, 7, 5, 4] 0 1 3 4⟩,
+    ⟨9953, 4800911969620754702, .k4 0 [0, 1, 3, 7, 6, 5, 2] 0 1 2 3⟩,
+    ⟨10977, 5801782698419233806, .k4 0 [0, 2, 3, 6, 7, 4, 5, 1] 0 1 2 3⟩
+  ],
+  [
+    ⟨226, 5836665118431117312, .sharedThree 3 7 0 4 6⟩,
+    ⟨482, 7036875776720920, .k4 0 [0, 3, 6] 0 3 4 6⟩,
+    ⟨738, 5806265819601043456, .k4 2 [2, 6, 7] 2 4 6 7⟩,
+    ⟨994, 1407374887830790, .k4 0 [0, 1, 2, 6] 0 1 2 6⟩,
+    ⟨1506, 22166329884700, .k4 0 [0, 4, 5, 2] 0 2 3 4⟩,
+    ⟨2018, 38843548983935242, .k4 0 [0, 1, 3, 6] 1 3 6 7⟩,
+    ⟨4066, 1301822600510488850, .k4 0 [0, 1, 7, 4, 6] 0 1 4 6⟩
+  ],
+  [
+    ⟨227, 5836754177514012672, .sharedThree 5 7 0 4 6⟩,
+    ⟨483, 7037187950379032, .k4 0 [0, 4, 6] 0 3 4 6⟩,
+    ⟨739, 5807391722983915520, .k4 3 [3, 6, 7] 3 4 6 7⟩,
+    ⟨995, 1407374887896326, .k4 0 [0, 1, 2, 6] 0 1 2 6⟩,
+    ⟨1507, 22179213803548, .k4 0 [0, 2, 5, 4] 0 2 3 4⟩,
+    ⟨2019, 38843549047343104, .k4 1 [1, 3, 6, 2] 2 3 6 7⟩,
+    ⟨6115, 27629524823070, .k4 0 [0, 2, 4, 1, 5] 0 1 3 5⟩,
+  ],
+  [
+    ⟨228, 7061644215723360256, .sharedThree 2 7 1 5 6⟩,
+    ⟨484, 9362341510537472, .k4 1 [1, 5, 6] 0 1 5 6⟩,
+    ⟨996, 1407374887960838, .k4 0 [0, 1, 2, 6] 0 1 2 6⟩,
+    ⟨1508, 22183508705308, .k4 0 [0, 4, 5, 2] 0 2 3 4⟩,
+    ⟨2788, 23231478309910, .k4 0 [0, 2, 4, 1, 5] 0 1 2 5⟩,
+    ⟨6884, 10224358634037526, .k4 0 [0, 1, 5, 6, 2] 0 2 4 5⟩,
+    ⟨8676, 2882519267964773642, .k4 0 [0, 1, 3, 2, 7, 5] 1 2 5 6⟩
+  ],
+  [
+    ⟨229, 7061644217361104896, .sharedThree 3 7 1 5 6⟩,
+    ⟨997, 1407374887961606, .k4 0 [0, 2, 1, 6] 0 1 2 6⟩,
+    ⟨3813, 13584887067975954, .k4 0 [0, 1, 5, 6, 4] 0 1 4 5⟩,
+    ⟨4325, 5227069485072015360, .k4 1 [1, 6, 7, 3, 5] 1 3 5 6⟩,
+    ⟨9957, 4800911982455849238, .k4 0 [0, 1, 4, 7, 6, 5, 2] 0 1 2 4⟩
+  ],
+  [
+    ⟨230, 7061644636623732736, .sharedThree 4 7 1 5 6⟩,
+    ⟨998, 1407375978856460, .k4 0 [0, 2, 3, 6] 0 2 3 6⟩,
+    ⟨4582, 74766847405068, .k4 0 [0, 2, 3, 5, 1] 1 2 5 6⟩,
+    ⟨8422, 12384938974405906, .k4 0 [0, 1, 4, 2, 3, 6] 1 2 5 6⟩,
+    ⟨10982, 5809715571966682382, .k4 0 [0, 1, 2, 3, 4, 7, 6, 5] 0 1 2 5⟩
+  ],
+  [
+    ⟨231, 7205759403792819200, .sharedThree 1 7 2 5 6⟩,
+    ⟨743, 5908723544333795328, .k4 1 [1, 7, 4] 1 4 6 7⟩,
+    ⟨1511, 23089831739420, .k4 0 [0, 3, 2, 5] 0 2 4 5⟩,
+    ⟨2791, 23231480341526, .k4 0 [0, 4, 5, 2, 1] 0 1 2 5⟩,
+    ⟨4071, 1310636148279795712, .k4 1 [1, 7, 4, 5, 6] 1 4 5 6⟩,
+    ⟨4327, 5228776099688742912, .k4 3 [3, 4, 7, 5, 6] 3 4 5 6⟩
+  ]
+]
+
+/-- Generated exact-table entries for this hash-bucket group. -/
+def hardBuckets28 : Array (List HardEntry) := #[
+  [
+    ⟨736, 5997049396192830750, .residual 712033508203476⟩,
+    ⟨992, 3714296387598904350, .residual 1836423914256852⟩,
+    ⟨1248, 5420526108164582430, .residual 4411674705290508⟩,
+    ⟨5600, 8688942511618187550, .residual 340011981866480⟩
+  ],
+  [
+    ⟨737, 6427699539260171550, .residual 2218913724493875⟩,
+    ⟨993, 7181504760096844830, .residual 3302014003546500⟩,
+    ⟨1249, 5993052807863823390, .residual 4240219047359687⟩,
+    ⟨5601, 8373204691001729310, .residual 332317275857392⟩
+  ],
+  [
+    ⟨738, 3723449702902621470, .residual 712048544259028⟩,
+    ⟨994, 2858049375519206430, .residual 3361692603540993⟩,
+    ⟨1250, 5418843855374085150, .residual 988043092366290⟩,
+    ⟨5602, 8230703860873355550, .residual 3300089858189832⟩
+  ],
+  [
+    ⟨739, 4154099845969962270, .residual 2218928760549427⟩,
+    ⟨995, 3149291443405286430, .residual 2702633194729776⟩,
+    ⟨1251, 5132295749192739870, .residual 1985458739798690⟩,
+    ⟨5603, 8229582359013024030, .residual 3300089858189833⟩
+  ],
+  [
+    ⟨740, 5420597722209281310, .residual 711896337513428⟩,
+    ⟨996, 2851856819445918750, .residual 4346975314200066⟩,
+    ⟨1252, 6463392430482877470, .residual 348930032675952⟩,
+    ⟨5604, 8401831412735074590, .residual 3917860810886402⟩
+  ],
+  [
+    ⟨741, 6425447996138415390, .residual 2773067585007667⟩,
+    ⟨997, 3714296126629309470, .residual 2122159506911923⟩,
+    ⟨1253, 4158110309638302750, .residual 4347907321983241⟩,
+    ⟨5605, 4149307735173423390, .residual 1549863436361298⟩
+  ],
+  [
+    ⟨742, 3149240895737652510, .residual 711911373568980⟩,
+    ⟨998, 3140070685995002910, .residual 3323205934277266⟩,
+    ⟨1254, 3725771342480501790, .residual 4347907321983240⟩,
+    ⟨5606, 3862203258928554270, .residual 3303381950818444⟩
+  ],
+  [
+    ⟨743, 4154091169666786590, .residual 2773082621063219⟩,
+    ⟨999, 2851840327023160350, .residual 4346855055058439⟩,
+    ⟨1255, 3870935739527162910, .residual 333533078752496⟩,
+    ⟨5607, 4147064731452760350, .residual 3105559389562567⟩
+  ]
+]
+
+end Erdos97Octagon.RawIncidence
diff --git a/LeanPool/Erdos97ConvexOctagon/CoverageData29.lean b/LeanPool/Erdos97ConvexOctagon/CoverageData29.lean
new file mode 100644
index 00000000..edffbde3
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/CoverageData29.lean
@@ -0,0 +1,127 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.CoverageDataTypes
+
+/-! # Coverage certificate data, buckets 232–239 -/
+
+namespace Erdos97Octagon.RawIncidence
+
+/-- Generated monotone-obstruction entries for this hash-bucket group. -/
+def patternBuckets29 : Array (List PatternEntry) := #[
+  [
+    ⟨488, 9570149214610432, .k4 1 [1, 2, 6] 1 2 5 6⟩,
+    ⟨744, 5945315291306131456, .k4 4 [4, 7, 6] 1 4 6 7⟩,
+    ⟨1768, 5629787302395926, .k4 0 [0, 4, 6, 2] 0 1 2 4⟩,
+    ⟨4072, 1310636285718749184, .k4 1 [1, 7, 4, 6, 5] 1 4 5 6⟩,
+    ⟨4328, 5228960684246564888, .k4 0 [0, 3, 4, 7, 6] 0 3 4 6⟩,
+    ⟨10984, 5809716671493514510, .k4 0 [0, 1, 2, 5, 6, 7, 4, 3] 0 1 2 3⟩
+  ],
+  [
+    ⟨489, 9570150852356096, .k4 1 [1, 3, 6] 1 3 5 6⟩,
+    ⟨2025, 39406498983510028, .k4 0 [0, 2, 3, 6] 2 3 6 7⟩
+  ],
+  [
+    ⟨234, 7493989779944531968, .sharedThree 1 7 3 5 6⟩,
+    ⟨746, 6052838191257354240, .k4 2 [2, 4, 7] 2 4 6 7⟩,
+    ⟨1002, 1407654061735956, .k4 0 [0, 2, 4, 6] 0 2 4 6⟩,
+    ⟨1514, 23231478113558, .k4 0 [0, 1, 4, 5] 0 1 2 5⟩,
+    ⟨4330, 5231010547297681408, .k4 3 [3, 5, 7, 6, 4] 3 4 5 6⟩
+  ],
+  [
+    ⟨747, 6052838723833298944, .k4 2 [2, 7, 4] 2 4 6 7⟩,
+    ⟨1003, 1407666946637844, .k4 0 [0, 2, 4, 6] 0 2 4 6⟩,
+    ⟨1771, 5629808777691164, .k4 0 [0, 2, 6, 4] 0 2 3 4⟩,
+    ⟨4331, 5233756715295467520, .k4 1 [1, 5, 6, 7, 3] 1 3 5 6⟩,
+    ⟨7403, 2594216321969368078, .k4 0 [0, 2, 3, 7, 5, 1] 0 1 2 3⟩,
+  ],
+  [
+    ⟨748, 6052838741004779520, .k4 2 [2, 4, 7] 2 4 6 7⟩,
+    ⟨1260, 10216663658528768, .k4 2 [2, 5, 3, 6] 2 3 5 6⟩,
+    ⟨2284, 5233182770796193792, .k4 1 [1, 3, 7, 6] 1 3 5 6⟩,
+    ⟨4332, 5234321864278933504, .k4 2 [2, 5, 6, 7, 3] 2 3 5 6⟩,
+    ⟨8684, 3458908004383534110, .k4 0 [0, 2, 4, 7, 5, 1] 0 1 2 3⟩,
+    ⟨9964, 4800916368251912462, .k4 0 [0, 1, 2, 7, 6, 5, 3] 0 1 2 3⟩
+  ],
+  [
+    ⟨749, 6052838741012119552, .k4 2 [2, 7, 4] 2 4 6 7⟩,
+    ⟨1773, 5629825956511772, .k4 0 [0, 2, 6, 4] 0 2 3 4⟩,
+    ⟨4333, 5235507137270016000, .k4 1 [1, 5, 6, 7, 3] 1 3 5 6⟩,
+    ⟨8685, 3458908004466830366, .k4 0 [0, 3, 4, 7, 5, 1] 0 1 2 3⟩
+  ],
+  [
+    ⟨238, 8070450532255268864, .sharedThree 2 7 4 5 6⟩,
+    ⟨494, 9854922719781120, .k4 1 [1, 5, 6] 0 1 5 6⟩,
+    ⟨750, 6089993437925343232, .k4 4 [4, 7, 6] 2 4 6 7⟩,
+    ⟨1774, 5629830251413532, .k4 0 [0, 4, 6, 2] 0 2 3 4⟩,
+    ⟨9966, 4800916381337944346, .k4 0 [0, 1, 4, 7, 6, 5, 3] 0 1 3 4⟩
+  ],
+  [
+    ⟨239, 8070450534126977024, .sharedThree 3 7 4 5 6⟩,
+    ⟨495, 9923092440703232, .k4 1 [1, 6, 5] 0 1 5 6⟩,
+    ⟨751, 6093370295845912576, .k4 2 [2, 7, 6] 2 4 6 7⟩,
+    ⟨1007, 1688850972298240, .k4 1 [1, 3, 6, 2] 1 2 3 6⟩,
+    ⟨1519, 23279007957020, .k4 0 [0, 3, 4, 5] 0 2 4 5⟩,
+    ⟨2287, 5233745720716060672, .k4 1 [1, 6, 7, 3] 1 3 5 6⟩,
+    ⟨4335, 5235522977109377024, .k4 3 [3, 7, 6, 5, 4] 3 4 5 6⟩,
+    ⟨4847, 149534145750028, .k4 0 [0, 2, 3, 1, 5] 1 2 5 7⟩,
+    ⟨6127, 74768420400140, .k4 0 [0, 2, 3, 1, 5] 1 3 5 6⟩
+  ]
+]
+
+/-- Generated exact-table entries for this hash-bucket group. -/
+def hardBuckets29 : Array (List HardEntry) := #[
+  [
+    ⟨744, 7689008565333484830, .residual 3362519384732035⟩,
+    ⟨1000, 6172702974236912670, .residual 739416805833664⟩,
+    ⟨1256, 4158101496566737950, .residual 1561370693492400⟩,
+    ⟨5608, 3285751302718152990, .residual 2182920559717970⟩
+  ],
+  [
+    ⟨745, 5446497559543768350, .residual 158131447544564⟩,
+    ⟨1001, 3871065734438415390, .residual 739418688551872⟩,
+    ⟨1257, 3140514888198220830, .residual 815713717961634⟩,
+    ⟨5609, 3858838753347559710, .residual 2605289118851666⟩
+  ],
+  [
+    ⟨746, 8263217235462677790, .residual 3362504352289155⟩,
+    ⟨1002, 5159386478491560990, .residual 174712139397489⟩,
+    ⟨1258, 3148677529412398110, .residual 3302014003546498⟩,
+    ⟨5610, 6428199515367072030, .residual 4161283991128770⟩
+  ],
+  [
+    ⟨747, 6020706229672961310, .residual 158116415101684⟩,
+    ⟨1003, 5168043070975994910, .residual 1140736403799778⟩,
+    ⟨1259, 4148742861646556190, .residual 2747106658840658⟩,
+    ⟨5611, 6141095039122202910, .residual 2912165811693381⟩
+  ],
+  [
+    ⟨748, 5446497533774357790, .residual 158131447544561⟩,
+    ⟨1004, 5445930199528074270, .residual 782651904673744⟩,
+    ⟨1260, 3718086147279252510, .residual 4240235966133447⟩,
+    ⟨5612, 6425956511646408990, .residual 2297906932433509⟩
+  ],
+  [
+    ⟨749, 8697231858341602590, .hubPentagon 0 [0, 1, 2, 3, 4, 5, 6, 7] 1 0 2 5 6 4⟩,
+    ⟨1005, 5159377661141806110, .residual 307643554354420⟩,
+    ⟨1261, 3141634191068851230, .residual 917676477322194⟩,
+    ⟨5613, 5564643082911801630, .residual 3105903200847554⟩
+  ],
+  [
+    ⟨750, 6455283802471752990, .residual 2471465258043600⟩,
+    ⟨1006, 5159377652585425950, .residual 307643554354417⟩,
+    ⟨1262, 3714160890768092190, .residual 2113500852842962⟩,
+    ⟨5614, 6137730533541208350, .residual 3528272008854210⟩
+  ],
+  [
+    ⟨751, 7680143312584008990, .residual 1166830687567330⟩,
+    ⟨1007, 5452051305548835870, .residual 2437683589634610⟩,
+    ⟨1263, 3139951938278353950, .residual 4350102050465036⟩,
+    ⟨5615, 3862196687628591390, .residual 1996449391768610⟩
+  ]
+]
+
+end Erdos97Octagon.RawIncidence
diff --git a/LeanPool/Erdos97ConvexOctagon/CoverageData30.lean b/LeanPool/Erdos97ConvexOctagon/CoverageData30.lean
new file mode 100644
index 00000000..edd0ea68
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/CoverageData30.lean
@@ -0,0 +1,133 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.CoverageDataTypes
+
+/-! # Coverage certificate data, buckets 240–247 -/
+
+namespace Erdos97Octagon.RawIncidence
+
+/-- Generated monotone-obstruction entries for this hash-bucket group. -/
+def patternBuckets30 : Array (List PatternEntry) := #[
+  [
+    ⟨240, 593166, .k4 0 [0, 1, 2] 0 1 2 3⟩,
+    ⟨752, 6341068588064964608, .k4 3 [3, 4, 7] 3 4 6 7⟩,
+    ⟨1776, 5910974516299030, .k4 0 [0, 1, 2, 6] 0 2 4 6⟩,
+    ⟨4080, 1441152447988432924, .k4 0 [0, 2, 3, 7, 4] 0 2 3 4⟩,
+    ⟨5104, 5066828754275358, .k4 0 [0, 2, 4, 6, 1] 0 1 2 3⟩
+  ],
+  [
+    ⟨241, 658702, .k4 0 [0, 1, 2] 0 1 2 3⟩,
+    ⟨753, 6341069103461040128, .k4 3 [3, 7, 4] 3 4 6 7⟩,
+    ⟨1009, 1688851001789440, .k4 1 [1, 2, 6, 3] 1 2 3 6⟩,
+    ⟨1521, 26539441782810, .k4 0 [0, 4, 5, 3] 0 1 3 4⟩,
+    ⟨1777, 5910974600577052, .k4 0 [0, 3, 2, 6] 0 2 4 6⟩,
+    ⟨5105, 5066828754340894, .k4 0 [0, 4, 6, 1, 2] 0 1 2 3⟩,
+    ⟨9969, 4800925326916157718, .k4 0 [0, 1, 2, 7, 6, 5, 4] 0 1 2 4⟩
+  ],
+  [
+    ⟨498, 10133099168031744, .k4 1 [1, 2, 6] 1 2 5 6⟩,
+    ⟨754, 6341069135673294848, .k4 3 [3, 4, 7] 3 4 6 7⟩,
+    ⟨2546, 9896175283214, .k4 0 [0, 2, 1, 3, 5] 0 1 3 5⟩,
+    ⟨4082, 1441152464967958556, .k4 0 [0, 3, 2, 7, 4] 0 2 3 4⟩,
+    ⟨8178, 9658251872914462, .k4 0 [0, 2, 4, 5, 6, 1] 0 1 2 3⟩
+  ],
+  [
+    ⟨243, 723982, .k4 0 [0, 2, 1] 0 1 2 3⟩,
+    ⟨755, 6341069137552343040, .k4 3 [3, 7, 4] 3 4 6 7⟩,
+    ⟨1779, 5911253683815702, .k4 0 [0, 1, 4, 6] 0 1 2 6⟩,
+    ⟨2291, 5237686817066582016, .k4 3 [3, 7, 6, 4] 3 4 5 6⟩,
+    ⟨3315, 9361242003170566, .k4 0 [0, 1, 2, 5, 6] 0 1 2 6⟩,
+    ⟨5107, 5066828837571614, .k4 0 [0, 3, 4, 6, 1] 0 1 2 3⟩,
+    ⟨9971, 4800925344146161946, .k4 0 [0, 1, 3, 7, 6, 5, 4] 0 1 3 4⟩
+  ],
+  [
+    ⟨756, 6379349731163766784, .k4 4 [4, 7, 6] 3 4 6 7⟩,
+    ⟨1268, 10225870458322944, .k4 2 [2, 5, 4, 6] 2 4 5 6⟩,
+    ⟨1524, 26569254895642, .k4 0 [0, 3, 5, 4] 0 1 3 4⟩,
+    ⟨2292, 5237783127144792064, .k4 3 [3, 7, 6, 5] 3 4 5 6⟩,
+    ⟨5108, 5066828854348830, .k4 0 [0, 4, 6, 1, 3] 0 1 2 3⟩,
+    ⟨8692, 3458913532291064846, .k4 0 [0, 3, 4, 7, 5, 1] 0 1 2 5⟩
+  ],
+  [
+    ⟨501, 10210064975553536, .k4 1 [1, 5, 6] 1 2 5 6⟩,
+    ⟨757, 6381600675473653760, .k4 3 [3, 7, 6] 3 4 6 7⟩,
+    ⟨1525, 26573533085722, .k4 0 [0, 4, 5, 3] 0 1 3 4⟩,
+    ⟨2293, 5271957047779262464, .k4 3 [3, 6, 7, 5] 0 5 6 7⟩,
+  ],
+  [
+    ⟨502, 10216663723016192, .k4 3 [3, 5, 6] 2 3 5 6⟩,
+    ⟨758, 6999087501654622208, .k4 5 [5, 6, 7] 0 5 6 7⟩,
+    ⟨2038, 41095909240520978, .k4 0 [0, 1, 4, 6] 1 4 6 7⟩,
+    ⟨2294, 5305672471796514816, .k4 3 [3, 5, 7, 6] 0 5 6 7⟩,
+    ⟨4342, 5802985736688893952, .k4 3 [3, 4, 5, 7, 6] 3 4 5 6⟩
+  ],
+  [
+    ⟨503, 10225887635046400, .k4 4 [4, 5, 6] 2 4 5 6⟩,
+    ⟨759, 7026109099418845184, .k4 5 [5, 7, 6] 0 5 6 7⟩,
+    ⟨1527, 26582156574748, .k4 0 [0, 4, 5, 3] 0 2 3 4⟩,
+    ⟨1783, 5911301213650972, .k4 0 [0, 3, 4, 6] 0 2 4 6⟩,
+    ⟨8439, 13583645823020062, .k4 0 [0, 2, 4, 6, 5, 1] 0 1 2 3⟩
+  ]
+]
+
+/-- Generated exact-table entries for this hash-bucket group. -/
+def hardBuckets30 : Array (List HardEntry) := #[
+  [
+    ⟨752, 4147201482135594270, .residual 1252425101647666⟩,
+    ⟨1008, 5163820946576993310, .residual 4346855055058437⟩,
+    ⟨1264, 6427634641840204830, .residual 2903612388423490⟩,
+    ⟨5616, 3718088070886252830, .residual 1379490129108002⟩
+  ],
+  [
+    ⟨753, 8230831648747971870, .residual 3746621203614352⟩,
+    ⟨1009, 2851861217024240670, .residual 1141835661672162⟩,
+    ⟨1265, 5996977927472901150, .residual 2316458848637029⟩,
+    ⟨5617, 8227330533664416030, .residual 1077587367712688⟩
+  ],
+  [
+    ⟨754, 8661485077465294110, .hubPentagon 0 [0, 1, 3, 4, 2, 5, 6, 7] 0 1 2 3 4 6⟩,
+    ⟨1010, 2860517809508674590, .residual 173612881525105⟩,
+    ⟨1266, 5420525971262499870, .residual 3607387453904194⟩,
+    ⟨5618, 6461703848537022750, .residual 4411539413806338⟩
+  ],
+  [
+    ⟨755, 3714723978626622750, .residual 712048544259025⟩,
+    ⟨1011, 3149304534265850910, .residual 782514723145680⟩,
+    ⟨1267, 5993052670961740830, .residual 4240459566044354⟩,
+    ⟨5619, 7825380016833880350, .residual 3918958175202562⟩
+  ],
+  [
+    ⟨756, 8694980340888986910, .hubPentagon 0 [0, 1, 2, 3, 4, 5, 6, 7] 1 0 2 5 6 3⟩,
+    ⟨1012, 2858265988438256670, .residual 307506372826356⟩,
+    ⟨1268, 5418843718472002590, .residual 4108415090800837⟩,
+    ⟨5364, 6168179608612757790, .residual 943464467575728⟩,
+    ⟨5620, 5600379407741149470, .residual 278422507013616⟩
+  ],
+  [
+    ⟨757, 6453032276462757150, .residual 1978884048742608⟩,
+    ⟨1013, 3140075083573324830, .residual 2446477549853234⟩,
+    ⟨1269, 2851721579306511390, .residual 1986420816143010⟩,
+    ⟨5365, 6455283811053461790, .residual 943466375984048⟩,
+    ⟨5621, 8686682433507221790, .residual 269643505780208⟩
+  ],
+  [
+    ⟨758, 6020706229438997790, .residual 158116415101681⟩,
+    ⟨1014, 2851844724601482270, .residual 4408427709883909⟩,
+    ⟨1270, 6032720999124986910, .residual 1489957486108339⟩,
+    ⟨5366, 6173477856109912350, .residual 4411674705290498⟩,
+    ⟨5622, 3867071920391512350, .residual 1006138292344752⟩
+  ],
+  [
+    ⟨759, 8254352418954896670, .residual 1158036741799394⟩,
+    ⟨1015, 2858265979881876510, .residual 307506372826353⟩,
+    ⟨1271, 3713174639592238110, .residual 1560309065096883⟩,
+    ⟨5367, 7824258500651639070, .residual 3919093466686722⟩,
+    ⟨5623, 4155289076868768030, .residual 3361797830289928⟩
+  ]
+]
+
+end Erdos97Octagon.RawIncidence
diff --git a/LeanPool/Erdos97ConvexOctagon/CoverageData31.lean b/LeanPool/Erdos97ConvexOctagon/CoverageData31.lean
new file mode 100644
index 00000000..0aa7caae
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/CoverageData31.lean
@@ -0,0 +1,147 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.CoverageDataTypes
+
+/-! # Coverage certificate data, buckets 248–255 -/
+
+namespace Erdos97Octagon.RawIncidence
+
+/-- Generated monotone-obstruction entries for this hash-bucket group. -/
+def patternBuckets31 : Array (List PatternEntry) := #[
+  [
+    ⟨248, 51052558, .k4 0 [0, 2, 3] 0 1 2 3⟩,
+    ⟨760, 7034975561185230848, .k4 5 [5, 6, 7] 0 5 6 7⟩,
+    ⟨4088, 1441171276841418772, .k4 0 [0, 2, 7, 4, 5] 0 2 4 5⟩,
+    ⟨4344, 5803170454122266648, .k4 0 [0, 3, 4, 7, 6] 0 3 4 6⟩
+  ],
+  [
+    ⟨249, 83889422, .k4 0 [0, 1, 3] 0 1 2 3⟩,
+    ⟨761, 7035045929929408512, .k4 5 [5, 7, 6] 0 5 6 7⟩,
+    ⟨1529, 27488347553820, .k4 0 [0, 2, 3, 5] 0 2 4 5⟩,
+    ⟨1785, 6755688579596314, .k4 0 [0, 4, 6, 3] 0 1 3 4⟩,
+    ⟨2297, 5372795191126130688, .k4 3 [3, 7, 6, 4] 1 3 4 7⟩
+  ],
+  [
+    ⟨250, 100666638, .k4 0 [0, 1, 3] 0 1 2 3⟩,
+    ⟨762, 7061716783484428288, .k4 1 [1, 5, 7] 1 5 6 7⟩,
+    ⟨1018, 1761417629950976, .k4 1 [1, 2, 5, 6] 1 2 5 6⟩,
+    ⟨1274, 10770815910028288, .k4 1 [1, 2, 6, 5] 1 2 5 6⟩,
+    ⟨1786, 6755692924895260, .k4 0 [0, 3, 6, 4] 0 2 3 4⟩,
+    ⟨2042, 41658850617655316, .k4 0 [0, 2, 4, 6] 2 4 6 7⟩,
+    ⟨2554, 9896211456262, .k4 0 [0, 1, 2, 3, 5] 0 1 2 5⟩,
+    ⟨2810, 26535130040602, .k4 0 [0, 1, 3, 5, 4] 0 1 3 4⟩,
+    ⟨3578, 10221481002951680, .k4 1 [1, 2, 6, 5, 4] 1 4 5 6⟩,
+    ⟨5882, 11008556016670, .k4 0 [0, 3, 4, 5, 1, 2] 0 1 2 4⟩,
+    ⟨7418, 2882446700193590286, .k4 0 [0, 2, 3, 7, 5, 1] 0 1 2 3⟩,
+    ⟨8442, 13583645906316318, .k4 0 [0, 3, 4, 6, 5, 1] 0 1 2 3⟩,
+    ⟨10746, 5809716641126755358, .k4 0 [0, 2, 4, 7, 6, 5, 1] 0 1 2 3⟩
+  ],
+  [
+    ⟨251, 101384206, .k4 0 [0, 2, 3] 0 1 2 3⟩,
+    ⟨763, 7071214364925157376, .k4 1 [1, 6, 7] 1 5 6 7⟩,
+    ⟨1019, 1761417634014208, .k4 1 [1, 5, 6, 2] 1 2 5 6⟩,
+    ⟨1531, 27488663699484, .k4 0 [0, 2, 3, 5] 0 3 4 5⟩,
+    ⟨2043, 41658867796475924, .k4 0 [0, 2, 4, 6] 2 4 6 7⟩,
+    ⟨5115, 5066875999895838, .k4 0 [0, 1, 6, 4, 2] 0 2 3 4⟩,
+    ⟨6907, 10696050746731786, .k4 0 [0, 1, 3, 2, 6] 1 3 5 6⟩
+  ],
+  [
+    ⟨252, 117441806, .k4 0 [0, 1, 3] 0 1 2 3⟩,
+    ⟨508, 10696049117258752, .k4 1 [1, 2, 6] 1 2 5 6⟩,
+    ⟨764, 7205834170598162432, .k4 2 [2, 5, 7] 2 5 6 7⟩,
+    ⟨1020, 1761417634128896, .k4 1 [1, 2, 5, 6] 1 2 5 6⟩,
+    ⟨1276, 11269995292026880, .k4 1 [1, 3, 5, 6] 1 3 5 6⟩,
+    ⟨1788, 6755718392709146, .k4 0 [0, 3, 6, 4] 0 1 3 4⟩,
+    ⟨2044, 41659125491367956, .k4 0 [0, 2, 4, 6] 2 4 6 7⟩,
+    ⟨6652, 6768896143654912, .k4 2 [2, 5, 3, 6, 4] 1 2 3 4⟩,
+    ⟨8188, 9658299117551902, .k4 0 [0, 1, 2, 6, 5, 4] 0 2 3 4⟩,
+    ⟨8700, 3458980572154717458, .k4 0 [0, 1, 4, 2, 7, 5] 1 2 5 6⟩
+  ],
+  [
+    ⟨253, 117443598, .k4 0 [0, 3, 1] 0 1 2 3⟩,
+    ⟨509, 10696049121321984, .k4 1 [1, 6, 2] 1 2 5 6⟩,
+    ⟨2045, 41659142670188564, .k4 0 [0, 2, 4, 6] 2 4 6 7⟩,
+    ⟨6653, 6768913122721792, .k4 2 [2, 5, 3, 6, 4] 1 2 3 4⟩,
+  ],
+  [
+    ⟨254, 117637134, .k4 0 [0, 2, 3] 0 1 2 3⟩,
+    ⟨510, 10696049121436672, .k4 1 [1, 2, 6] 1 2 5 6⟩,
+    ⟨766, 7494068948539801600, .k4 3 [3, 5, 7] 3 5 6 7⟩,
+    ⟨1022, 1763616653206528, .k4 1 [1, 2, 6, 5] 1 2 5 6⟩,
+    ⟨2046, 42784754017239064, .k4 0 [0, 3, 4, 6] 3 4 6 7⟩,
+    ⟨4094, 1445937797188878356, .k4 0 [0, 2, 7, 4, 6] 0 2 4 6⟩,
+  ],
+  [
+    ⟨255, 118095886, .k4 0 [0, 3, 2] 0 1 2 3⟩,
+    ⟨511, 10696049121452032, .k4 1 [1, 6, 2] 1 2 5 6⟩,
+    ⟨1279, 11269995828895744, .k4 1 [1, 5, 3, 6] 1 3 5 6⟩,
+    ⟨1791, 6755731294388252, .k4 0 [0, 4, 6, 3] 0 2 3 4⟩,
+    ⟨2047, 42784788108541976, .k4 0 [0, 3, 4, 6] 3 4 6 7⟩
+  ]
+]
+
+/-- Generated exact-table entries for this hash-bucket group. -/
+def hardBuckets31 : Array (List HardEntry) := #[
+  [
+    ⟨760, 4149444092129076510, .residual 1253507433520946⟩,
+    ⟨1016, 6459803068812979230, .residual 809648111079360⟩,
+    ⟨1272, 6166509996778613790, .residual 3916658220028288⟩,
+    ⟨5368, 5599269331305488670, .residual 4410712632558850⟩,
+    ⟨5624, 3290611142553166110, .residual 3361797830289929⟩
+  ],
+  [
+    ⟨761, 7654379448547042590, .residual 3746484032924304⟩,
+    ⟨1017, 4158165829014481950, .residual 809649993797568⟩,
+    ⟨1273, 6164258179986385950, .residual 2317466015335520⟩,
+    ⟨5369, 6453032276488085790, .residual 952245289309104⟩,
+    ⟨5625, 7794492519778279710, .residual 261950678876656⟩
+  ],
+  [
+    ⟨762, 3140515171461653790, .residual 711911373568977⟩,
+    ⟨1018, 5420581203999943710, .residual 3271614728478994⟩,
+    ⟨1274, 6163132297259412510, .residual 3581804281346598⟩,
+    ⟨5370, 8398467607022526750, .residual 3918131393955074⟩,
+    ⟨5626, 3294477184635429150, .residual 3301172189950210⟩
+  ],
+  [
+    ⟨763, 8659233020960728350, .hubPentagon 0 [0, 1, 3, 4, 2, 5, 6, 7] 0 1 2 4 3 6⟩,
+    ⟨1019, 3145018745552071710, .residual 3764195941392658⟩,
+    ⟨1275, 5420594007302630430, .residual 3794715475545351⟩,
+    ⟨5371, 5591718573949313310, .residual 952243380900784⟩,
+    ⟨5627, 4149308025956655390, .residual 3035328084166343⟩
+  ],
+  [
+    ⟨764, 7678023588938016030, .residual 4409615268393217⟩,
+    ⟨1020, 8190590077489474590, .residual 3300119923025414⟩,
+    ⟨1276, 3714161023375272990, .residual 2317466015335521⟩,
+    ⟨5372, 6164801900303212830, .residual 4408547969025545⟩,
+    ⟨5628, 3862203549711786270, .residual 2745870245105234⟩
+  ],
+  [
+    ⟨765, 5446484326750905630, .residual 113169553246065⟩,
+    ⟨1021, 8192689607827614750, .residual 1338878243561043⟩,
+    ⟨1277, 5420526103869680670, .residual 347261441049714⟩,
+    ⟨5373, 5590592947813474590, .residual 4408547969025544⟩,
+    ⟨5629, 4147065022235992350, .residual 1549726265671250⟩
+  ],
+  [
+    ⟨766, 3138398451255502110, .residual 596611038423010⟩,
+    ⟨1022, 8189173906731002910, .residual 307643554354419⟩,
+    ⟨1278, 3871005833376721950, .residual 3362504352289152⟩,
+    ⟨5374, 6173458492787646750, .residual 208057789389296⟩,
+    ⟨5630, 3285751593501384990, .residual 3302419878086796⟩
+  ],
+  [
+    ⟨767, 3138395165605520670, .residual 4410727664945285⟩,
+    ⟨1023, 8192832944308055070, .residual 3792701135939078⟩,
+    ⟨1279, 3870997020305157150, .residual 2317586278089824⟩,
+    ⟨5375, 6164801626499047710, .residual 3915966730421768⟩,
+    ⟨5631, 3284630091641053470, .residual 2042476604154450⟩
+  ]
+]
+
+end Erdos97Octagon.RawIncidence
diff --git a/LeanPool/Erdos97ConvexOctagon/CoverageDataTypes.lean b/LeanPool/Erdos97ConvexOctagon/CoverageDataTypes.lean
new file mode 100644
index 00000000..c740f967
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/CoverageDataTypes.lean
@@ -0,0 +1,51 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.Certificates
+
+/-! # Erdős 97 convex-octagon formalization: Coverage Data Types -/
+
+namespace Erdos97Octagon.RawIncidence
+
+/-- A monotone obstruction pattern paired with its checked witness. -/
+structure PatternEntry where
+  /-- Identifier of the source classifier record. -/
+  origin : ℕ
+  /-- Packed incidences required by this monotone obstruction. -/
+  mask : UInt64
+  /-- The obstruction witness attached to the mask. -/
+  certificate : PrefixCertificate
+
+/-- An exact complete table paired with its checked witness. -/
+structure HardEntry where
+  /-- Identifier of the source classifier record. -/
+  origin : ℕ
+  /-- Packed code for the complete incidence table. -/
+  code : UInt64
+  /-- The obstruction witness attached to the exact table. -/
+  certificate : Certificate
+
+/-- Validate a pattern witness against precisely its required incidences. -/
+def PatternEntry.validB (entry : PatternEntry) : Bool :=
+  entry.certificate.toCertificate.validB (packedIncidence entry.mask)
+
+/-- Validate an exact-table witness against its decoded incidence table. -/
+def HardEntry.validB (entry : HardEntry) : Bool :=
+  entry.certificate.validB (packedIncidence entry.code)
+
+/-- A successful pattern audit supplies its mathematical witness. -/
+theorem PatternEntry.valid_of_validB
+    {entry : PatternEntry} (hvalid : entry.validB = true) :
+    entry.certificate.toCertificate.Valid (packedIncidence entry.mask) :=
+  Certificate.valid_of_validB hvalid
+
+/-- A successful exact-table audit supplies its mathematical witness. -/
+theorem HardEntry.valid_of_validB
+    {entry : HardEntry} (hvalid : entry.validB = true) :
+    entry.certificate.Valid (packedIncidence entry.code) :=
+  Certificate.valid_of_validB hvalid
+
+end Erdos97Octagon.RawIncidence
diff --git a/LeanPool/Erdos97ConvexOctagon/CoverageFormula.lean b/LeanPool/Erdos97ConvexOctagon/CoverageFormula.lean
new file mode 100644
index 00000000..57ebf777
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/CoverageFormula.lean
@@ -0,0 +1,512 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.CoverageData
+import LeanPool.Erdos97ConvexOctagon.LRAT.Semantics
+
+/-!
+# Exhaustive coverage formula
+
+This module gives mathematical meaning to every clause identifier used by the
+checked LRAT certificates.  The formula describes normalized balanced
+four-out incidence tables, pair sparsity, and the audited geometric
+obstructions.
+-/
+
+namespace Erdos97Octagon
+
+open LRAT
+
+namespace RawIncidence
+
+/-- Decode an eight-bit row mask as a set of octagon vertices. -/
+def packedRow (mask : UInt64) : Finset Vertex :=
+  Finset.univ.filter fun target => bitSetB mask target.val
+
+@[simp] theorem mem_packedRow (mask : UInt64) (target : Vertex) :
+    target ∈ packedRow mask ↔ bitSetB mask target.val = true := by
+  simp [packedRow]
+
+/-- Five-, two-, and three-subsets in the lexicographic order used by the generator. -/
+def fiveSubsets : List (List Vertex) :=
+  ((List.finRange 8).sublistsLen 5).reverse
+
+/-- Vertex pairs in the lexicographic order used by the generator. -/
+def vertexPairs : List (List Vertex) :=
+  ((List.finRange 8).sublistsLen 2).reverse
+
+/-- Vertex triples in the lexicographic order used by the generator. -/
+def vertexTriples : List (List Vertex) :=
+  ((List.finRange 8).sublistsLen 3).reverse
+
+private def pairAt (index : ℕ) : Vertex × Vertex :=
+  match vertexPairs.getD index [] with
+  | [a, b] => (a, b)
+  | _ => (0, 0)
+
+/-- Semantic tags for clauses shared by every branch certificate. -/
+inductive BaseClauseTag where
+  | diagonal (vertex : Vertex)
+  | normalized (target : Vertex)
+  | rowAtMost (centre : Vertex) (subset : List Vertex)
+  | rowAtLeast (centre : Vertex) (subset : List Vertex)
+  | columnAtMost (target : Vertex) (centres : List Vertex)
+  | columnAtLeast (target : Vertex) (centres : List Vertex)
+  | pairSparse (a b : Vertex) (centres : List Vertex)
+  | pattern (origin : ℕ)
+  | hard (origin : ℕ)
+
+/-- A shared clause or one of the sixteen row-fixing clauses for a branch. -/
+inductive ClauseTag where
+  | base (tag : BaseClauseTag)
+  | branchOne (target : Vertex) (selected : Bool)
+  | branchTwo (target : Vertex) (selected : Bool)
+
+private def patternMask (origin : ℕ) : UInt64 :=
+  match patternEntry origin with
+  | some entry => entry.mask
+  | none => 0
+
+private def hardCode (origin : ℕ) : UInt64 :=
+  match hardEntry origin with
+  | some entry => entry.code
+  | none => 0
+
+private def unitClause (centre target : Vertex) (selected : Bool) : Clause :=
+  [if selected then .positive (varIndex centre target) else .negative (varIndex centre target)]
+
+/-- The literal list represented by a shared semantic clause tag. -/
+def BaseClauseTag.toClause : BaseClauseTag → Clause
+  | .diagonal vertex => [.negative (varIndex vertex vertex)]
+  | .normalized target => unitClause 0 target (bitSetB 30 target.val)
+  | .rowAtMost centre subset => subset.map fun target => .negative (varIndex centre target)
+  | .rowAtLeast centre subset => subset.map fun target => .positive (varIndex centre target)
+  | .columnAtMost target centres => centres.map fun centre => .negative (varIndex centre target)
+  | .columnAtLeast target centres => centres.map fun centre => .positive (varIndex centre target)
+  | .pairSparse a b centres => centres.flatMap fun centre =>
+      [.negative (varIndex centre a), .negative (varIndex centre b)]
+  | .pattern origin =>
+      ((List.range 64).filter fun index => bitSetB (patternMask origin) index).map .negative
+  | .hard origin => (List.range 64).map fun index =>
+      if bitSetB (hardCode origin) index then .negative index else .positive index
+
+/-- The literal list represented by any semantic clause tag. -/
+def ClauseTag.toClause : ClauseTag → Clause
+  | .base tag => tag.toClause
+  | .branchOne target selected => unitClause 1 target selected
+  | .branchTwo target selected => unitClause 2 target selected
+
+/-- Structural and lookup conditions needed for a shared tag to be meaningful. -/
+def BaseClauseTag.Valid : BaseClauseTag → Prop
+  | .rowAtMost _ subset | .rowAtLeast _ subset |
+      .columnAtMost _ subset | .columnAtLeast _ subset =>
+      subset.Nodup ∧ subset.length = 5
+  | .pairSparse a b centres => a ≠ b ∧ centres.Nodup ∧ centres.length = 3
+  | .pattern origin =>
+      match patternEntry origin with
+      | some entry => entry.validB = true
+      | none => False
+  | .hard origin =>
+      match hardEntry origin with
+      | some entry => entry.validB = true
+      | none => False
+  | _ => True
+
+/-- Structural and lookup conditions needed for any tag to be meaningful. -/
+def ClauseTag.Valid : ClauseTag → Prop
+  | .base tag => tag.Valid
+  | _ => True
+
+/-- The two branch-unit tags agree with the two rows fixed for this SAT branch. -/
+def ClauseTag.BranchValid (Q : OctagonIncidence) : ClauseTag → Prop
+  | .branchOne target selected => selected = true ↔ target ∈ Q.targets 1
+  | .branchTwo target selected => selected = true ↔ target ∈ Q.targets 2
+  | _ => True
+
+/-- Boolean checker for the structural validity of a semantic clause tag. -/
+def ClauseTag.validB : ClauseTag → Bool
+  | .base (.rowAtMost _ subset) | .base (.rowAtLeast _ subset) |
+      .base (.columnAtMost _ subset) | .base (.columnAtLeast _ subset) =>
+      decide (subset.Nodup ∧ subset.length = 5)
+  | .base (.pairSparse a b centres) =>
+      decide (a ≠ b ∧ centres.Nodup ∧ centres.length = 3)
+  | .base (.pattern origin) => match patternEntry origin with
+    | some entry => entry.validB
+    | none => false
+  | .base (.hard origin) => match hardEntry origin with
+    | some entry => entry.validB
+    | none => false
+  | _ => true
+
+theorem ClauseTag.valid_of_validB {tag : ClauseTag} (h : tag.validB = true) : tag.Valid :=
+  by
+    cases tag with
+    | base tag =>
+        cases tag <;> simp only [ClauseTag.validB, ClauseTag.Valid,
+          BaseClauseTag.Valid, decide_eq_true_eq] at h ⊢
+        all_goals try exact h
+        all_goals split <;> simp_all
+    | branchOne | branchTwo => trivial
+
+private def branchStart : ℕ := 20659
+private def branchEnd : ℕ := branchStart + 16
+
+/-- Decode a generator clause identifier. -/
+def tagOfRef (rowOne rowTwo : UInt64) (reference : ℕ) : ClauseTag :=
+  if reference < 8 then
+    .base (.diagonal (Fin.ofNat 8 reference))
+  else if reference < 16 then
+    .base (.normalized (Fin.ofNat 8 (reference - 8)))
+  else if reference < 912 then
+    let offset := reference - 16
+    let centre := Fin.ofNat 8 (offset / 112)
+    let subset := fiveSubsets.getD ((offset % 112) / 2) []
+    .base (if offset % 2 = 0 then .rowAtMost centre subset else .rowAtLeast centre subset)
+  else if reference < 1808 then
+    let offset := reference - 912
+    let target := Fin.ofNat 8 (offset / 112)
+    let centres := fiveSubsets.getD ((offset % 112) / 2) []
+    .base (if offset % 2 = 0 then .columnAtMost target centres else .columnAtLeast target centres)
+  else if reference < 3376 then
+    let offset := reference - 1808
+    let pair := pairAt (offset / 56)
+    .base (.pairSparse pair.1 pair.2 (vertexTriples.getD (offset % 56) []))
+  else if reference < 14419 then
+    .base (.pattern (reference - 3376))
+  else if reference < branchStart then
+    .base (.hard (reference - 14419))
+  else if reference < branchStart + 8 then
+    let target := Fin.ofNat 8 (reference - branchStart)
+    .branchOne target (bitSetB rowOne target.val)
+  else
+    let target := Fin.ofNat 8 (reference - branchStart - 8)
+    .branchTwo target (bitSetB rowTwo target.val)
+
+private theorem tagOfRef_branchValid
+    (Q : OctagonIncidence) {rowOne rowTwo : UInt64}
+    (hrowOne : Q.targets 1 = packedRow rowOne)
+    (hrowTwo : Q.targets 2 = packedRow rowTwo) (reference : ℕ) :
+    (tagOfRef rowOne rowTwo reference).BranchValid Q := by
+  unfold tagOfRef
+  split
+  · trivial
+  split
+  · trivial
+  split
+  · trivial
+  split
+  · trivial
+  split
+  · trivial
+  split
+  · trivial
+  split
+  · trivial
+  split
+  · dsimp only [ClauseTag.BranchValid]
+    rw [hrowOne, mem_packedRow]
+  · dsimp only [ClauseTag.BranchValid]
+    rw [hrowTwo, mem_packedRow]
+
+/-- A shared-clause reference has no branch-specific semantic condition. -/
+theorem tagOfRef_baseBranchValid
+    (Q : OctagonIncidence) {reference : ℕ} (hreference : reference < branchStart) :
+    (tagOfRef 0 0 reference).BranchValid Q := by
+  unfold tagOfRef
+  split <;> try trivial
+  split <;> try trivial
+  split <;> try trivial
+  split <;> try trivial
+  split <;> try trivial
+  split <;> try trivial
+
+/-- Check that a clause reference is in range and has an audited semantic payload. -/
+def coveredB (rowOne rowTwo : UInt64) (reference : ℕ) : Bool :=
+  decide (reference < branchEnd) && (tagOfRef rowOne rowTwo reference).validB
+
+/-- The formula encoded by a branch's ordered list of clause references. -/
+def coverageFormula (rowOne rowTwo : UInt64) (references : List ℕ) : Formula :=
+  references.map fun reference => (tagOfRef rowOne rowTwo reference).toClause
+
+private theorem satisfies_of_not_all_neg
+    (valuation : Valuation) (clause : Clause)
+    (h : ¬ List.Forall valuation.falsifies clause) :
+    valuation.satisfies clause := by
+  induction clause with
+  | nil => simp at h
+  | cons literal clause ih =>
+      intro hliteral
+      apply ih
+      intro hrest
+      apply h
+      simpa using And.intro hliteral hrest
+
+private theorem no_five_inside_card_four
+    {selected : Finset Vertex} (hcard : selected.card = 4)
+    {vertices : List Vertex} (hnodup : vertices.Nodup) (hlength : vertices.length = 5)
+    (hsubset : vertices.toFinset ⊆ selected) : False := by
+  have hfive : vertices.toFinset.card = 5 := by
+    rw [List.toFinset_card_of_nodup hnodup, hlength]
+  have hle := Finset.card_le_card hsubset
+  rw [hfive, hcard] at hle
+  omega
+
+private theorem no_card_four_avoids_five
+    {selected : Finset Vertex} (hcard : selected.card = 4)
+    {vertices : List Vertex} (hnodup : vertices.Nodup) (hlength : vertices.length = 5)
+    (havoid : ∀ vertex ∈ vertices, vertex ∉ selected) : False := by
+  have hfive : vertices.toFinset.card = 5 := by
+    rw [List.toFinset_card_of_nodup hnodup, hlength]
+  have hsubset : selected ⊆ Finset.univ \ vertices.toFinset := by
+    intro vertex hselected
+    simp only [Finset.mem_sdiff, Finset.mem_univ, true_and, List.mem_toFinset]
+    exact fun hvertex => havoid vertex hvertex hselected
+  have hcomplement : (Finset.univ \ vertices.toFinset).card = 3 := by
+    rw [Finset.card_sdiff_of_subset (Finset.subset_univ _), Finset.card_univ,
+      Fintype.card_fin, hfive]
+  have hle := Finset.card_le_card hsubset
+  rw [hcard, hcomplement] at hle
+  omega
+
+private def predecessors (Q : OctagonIncidence) (target : Vertex) : Finset Vertex :=
+  Finset.univ.filter fun centre => target ∈ Q.targets centre
+
+private theorem card_predecessors (Q : OctagonIncidence) (target : Vertex) :
+    (predecessors Q target).card = Q.indegree target := by
+  unfold predecessors OctagonIncidence.indegree
+  rw [Finset.sum_boole]
+  norm_num
+
+private def jointPredecessors
+    (Q : OctagonIncidence) (a b : Vertex) : Finset Vertex :=
+  Finset.univ.filter fun centre => a ∈ Q.targets centre ∧ b ∈ Q.targets centre
+
+private theorem card_jointPredecessors (Q : OctagonIncidence) (a b : Vertex) :
+    (jointPredecessors Q a b).card = Q.pairMultiplicity a b := by
+  unfold jointPredecessors OctagonIncidence.pairMultiplicity
+  rw [Finset.sum_boole]
+  norm_num
+
+private theorem unitClause_satisfied
+    (R : RawIncidence) (centre target : Vertex) (selected : Bool)
+    (hselected : selected = true ↔ target ∈ R centre) :
+    (valuation R).satisfies (unitClause centre target selected) := by
+  cases selected <;>
+    simpa [unitClause, LRAT.Valuation.satisfies, LRAT.Valuation.falsifies,
+      valuation_variable] using hselected
+
+private theorem standardTargets_bit (target : Vertex) :
+    bitSetB 30 target.val = true ↔ target ∈ standardTargets := by
+  fin_cases target <;> decide
+
+/-- Every audited semantic clause is satisfied by the corresponding geometric incidence table. -/
+theorem BaseClauseTag.satisfies
+    {p : Vertex → Plane} {Q : OctagonIncidence}
+    (hC : ConvexIndependent ℝ p) (hR : Realises p Q)
+    (hN : Q.Normalized) (hSparse : Q.PairSparse) (hBalanced : Q.Balanced)
+    (tag : BaseClauseTag) (hvalid : tag.Valid) :
+    (valuation Q.targets).satisfies tag.toClause := by
+  cases tag with
+  | diagonal vertex =>
+      simp only [BaseClauseTag.toClause, LRAT.Valuation.satisfies,
+        LRAT.Valuation.falsifies]
+      intro hselected
+      exact Q.centre_not_mem vertex ((valuation_variable _ _ _).mp hselected)
+  | normalized target =>
+      apply unitClause_satisfied
+      rw [hN]
+      exact standardTargets_bit target
+  | rowAtMost centre subset =>
+      simp only [BaseClauseTag.Valid] at hvalid
+      apply satisfies_of_not_all_neg
+      intro hall
+      rw [List.forall_iff_forall_mem] at hall
+      apply no_five_inside_card_four (Q.card_targets centre) hvalid.1 hvalid.2
+      intro target htarget
+      have htargetList : target ∈ subset := by simpa using htarget
+      apply (valuation_variable Q.targets centre target).mp
+      exact hall (.negative (varIndex centre target))
+        (List.mem_map.mpr ⟨target, htargetList, rfl⟩)
+  | rowAtLeast centre subset =>
+      simp only [BaseClauseTag.Valid] at hvalid
+      apply satisfies_of_not_all_neg
+      intro hall
+      rw [List.forall_iff_forall_mem] at hall
+      apply no_card_four_avoids_five (Q.card_targets centre) hvalid.1 hvalid.2
+      intro target htarget hselected
+      exact (hall (.positive (varIndex centre target))
+        (List.mem_map.mpr ⟨target, htarget, rfl⟩))
+        ((valuation_variable Q.targets centre target).mpr hselected)
+  | columnAtMost target centres =>
+      simp only [BaseClauseTag.Valid] at hvalid
+      apply satisfies_of_not_all_neg
+      intro hall
+      rw [List.forall_iff_forall_mem] at hall
+      have hcard : (predecessors Q target).card = 4 := by
+        rw [card_predecessors, hBalanced target]
+      apply no_five_inside_card_four hcard hvalid.1 hvalid.2
+      intro centre hcentre
+      have hcentreList : centre ∈ centres := by simpa using hcentre
+      rw [predecessors, Finset.mem_filter]
+      exact ⟨Finset.mem_univ _, (valuation_variable Q.targets centre target).mp
+        (hall (.negative (varIndex centre target))
+          (List.mem_map.mpr ⟨centre, hcentreList, rfl⟩))⟩
+  | columnAtLeast target centres =>
+      simp only [BaseClauseTag.Valid] at hvalid
+      apply satisfies_of_not_all_neg
+      intro hall
+      rw [List.forall_iff_forall_mem] at hall
+      have hcard : (predecessors Q target).card = 4 := by
+        rw [card_predecessors, hBalanced target]
+      apply no_card_four_avoids_five hcard hvalid.1 hvalid.2
+      intro centre hcentre hselected
+      have htarget : target ∈ Q.targets centre :=
+        (Finset.mem_filter.mp (show centre ∈ Finset.univ.filter
+          (fun centre => target ∈ Q.targets centre) from hselected)).2
+      exact (hall (.positive (varIndex centre target))
+        (List.mem_map.mpr ⟨centre, hcentre, rfl⟩))
+        ((valuation_variable Q.targets centre target).mpr htarget)
+  | pairSparse a b centres =>
+      simp only [BaseClauseTag.Valid] at hvalid
+      apply satisfies_of_not_all_neg
+      intro hall
+      rw [List.forall_iff_forall_mem] at hall
+      have hsubset : centres.toFinset ⊆ jointPredecessors Q a b := by
+        intro centre hcentre
+        have hcentreList : centre ∈ centres := by simpa using hcentre
+        rw [jointPredecessors, Finset.mem_filter]
+        refine ⟨Finset.mem_univ _, ?_, ?_⟩
+        · apply (valuation_variable Q.targets centre a).mp
+          apply hall (.negative (varIndex centre a))
+          change LRAT.Literal.negative (varIndex centre a) ∈ centres.flatMap (fun centre =>
+            [LRAT.Literal.negative (varIndex centre a),
+              LRAT.Literal.negative (varIndex centre b)])
+          rw [List.mem_flatMap]
+          exact ⟨centre, hcentreList, by simp⟩
+        · apply (valuation_variable Q.targets centre b).mp
+          apply hall (.negative (varIndex centre b))
+          change LRAT.Literal.negative (varIndex centre b) ∈ centres.flatMap (fun centre =>
+            [LRAT.Literal.negative (varIndex centre a),
+              LRAT.Literal.negative (varIndex centre b)])
+          rw [List.mem_flatMap]
+          exact ⟨centre, hcentreList, by simp⟩
+      have hthree : centres.toFinset.card = 3 := by
+        rw [List.toFinset_card_of_nodup hvalid.2.1, hvalid.2.2]
+      have hle := Finset.card_le_card hsubset
+      have hsparse : (jointPredecessors Q a b).card ≤ 2 := by
+        rw [card_jointPredecessors]
+        exact hSparse hvalid.1
+      rw [hthree] at hle
+      omega
+  | pattern origin =>
+      simp only [BaseClauseTag.Valid] at hvalid
+      cases hfind : patternEntry origin with
+      | none => simp [hfind] at hvalid
+      | some entry =>
+          have hentryValid : entry.certificate.toCertificate.Valid
+              (packedIncidence entry.mask) :=
+            PatternEntry.valid_of_validB (by simpa only [hfind] using hvalid)
+          have hmask : patternMask origin = entry.mask := by simp [patternMask, hfind]
+          apply satisfies_of_not_all_neg
+          intro hall
+          rw [List.forall_iff_forall_mem] at hall
+          have hextends : Extends (packedIncidence entry.mask) Q.targets := by
+            intro centre target hselected
+            apply (valuation_variable Q.targets centre target).mp
+            apply hall (.negative (varIndex centre target))
+            simp only [BaseClauseTag.toClause, hmask, List.mem_map]
+            refine ⟨varIndex centre target, ?_, rfl⟩
+            rw [List.mem_filter]
+            refine ⟨List.mem_range.mpr ?_, ?_⟩
+            · unfold varIndex
+              omega
+            · simpa [packedSelectsB] using
+                (mem_packedIncidence entry.mask centre target).mp hselected
+          exact Certificate.not_convex_realises entry.certificate.toCertificate
+            (entry.certificate.valid_mono hextends hentryValid) hC hR
+  | hard origin =>
+      simp only [BaseClauseTag.Valid] at hvalid
+      cases hfind : hardEntry origin with
+      | none => simp [hfind] at hvalid
+      | some entry =>
+          have hentryValid : entry.certificate.Valid (packedIncidence entry.code) :=
+            HardEntry.valid_of_validB (by simpa only [hfind] using hvalid)
+          have hcode : hardCode origin = entry.code := by simp [hardCode, hfind]
+          apply satisfies_of_not_all_neg
+          intro hall
+          rw [List.forall_iff_forall_mem] at hall
+          have htargets : Q.targets = packedIncidence entry.code := by
+            funext centre
+            ext target
+            rw [mem_packedIncidence]
+            unfold packedSelectsB
+            cases hbit : bitSetB entry.code (varIndex centre target) with
+            | false =>
+                simp only [Bool.false_eq_true, iff_false]
+                intro hselected
+                have hfalsified := hall (.positive (varIndex centre target)) (by
+                  simp only [BaseClauseTag.toClause, hcode, List.mem_map]
+                  refine ⟨varIndex centre target, List.mem_range.mpr ?_, ?_⟩
+                  · unfold varIndex
+                    omega
+                  · simp [hbit])
+                exact hfalsified ((valuation_variable Q.targets centre target).mpr hselected)
+            | true =>
+                constructor
+                · intro _
+                  trivial
+                · intro _
+                  apply (valuation_variable Q.targets centre target).mp
+                  apply hall (.negative (varIndex centre target))
+                  simp only [BaseClauseTag.toClause, hcode, List.mem_map]
+                  refine ⟨varIndex centre target, List.mem_range.mpr ?_, ?_⟩
+                  · unfold varIndex
+                    omega
+                  · simp [hbit]
+          have hcertificate : entry.certificate.Valid Q.targets := by
+            rw [htargets]
+            exact hentryValid
+          exact Certificate.not_convex_realises entry.certificate hcertificate hC hR
+
+/-- Every audited shared or branch clause is satisfied by the incidence table. -/
+theorem ClauseTag.satisfies
+    {p : Vertex → Plane} {Q : OctagonIncidence}
+    (hC : ConvexIndependent ℝ p) (hR : Realises p Q)
+    (hN : Q.Normalized) (hSparse : Q.PairSparse) (hBalanced : Q.Balanced)
+    (tag : ClauseTag) (hvalid : tag.Valid) (hbranch : tag.BranchValid Q) :
+    (valuation Q.targets).satisfies tag.toClause := by
+  cases tag with
+  | base baseTag =>
+      exact baseTag.satisfies hC hR hN hSparse hBalanced hvalid
+  | branchOne target selected =>
+      exact unitClause_satisfied Q.targets 1 target selected hbranch
+  | branchTwo target selected =>
+      exact unitClause_satisfied Q.targets 2 target selected hbranch
+
+/-- A covered reference list is satisfied by the corresponding incidence table. -/
+theorem coverageFormula_satisfied
+    {p : Vertex → Plane} {Q : OctagonIncidence}
+    (hC : ConvexIndependent ℝ p) (hR : Realises p Q)
+    (hN : Q.Normalized) (hSparse : Q.PairSparse) (hBalanced : Q.Balanced)
+    {rowOne rowTwo : UInt64}
+    (hrowOne : Q.targets 1 = packedRow rowOne)
+    (hrowTwo : Q.targets 2 = packedRow rowTwo)
+    (references : List ℕ)
+    (hcovered : references.all (coveredB rowOne rowTwo) = true) :
+    (valuation Q.targets).SatisfiesFormula (coverageFormula rowOne rowTwo references) := by
+  constructor
+  intro clause hclause
+  rw [coverageFormula, List.mem_map] at hclause
+  obtain ⟨reference, hreference, rfl⟩ := hclause
+  have hcoveredReference := (List.all_eq_true.mp hcovered) reference hreference
+  simp only [coveredB, Bool.and_eq_true] at hcoveredReference
+  exact (tagOfRef rowOne rowTwo reference).satisfies hC hR hN hSparse hBalanced
+    ((tagOfRef rowOne rowTwo reference).valid_of_validB hcoveredReference.2)
+    (tagOfRef_branchValid Q hrowOne hrowTwo reference)
+
+end RawIncidence
+
+end Erdos97Octagon
diff --git a/LeanPool/Erdos97ConvexOctagon/CycleStrip.lean b/LeanPool/Erdos97ConvexOctagon/CycleStrip.lean
new file mode 100644
index 00000000..ae50c246
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/CycleStrip.lean
@@ -0,0 +1,161 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.Gram
+
+/-! # Erdős 97 convex-octagon formalization: Cycle Strip -/
+
+namespace Erdos97Octagon
+
+open scoped InnerProductSpace
+
+private lemma cycle_strip_core
+    (u1 u2 u3 u4 u5 u6 : Plane) (s s3 s4 s5 : ℝ) (hs0 : 0 < s)
+    (n1 : ⟪u1, u1⟫_ℝ = s) (n2 : ⟪u2, u2⟫_ℝ = s) (n6 : ⟪u6, u6⟫_ℝ = s)
+    (ns3 : ⟪u3, u3⟫_ℝ = s3) (ns4 : ⟪u4, u4⟫_ℝ = s4)
+    (ns5 : ⟪u5, u5⟫_ℝ = s5)
+    (i12 : ⟪u1, u2⟫_ℝ = s / 2) (i21 : ⟪u2, u1⟫_ℝ = s / 2)
+    (i23 : ⟪u2, u3⟫_ℝ = s3 / 2) (i32 : ⟪u3, u2⟫_ℝ = s3 / 2)
+    (i13 : ⟪u1, u3⟫_ℝ = s3 / 2) (i31 : ⟪u3, u1⟫_ℝ = s3 / 2)
+    (i34 : ⟪u3, u4⟫_ℝ = (s3 + s4 - s) / 2)
+    (i43 : ⟪u4, u3⟫_ℝ = (s3 + s4 - s) / 2)
+    (i24 : ⟪u2, u4⟫_ℝ = s4 / 2) (i42 : ⟪u4, u2⟫_ℝ = s4 / 2)
+    (i45 : ⟪u4, u5⟫_ℝ = (s4 + s5 - s) / 2)
+    (i54 : ⟪u5, u4⟫_ℝ = (s4 + s5 - s) / 2)
+    (i35 : ⟪u3, u5⟫_ℝ = (s3 + s5 - s) / 2)
+    (i53 : ⟪u5, u3⟫_ℝ = (s3 + s5 - s) / 2)
+    (i56 : ⟪u5, u6⟫_ℝ = s5 / 2) (i65 : ⟪u6, u5⟫_ℝ = s5 / 2)
+    (i46 : ⟪u4, u6⟫_ℝ = s4 / 2) (i64 : ⟪u6, u4⟫_ℝ = s4 / 2) :
+    False := by
+  have hM1 := gram_det_eq_zero ![u1, u2, u3]
+  rw [gram3_expand] at hM1
+  simp only [n1, n2, ns3, i12, i21, i23, i32, i13, i31] at hM1
+  have hM2 := gram_det_eq_zero ![u2, u3, u4]
+  rw [gram3_expand] at hM2
+  simp only [n2, ns3, ns4, i23, i32, i34, i43, i24, i42] at hM2
+  have hM3 := gram_det_eq_zero ![u3, u4, u5]
+  rw [gram3_expand] at hM3
+  simp only [ns3, ns4, ns5, i34, i43, i45, i54, i35, i53] at hM3
+  have hM4 := gram_det_eq_zero ![u4, u5, u6]
+  rw [gram3_expand] at hM4
+  simp only [ns4, ns5, n6, i45, i54, i56, i65, i46, i64] at hM4
+  have h1s : s * (s3 * (s3 - 3 * s)) = 0 := by
+    nlinarith only [hM1]
+  have h1 : s3 * (s3 - 3 * s) = 0 :=
+    (mul_eq_zero.mp h1s).resolve_left (ne_of_gt hs0)
+  rcases mul_eq_zero.mp h1 with hc | hc
+  · rw [hc] at hM2 hM3
+    have h2s : s * ((s4 - s) ^ 2) = 0 := by
+      nlinarith only [hM2]
+    have hs4 : s4 = s := by
+      have hh := (mul_eq_zero.mp h2s).resolve_left (ne_of_gt hs0)
+      have hz := (pow_eq_zero_iff (n := 2) (by norm_num)).1 hh
+      linarith only [hz]
+    rw [hs4] at hM3 hM4
+    have h3s : s * ((s5 - s) ^ 2) = 0 := by
+      nlinarith only [hM3]
+    have hs5 : s5 = s := by
+      have hh := (mul_eq_zero.mp h3s).resolve_left (ne_of_gt hs0)
+      have hz := (pow_eq_zero_iff (n := 2) (by norm_num)).1 hh
+      linarith only [hz]
+    rw [hs5] at hM4
+    have hpos : (0 : ℝ) < s ^ 3 := by positivity
+    nlinarith only [hM4, hpos]
+  · have es3 : s3 = 3 * s := by linarith only [hc]
+    rw [es3] at hM2 hM3
+    have h2s : s * ((s4 - 4 * s) * (s4 - s)) = 0 := by
+      nlinarith only [hM2]
+    have h2 : (s4 - 4 * s) * (s4 - s) = 0 :=
+      (mul_eq_zero.mp h2s).resolve_left (ne_of_gt hs0)
+    rcases mul_eq_zero.mp h2 with hc2 | hc2
+    · have es4 : s4 = 4 * s := by linarith only [hc2]
+      rw [es4] at hM3 hM4
+      have h4s : s * ((s5 - 3 * s) ^ 2) = 0 := by
+        nlinarith only [hM4]
+      have hs5 : s5 = 3 * s := by
+        have hh := (mul_eq_zero.mp h4s).resolve_left (ne_of_gt hs0)
+        have hz := (pow_eq_zero_iff (n := 2) (by norm_num)).1 hh
+        linarith only [hz]
+      rw [hs5] at hM3
+      have hpos : (0 : ℝ) < s ^ 3 := by positivity
+      nlinarith only [hM3, hpos]
+    · have es4 : s4 = s := by linarith only [hc2]
+      rw [es4] at hM3 hM4
+      have h3s : s * ((s5 - s) * (s5 - 4 * s)) = 0 := by
+        nlinarith only [hM3]
+      have h3 : (s5 - s) * (s5 - 4 * s) = 0 :=
+        (mul_eq_zero.mp h3s).resolve_left (ne_of_gt hs0)
+      have h4s : s * (s5 * (s5 - 3 * s)) = 0 := by
+        nlinarith only [hM4]
+      have h4 : s5 * (s5 - 3 * s) = 0 :=
+        (mul_eq_zero.mp h4s).resolve_left (ne_of_gt hs0)
+      rcases mul_eq_zero.mp h3 with q | q <;>
+        rcases mul_eq_zero.mp h4 with r | r <;>
+        nlinarith only [q, r, hs0]
+
+/-- The twelve listed equal-length edges cannot form this planar cycle-square strip. -/
+theorem no_unit_cycle_square_strip
+    {o x1 x2 x3 x4 x5 x6 : Plane} {R : ℝ} (hR : 0 < R)
+    (e01 : dist o x1 = R) (e02 : dist o x2 = R) (e06 : dist o x6 = R)
+    (e12 : dist x1 x2 = R) (e13 : dist x1 x3 = R) (e23 : dist x2 x3 = R)
+    (e24 : dist x2 x4 = R) (e34 : dist x3 x4 = R) (e35 : dist x3 x5 = R)
+    (e45 : dist x4 x5 = R) (e46 : dist x4 x6 = R) (e56 : dist x5 x6 = R) :
+    False := by
+  set s : ℝ := R ^ 2 with hs
+  have hs0 : 0 < s := by positivity
+  have norm_sq : ∀ {x : Plane}, dist o x = R → ⟪x - o, x - o⟫_ℝ = s := by
+    intro x hx
+    rw [real_inner_self_eq_norm_sq, ← dist_eq_norm, dist_comm, hx, hs]
+  have inner_pol : ∀ {x y : Plane}, dist x y = R →
+      ⟪x - o, y - o⟫_ℝ =
+        (⟪x - o, x - o⟫_ℝ + ⟪y - o, y - o⟫_ℝ - s) / 2 := by
+    intro x y hxy
+    have hsub : (x - o) - (y - o) = x - y := by abel
+    have hxynorm : ‖(x - o) - (y - o)‖ = R := by
+      rw [hsub, ← dist_eq_norm, hxy]
+    have hpolar := norm_sub_sq_real (x - o) (y - o)
+    rw [hxynorm] at hpolar
+    simp only [real_inner_self_eq_norm_sq]
+    have hR2 : R ^ 2 = s := hs.symm
+    nlinarith only [hpolar, hR2]
+  set s3 : ℝ := ⟪x3 - o, x3 - o⟫_ℝ with hs3
+  set s4 : ℝ := ⟪x4 - o, x4 - o⟫_ℝ with hs4
+  set s5 : ℝ := ⟪x5 - o, x5 - o⟫_ℝ with hs5
+  refine cycle_strip_core (x1 - o) (x2 - o) (x3 - o) (x4 - o) (x5 - o) (x6 - o)
+    s s3 s4 s5 hs0 (norm_sq e01) (norm_sq e02) (norm_sq e06) rfl rfl rfl
+    ?_ ?_ ?_ ?_ ?_ ?_ ?_ ?_ ?_ ?_ ?_ ?_ ?_ ?_ ?_ ?_ ?_ ?_
+  · rw [inner_pol e12, norm_sq e01, norm_sq e02]
+    ring
+  · rw [real_inner_comm, inner_pol e12, norm_sq e01, norm_sq e02]
+    ring
+  · rw [inner_pol e23, norm_sq e02, ← hs3]
+    ring
+  · rw [real_inner_comm, inner_pol e23, norm_sq e02, ← hs3]
+    ring
+  · rw [inner_pol e13, norm_sq e01, ← hs3]
+    ring
+  · rw [real_inner_comm, inner_pol e13, norm_sq e01, ← hs3]
+    ring
+  · rw [inner_pol e34, ← hs3, ← hs4]
+  · rw [real_inner_comm, inner_pol e34, ← hs3, ← hs4]
+  · rw [inner_pol e24, norm_sq e02, ← hs4]
+    ring
+  · rw [real_inner_comm, inner_pol e24, norm_sq e02, ← hs4]
+    ring
+  · rw [inner_pol e45, ← hs4, ← hs5]
+  · rw [real_inner_comm, inner_pol e45, ← hs4, ← hs5]
+  · rw [inner_pol e35, ← hs3, ← hs5]
+  · rw [real_inner_comm, inner_pol e35, ← hs3, ← hs5]
+  · rw [inner_pol e56, norm_sq e06, ← hs5]
+    ring
+  · rw [real_inner_comm, inner_pol e56, norm_sq e06, ← hs5]
+    ring
+  · rw [inner_pol e46, norm_sq e06, ← hs4]
+    ring
+  · rw [real_inner_comm, inner_pol e46, norm_sq e06, ← hs4]
+    ring
+
+end Erdos97Octagon
diff --git a/LeanPool/Erdos97ConvexOctagon/EquidistantFour.lean b/LeanPool/Erdos97ConvexOctagon/EquidistantFour.lean
new file mode 100644
index 00000000..f267dc5a
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/EquidistantFour.lean
@@ -0,0 +1,102 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.Basic
+
+/-! # Erdős 97 convex-octagon formalization: Equidistant Four -/
+
+namespace Erdos97Octagon
+
+open scoped InnerProductSpace
+open Module
+
+/-- Three vectors with the regular-simplex Gram matrix are linearly independent. -/
+theorem linearIndependent_of_regular_gram
+    {E : Type*} [NormedAddCommGroup E] [InnerProductSpace ℝ E]
+    {u v w : E} {s : ℝ} (hs : 0 < s)
+    (huu : ⟪u, u⟫_ℝ = s) (hvv : ⟪v, v⟫_ℝ = s) (hww : ⟪w, w⟫_ℝ = s)
+    (huv : ⟪u, v⟫_ℝ = s / 2) (huw : ⟪u, w⟫_ℝ = s / 2)
+    (hvw : ⟪v, w⟫_ℝ = s / 2) :
+    LinearIndependent ℝ ![u, v, w] := by
+  rw [Fintype.linearIndependent_iff]
+  intro g hg
+  have hsum : g 0 • u + g 1 • v + g 2 • w = 0 := by
+    have h := hg
+    simp only [Fin.sum_univ_three, Matrix.cons_val_zero, Matrix.cons_val_one,
+      Matrix.head_cons, Matrix.cons_val_two, Matrix.tail_cons] at h
+    simpa [add_assoc] using h
+  have e1 : ⟪g 0 • u + g 1 • v + g 2 • w, u⟫_ℝ = 0 := by rw [hsum]; simp
+  have e2 : ⟪g 0 • u + g 1 • v + g 2 • w, v⟫_ℝ = 0 := by rw [hsum]; simp
+  have e3 : ⟪g 0 • u + g 1 • v + g 2 • w, w⟫_ℝ = 0 := by rw [hsum]; simp
+  simp only [inner_add_left, real_inner_smul_left] at e1 e2 e3
+  have cvu : ⟪v, u⟫_ℝ = s / 2 := by rw [real_inner_comm]; exact huv
+  have cwu : ⟪w, u⟫_ℝ = s / 2 := by rw [real_inner_comm]; exact huw
+  have cwv : ⟪w, v⟫_ℝ = s / 2 := by rw [real_inner_comm]; exact hvw
+  rw [huu, cvu, cwu] at e1
+  rw [huv, hvv, cwv] at e2
+  rw [huw, hvw, hww] at e3
+  have hg0 : g 0 = 0 := by nlinarith only [e1, e2, e3, hs]
+  have hg1 : g 1 = 0 := by nlinarith only [e1, e2, e3, hs]
+  have hg2 : g 2 = 0 := by nlinarith only [e1, e2, e3, hs]
+  intro i
+  fin_cases i <;> assumption
+
+/-- Four distinct planar points cannot have all six distances equal. -/
+theorem four_points_not_pairwise_equidistant
+    {a b c d : Plane} {r : ℝ}
+    (had : a ≠ d)
+    (dab : dist a b = r) (dac : dist a c = r) (dad : dist a d = r)
+    (dbc : dist b c = r) (dbd : dist b d = r) (dcd : dist c d = r) :
+    False := by
+  set u : Plane := a - d with hu
+  set v : Plane := b - d with hv
+  set w : Plane := c - d with hw
+  have hr0 : 0 < r := by
+    have h : (0 : ℝ) < dist a d := dist_pos.mpr had
+    rwa [dad] at h
+  set s : ℝ := r ^ 2 with hsdef
+  have hs : 0 < s := by positivity
+  have nu : ⟪u, u⟫_ℝ = s := by
+    rw [real_inner_self_eq_norm_sq, hu, ← dist_eq_norm, dad, hsdef]
+  have nv : ⟪v, v⟫_ℝ = s := by
+    rw [real_inner_self_eq_norm_sq, hv, ← dist_eq_norm, dbd, hsdef]
+  have nw : ⟪w, w⟫_ℝ = s := by
+    rw [real_inner_self_eq_norm_sq, hw, ← dist_eq_norm, dcd, hsdef]
+  have huv_norm : ‖u - v‖ = r := by
+    have h : u - v = a - b := by rw [hu, hv]; abel
+    rw [h, ← dist_eq_norm, dab]
+  have huw_norm : ‖u - w‖ = r := by
+    have h : u - w = a - c := by rw [hu, hw]; abel
+    rw [h, ← dist_eq_norm, dac]
+  have hvw_norm : ‖v - w‖ = r := by
+    have h : v - w = b - c := by rw [hv, hw]; abel
+    rw [h, ← dist_eq_norm, dbc]
+  have hnu : ‖u‖ ^ 2 = s := by rw [← real_inner_self_eq_norm_sq]; exact nu
+  have hnv : ‖v‖ ^ 2 = s := by rw [← real_inner_self_eq_norm_sq]; exact nv
+  have hnw : ‖w‖ ^ 2 = s := by rw [← real_inner_self_eq_norm_sq]; exact nw
+  have iuv : ⟪u, v⟫_ℝ = s / 2 := by
+    have h := norm_sub_sq_real u v
+    rw [huv_norm, hnu, hnv] at h
+    rw [hsdef]
+    linarith
+  have iuw : ⟪u, w⟫_ℝ = s / 2 := by
+    have h := norm_sub_sq_real u w
+    rw [huw_norm, hnu, hnw] at h
+    rw [hsdef]
+    linarith
+  have ivw : ⟪v, w⟫_ℝ = s / 2 := by
+    have h := norm_sub_sq_real v w
+    rw [hvw_norm, hnv, hnw] at h
+    rw [hsdef]
+    linarith
+  have hli : LinearIndependent ℝ ![u, v, w] :=
+    linearIndependent_of_regular_gram hs nu nv nw iuv iuw ivw
+  have hcard := hli.fintype_card_le_finrank
+  have hfr : finrank ℝ Plane = 2 := by simp [Plane]
+  rw [hfr, Fintype.card_fin] at hcard
+  omega
+
+end Erdos97Octagon
diff --git a/LeanPool/Erdos97ConvexOctagon/FiniteModel.lean b/LeanPool/Erdos97ConvexOctagon/FiniteModel.lean
new file mode 100644
index 00000000..c2a166d6
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/FiniteModel.lean
@@ -0,0 +1,107 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.Relabelling
+import LeanPool.Erdos97ConvexOctagon.LRAT.Semantics
+import Mathlib.Data.List.Sort
+
+/-! # Erdős 97 convex-octagon formalization: Finite Model -/
+
+namespace Erdos97Octagon
+
+/-- An unbundled eight-row incidence table used by the finite certificate. -/
+abbrev RawIncidence := Vertex → Finset Vertex
+
+namespace RawIncidence
+
+/-- A four-entry row used by the finite certificate. -/
+abbrev SearchRow := Finset Vertex
+
+/-- All four-element rows available at a specified centre. -/
+def rowOptions (v : Vertex) : List SearchRow :=
+  (((List.finRange 8).filter (· ≠ v)).sublistsLen 4).map List.toFinset
+
+/-- Every row of an octagon incidence system occurs in the finite row list. -/
+theorem target_row_mem_rowOptions (Q : OctagonIncidence) (v : Vertex) :
+    Q.targets v ∈ rowOptions v := by
+  let row := (Q.targets v).sort (· ≤ ·)
+  have hnodup : row.Nodup := Finset.sort_nodup _ _
+  have hsubset : row ⊆ (List.finRange 8).filter (· ≠ v) := by
+    intro x hx
+    rw [List.mem_filter]
+    have hxQ : x ∈ Q.targets v := by
+      simpa [row] using hx
+    exact ⟨List.mem_finRange x,
+      decide_eq_true (fun h => Q.centre_not_mem v (h ▸ hxQ))⟩
+  have hsubperm : row.Subperm ((List.finRange 8).filter (· ≠ v)) :=
+    hnodup.subperm hsubset
+  have hsortedRow : row.SortedLE :=
+    (Finset.pairwise_sort (Q.targets v) (· ≤ ·)).sortedLE
+  have hsortedAll : ((List.finRange 8).filter (· ≠ v)).SortedLE :=
+    ((List.sortedLT_finRange 8).sortedLE.pairwise.filter _).sortedLE
+  have hsublist : row.Sublist ((List.finRange 8).filter (· ≠ v)) :=
+    List.sublist_of_subperm_of_sortedLE hsubperm hsortedRow hsortedAll
+  have hlength : row.length = 4 := by
+    rw [← List.toFinset_card_of_nodup hnodup, Finset.sort_toFinset, Q.card_targets]
+  rw [rowOptions, List.mem_map]
+  exact ⟨row, List.mem_sublistsLen.mpr ⟨hsublist, hlength⟩,
+    Finset.sort_toFinset _ _⟩
+
+/-- The zero-based SAT variable representing one directed incidence. -/
+def varIndex (centre target : Vertex) : ℕ :=
+  8 * centre.val + target.val
+
+/-- A proposition-valued SAT assignment obtained from an incidence table. -/
+def valuation (R : RawIncidence) : LRAT.Valuation := fun index =>
+  ∃ centre target : Vertex,
+    index = varIndex centre target ∧ target ∈ R centre
+
+/-- Reading the SAT assignment at an incidence variable recovers membership. -/
+theorem valuation_variable (R : RawIncidence) (centre target : Vertex) :
+    valuation R (varIndex centre target) ↔ target ∈ R centre := by
+  constructor
+  · rintro ⟨centre', target', hindex, hmem⟩
+    have hcentreVal : centre'.val = centre.val := by
+      unfold varIndex at hindex
+      omega
+    have htargetVal : target'.val = target.val := by
+      unfold varIndex at hindex
+      omega
+    have hcentre : centre' = centre := Fin.ext hcentreVal
+    have htarget : target' = target := Fin.ext htargetVal
+    simpa [hcentre, htarget] using hmem
+  · intro hmem
+    exact ⟨centre, target, rfl, hmem⟩
+
+/-- Test one bit of a packed 64-bit incidence table. -/
+def bitSetB (code : UInt64) (index : ℕ) : Bool :=
+  ((code >>> UInt64.ofNat index) &&& 1) != 0
+
+/-- Read one directed incidence from a packed table. -/
+def packedSelectsB (code : UInt64) (centre target : Vertex) : Bool :=
+  bitSetB code (varIndex centre target)
+
+/-- Decode a packed table to the mathematical finite-set model. -/
+def packedIncidence (code : UInt64) : RawIncidence := fun centre =>
+  Finset.univ.filter fun target => packedSelectsB code centre target
+
+@[simp] theorem mem_packedIncidence (code : UInt64) (centre target : Vertex) :
+    target ∈ packedIncidence code centre ↔ packedSelectsB code centre target = true := by
+  simp [packedIncidence]
+
+/-- Pack one finite row into its eight-bit position. -/
+def rowMask (row : SearchRow) : UInt64 :=
+  (List.finRange 8).foldl (fun mask target =>
+    if target ∈ row then mask ||| (1 <<< UInt64.ofNat target.val) else mask) 0
+
+/-- Pack all eight rows into one 64-bit key. -/
+def systemCode (R : RawIncidence) : UInt64 :=
+  (List.finRange 8).foldl (fun packed centre =>
+    packed ||| (rowMask (R centre) <<< UInt64.ofNat (8 * centre.val))) 0
+
+end RawIncidence
+
+end Erdos97Octagon
diff --git a/LeanPool/Erdos97ConvexOctagon/GeometryReduction.lean b/LeanPool/Erdos97ConvexOctagon/GeometryReduction.lean
new file mode 100644
index 00000000..fde67bb6
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/GeometryReduction.lean
@@ -0,0 +1,164 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.Basic
+import LeanPool.Erdos97ConvexOctagon.Incidence
+import Mathlib.Analysis.Convex.Between
+import Mathlib.Analysis.Convex.Independent
+import Mathlib.Geometry.Euclidean.PerpBisector
+
+/-! # Erdős 97 convex-octagon formalization: Geometry Reduction -/
+
+namespace Erdos97Octagon
+
+open scoped RealInnerProductSpace
+
+/-- A vertex has four other labelled vertices at one common distance. -/
+def HasFourEquidistant (p : Vertex → Plane) (v : Vertex) : Prop :=
+  ∃ S : Finset Vertex, S.card = 4 ∧ v ∉ S ∧
+    ∃ r : ℝ, ∀ w ∈ S, dist (p v) (p w) = r
+
+/-- A labelled incidence system is realised by equal-distance rows in the plane. -/
+def Realises (p : Vertex → Plane) (Q : OctagonIncidence) : Prop :=
+  ∀ v, ∃ r : ℝ, ∀ w ∈ Q.targets v, dist (p v) (p w) = r
+
+private lemma three_centres_collinear
+    {a b v₁ v₂ v₃ : Plane} (hab : a ≠ b)
+    (h1 : dist v₁ a = dist v₁ b)
+    (h2 : dist v₂ a = dist v₂ b)
+    (h3 : dist v₃ a = dist v₃ b) :
+    Collinear ℝ ({v₁, v₂, v₃} : Set Plane) := by
+  have hne : b -ᵥ a ≠ 0 := fun h => hab (vsub_eq_zero_iff_eq.mp h).symm
+  have h1' : dist a v₁ = dist b v₁ := by
+    rw [dist_comm a, dist_comm b]
+    exact h1
+  have h2' : dist a v₂ = dist b v₂ := by
+    rw [dist_comm a, dist_comm b]
+    exact h2
+  have h3' : dist a v₃ = dist b v₃ := by
+    rw [dist_comm a, dist_comm b]
+    exact h3
+  have hinn₁₂ : ⟪v₂ -ᵥ v₁, b -ᵥ a⟫ = (0 : ℝ) :=
+    EuclideanGeometry.inner_vsub_vsub_of_dist_eq_of_dist_eq h1' h2'
+  have hinn₁₃ : ⟪v₃ -ᵥ v₁, b -ᵥ a⟫ = (0 : ℝ) :=
+    EuclideanGeometry.inner_vsub_vsub_of_dist_eq_of_dist_eq h1' h3'
+  have hfd : Module.finrank ℝ Plane = 1 + 1 := by
+    rw [finrank_euclideanSpace]
+    norm_num
+  letI : Fact (Module.finrank ℝ Plane = 1 + 1) := ⟨hfd⟩
+  have hfo : Module.finrank ℝ ((ℝ ∙ (b -ᵥ a) : Submodule ℝ Plane))ᗮ = 1 :=
+    Submodule.finrank_orthogonal_span_singleton hne
+  have horth : vectorSpan ℝ ({v₁, v₂, v₃} : Set Plane) ≤
+      (ℝ ∙ (b -ᵥ a) : Submodule ℝ Plane)ᗮ := by
+    rw [vectorSpan_eq_span_vsub_set_right_ne ℝ (Set.mem_insert v₁ _)]
+    rw [Submodule.span_le]
+    intro w hw
+    rw [Set.mem_image] at hw
+    obtain ⟨q, hq, rfl⟩ := hw
+    have hq_ne : q ≠ v₁ := fun h => hq.2 (by simpa using h)
+    have hq_cases : q = v₂ ∨ q = v₃ := by
+      rcases hq.1 with hq | hq
+      · exact absurd hq hq_ne
+      rcases hq with hq | hq
+      · exact Or.inl hq
+      · simpa using Or.inr hq
+    rw [SetLike.mem_coe, Submodule.mem_orthogonal_singleton_iff_inner_left]
+    rcases hq_cases with rfl | rfl
+    · exact hinn₁₂
+    · exact hinn₁₃
+  letI : FiniteDimensional ℝ (vectorSpan ℝ ({v₁, v₂, v₃} : Set Plane)) :=
+    Submodule.finiteDimensional_of_le horth
+  rw [collinear_iff_finrank_le_one]
+  calc
+    Module.finrank ℝ (vectorSpan ℝ ({v₁, v₂, v₃} : Set Plane)) ≤
+        Module.finrank ℝ ((ℝ ∙ (b -ᵥ a) : Submodule ℝ Plane))ᗮ :=
+      Submodule.finrank_mono horth
+    _ = 1 := hfo
+
+/-- Three distinct members of a convex-independent family cannot be collinear. -/
+theorem three_collinear_not_convexIndependent
+    {p : Vertex → Plane} (hC : ConvexIndependent ℝ p)
+    {i j k : Vertex} (hij : i ≠ j) (hik : i ≠ k) (hjk : j ≠ k)
+    (hCol : Collinear ℝ ({p i, p j, p k} : Set Plane)) :
+    False := by
+  rcases hCol.wbtw_or_wbtw_or_wbtw with hW | hW | hW
+  · have hj : j ∈ ({i, k} : Set Vertex) := hC {i, k} j (by
+      simpa only [Set.image_insert_eq, Set.image_singleton, convexHull_pair] using hW.mem_segment)
+    simp [hij.symm, hjk] at hj
+  · have hk : k ∈ ({j, i} : Set Vertex) := hC {j, i} k (by
+      simpa only [Set.image_insert_eq, Set.image_singleton, convexHull_pair] using hW.mem_segment)
+    simp [hjk.symm, hik.symm] at hk
+  · have hi : i ∈ ({k, j} : Set Vertex) := hC {k, j} i (by
+      simpa only [Set.image_insert_eq, Set.image_singleton, convexHull_pair] using hW.mem_segment)
+    simp [hij, hik] at hi
+
+/-- At most two vertices of a convex-independent planar family are equidistant
+from any fixed pair of distinct vertices. -/
+theorem equidistantCentres_card_le_two
+    {p : Vertex → Plane} (hC : ConvexIndependent ℝ p)
+    {a b : Vertex} (hab : a ≠ b) :
+    (Finset.univ.filter fun v => dist (p v) (p a) = dist (p v) (p b)).card ≤ 2 := by
+  classical
+  by_contra hgt
+  let S := Finset.univ.filter fun v => dist (p v) (p a) = dist (p v) (p b)
+  change ¬ S.card ≤ 2 at hgt
+  have h3 : 3 ≤ S.card := by omega
+  obtain ⟨v₁, v₂, v₃, hv₁S, hv₂S, hv₃S, h12, h13, h23⟩ :
+      ∃ v₁ v₂ v₃ : Vertex, v₁ ∈ S ∧ v₂ ∈ S ∧ v₃ ∈ S ∧
+        v₁ ≠ v₂ ∧ v₁ ≠ v₃ ∧ v₂ ≠ v₃ := by
+    obtain ⟨T, hTS, hTcard⟩ := Finset.exists_subset_card_eq h3
+    rw [Finset.card_eq_three] at hTcard
+    obtain ⟨v₁, v₂, v₃, h12, h13, h23, rfl⟩ := hTcard
+    exact ⟨v₁, v₂, v₃, hTS (by simp), hTS (by simp), hTS (by simp), h12, h13, h23⟩
+  have e1 : dist (p v₁) (p a) = dist (p v₁) (p b) := (Finset.mem_filter.mp hv₁S).2
+  have e2 : dist (p v₂) (p a) = dist (p v₂) (p b) := (Finset.mem_filter.mp hv₂S).2
+  have e3 : dist (p v₃) (p a) = dist (p v₃) (p b) := (Finset.mem_filter.mp hv₃S).2
+  have hCol : Collinear ℝ ({p v₁, p v₂, p v₃} : Set Plane) :=
+    three_centres_collinear (hC.injective.ne hab) e1 e2 e3
+  exact three_collinear_not_convexIndependent hC h12 h13 h23 hCol
+
+/-- A realisation in convex position has pair multiplicity at most two. -/
+theorem pairSparse_of_realises
+    {p : Vertex → Plane} (hC : ConvexIndependent ℝ p)
+    (Q : OctagonIncidence) (hR : Realises p Q) :
+    Q.PairSparse := by
+  classical
+  intro a b hab
+  have hsubset :
+      (Finset.univ.filter fun v => a ∈ Q.targets v ∧ b ∈ Q.targets v) ⊆
+        Finset.univ.filter fun v => dist (p v) (p a) = dist (p v) (p b) := by
+    intro v hv
+    rw [Finset.mem_filter] at hv ⊢
+    obtain ⟨r, hr⟩ := hR v
+    exact ⟨Finset.mem_univ _, (hr a hv.2.1).trans (hr b hv.2.2).symm⟩
+  unfold OctagonIncidence.pairMultiplicity
+  rw [Finset.sum_boole]
+  norm_num
+  exact (Finset.card_le_card hsubset).trans (equidistantCentres_card_le_two hC hab)
+
+/-- Failure at every vertex canonically yields a four-target incidence system. -/
+theorem incidence_of_all_hasFour
+    {p : Vertex → Plane} (h : ∀ v, HasFourEquidistant p v) :
+    ∃ Q : OctagonIncidence, Realises p Q := by
+  classical
+  let Q : OctagonIncidence :=
+    { targets := fun v => (h v).choose
+      card_targets := fun v => (h v).choose_spec.1
+      centre_not_mem := fun v => (h v).choose_spec.2.1 }
+  refine ⟨Q, ?_⟩
+  intro v
+  exact (h v).choose_spec.2.2
+
+/-- Any failed convex octagon produces a balanced, pair-sparse incidence system. -/
+theorem reduction_of_all_hasFour
+    {p : Vertex → Plane} (hC : ConvexIndependent ℝ p)
+    (h : ∀ v, HasFourEquidistant p v) :
+    ∃ Q : OctagonIncidence, Realises p Q ∧ Q.PairSparse ∧ Q.Balanced := by
+  obtain ⟨Q, hR⟩ := incidence_of_all_hasFour h
+  have hS := pairSparse_of_realises hC Q hR
+  exact ⟨Q, hR, hS, Q.balanced_of_pairSparse hS⟩
+
+end Erdos97Octagon
diff --git a/LeanPool/Erdos97ConvexOctagon/Gram.lean b/LeanPool/Erdos97ConvexOctagon/Gram.lean
new file mode 100644
index 00000000..3cd2d14a
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/Gram.lean
@@ -0,0 +1,62 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.Basic
+import Mathlib.LinearAlgebra.Matrix.Determinant.Basic
+import Mathlib.LinearAlgebra.Matrix.ToLinearEquiv
+
+/-! # Erdős 97 convex-octagon formalization: Gram -/
+
+namespace Erdos97Octagon
+
+open scoped InnerProductSpace
+open Module Matrix
+
+/-- Three vectors in the Euclidean plane cannot be linearly independent. -/
+lemma not_linearIndependent_three (u : Fin 3 → Plane) :
+    ¬ LinearIndependent ℝ u := by
+  intro h
+  have hcard := h.fintype_card_le_finrank
+  have hfr : finrank ℝ Plane = 2 := by simp [Plane]
+  rw [hfr, Fintype.card_fin] at hcard
+  omega
+
+/-- The determinant of the Gram matrix of three planar vectors vanishes. -/
+lemma gram_det_eq_zero (u : Fin 3 → Plane) :
+    (Matrix.of fun i j => (⟪u i, u j⟫_ℝ : ℝ)).det = 0 := by
+  obtain ⟨g, hg, i0, hi0⟩ :=
+    (Fintype.not_linearIndependent_iff).1 (not_linearIndependent_three u)
+  set G : Matrix (Fin 3) (Fin 3) ℝ :=
+    Matrix.of fun i j => (⟪u i, u j⟫_ℝ : ℝ) with hG
+  have hker : G *ᵥ g = 0 := by
+    funext i
+    rw [Matrix.mulVec, Pi.zero_apply, dotProduct]
+    have hrew : (∑ j, G i j * g j) = ⟪u i, ∑ j, g j • u j⟫_ℝ := by
+      rw [inner_sum]
+      apply Finset.sum_congr rfl
+      intro j _
+      rw [hG, Matrix.of_apply, real_inner_smul_right]
+      ring
+    rw [hrew, hg, inner_zero_right]
+  have hgne : g ≠ 0 := by
+    intro h
+    exact hi0 (by rw [h]; rfl)
+  exact Matrix.exists_mulVec_eq_zero_iff.1 ⟨g, hgne, hker⟩
+
+/-- Expands a `3 × 3` Gram determinant into scalar inner products. -/
+lemma gram3_expand (a b c : Plane) :
+    (Matrix.of fun i j => (⟪(![a, b, c]) i, (![a, b, c]) j⟫_ℝ : ℝ)).det =
+      ⟪a, a⟫_ℝ * ⟪b, b⟫_ℝ * ⟪c, c⟫_ℝ -
+        ⟪a, a⟫_ℝ * ⟪b, c⟫_ℝ * ⟪c, b⟫_ℝ -
+        ⟪a, b⟫_ℝ * ⟪b, a⟫_ℝ * ⟪c, c⟫_ℝ +
+        ⟪a, b⟫_ℝ * ⟪b, c⟫_ℝ * ⟪c, a⟫_ℝ +
+        ⟪a, c⟫_ℝ * ⟪b, a⟫_ℝ * ⟪c, b⟫_ℝ -
+        ⟪a, c⟫_ℝ * ⟪b, b⟫_ℝ * ⟪c, a⟫_ℝ := by
+  rw [Matrix.det_fin_three]
+  simp only [Matrix.of_apply, Matrix.cons_val_zero, Matrix.cons_val_one,
+    Matrix.head_cons, Matrix.cons_val_two, Matrix.tail_cons, Fin.isValue]
+
+end Erdos97Octagon
diff --git a/LeanPool/Erdos97ConvexOctagon/Incidence.lean b/LeanPool/Erdos97ConvexOctagon/Incidence.lean
new file mode 100644
index 00000000..0238c835
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/Incidence.lean
@@ -0,0 +1,154 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import Mathlib.Algebra.BigOperators.Ring.Finset
+import Mathlib.Algebra.BigOperators.Group.Finset.Sigma
+import Mathlib.Algebra.Order.BigOperators.Group.Finset
+import Mathlib.Data.Finset.Card
+import Mathlib.Tactic.NormNum
+import Lean.Elab.Tactic.Omega
+
+/-! # Erdős 97 convex-octagon formalization: Incidence -/
+
+namespace Erdos97Octagon
+
+open scoped BigOperators
+
+/-- The labelled vertex set of an octagon. -/
+abbrev Vertex := Fin 8
+
+/-- Four selected equidistant witnesses around every labelled octagon vertex. -/
+structure OctagonIncidence where
+  /-- The four selected witnesses associated with a centre. -/
+  targets : Vertex → Finset Vertex
+  /-- Every witness row has exactly four vertices. -/
+  card_targets : ∀ v, (targets v).card = 4
+  /-- A centre is not one of its own positive-radius witnesses. -/
+  centre_not_mem : ∀ v, v ∉ targets v
+
+@[ext]
+theorem OctagonIncidence.ext {Q R : OctagonIncidence} (h : Q.targets = R.targets) : Q = R := by
+  cases Q
+  cases R
+  cases h
+  rfl
+
+namespace OctagonIncidence
+
+/-- The number of witness rows containing `a`. -/
+def indegree (Q : OctagonIncidence) (a : Vertex) : ℕ :=
+  ∑ v, if a ∈ Q.targets v then 1 else 0
+
+/-- The number of witness rows containing both `a` and `b`. -/
+def pairMultiplicity (Q : OctagonIncidence) (a b : Vertex) : ℕ :=
+  ∑ v, if a ∈ Q.targets v ∧ b ∈ Q.targets v then 1 else 0
+
+/-- No distinct pair occurs together in more than two witness rows. -/
+def PairSparse (Q : OctagonIncidence) : Prop :=
+  ∀ ⦃a b⦄, a ≠ b → Q.pairMultiplicity a b ≤ 2
+
+/-- Every vertex occurs in exactly four witness rows. -/
+def Balanced (Q : OctagonIncidence) : Prop :=
+  ∀ a, Q.indegree a = 4
+
+private lemma row_pair_sum (Q : OctagonIncidence) (a v : Vertex) :
+    (∑ b ∈ Finset.univ.erase a,
+        if a ∈ Q.targets v ∧ b ∈ Q.targets v then (1 : ℕ) else 0) =
+      if a ∈ Q.targets v then 3 else 0 := by
+  classical
+  by_cases ha : a ∈ Q.targets v
+  · have hfilter :
+        (Finset.univ.erase a).filter (fun b => b ∈ Q.targets v) =
+          (Q.targets v).erase a := by
+      ext b
+      simp [and_comm]
+    rw [if_pos ha]
+    simp only [ha, true_and, Finset.sum_boole, hfilter]
+    rw [Finset.card_erase_of_mem ha, Q.card_targets]
+    norm_num
+  · simp [ha]
+
+/-- Double-count pairs in the witness rows containing a fixed vertex. -/
+theorem sum_pairMultiplicity (Q : OctagonIncidence) (a : Vertex) :
+    (∑ b ∈ Finset.univ.erase a, Q.pairMultiplicity a b) =
+      3 * Q.indegree a := by
+  classical
+  simp only [pairMultiplicity, indegree]
+  rw [Finset.sum_comm]
+  simp_rw [row_pair_sum]
+  simp only [Finset.mul_sum]
+  apply Finset.sum_congr rfl
+  intro v _
+  by_cases ha : a ∈ Q.targets v <;> simp [ha]
+
+/-- Every vertex has indegree at most four when pair multiplicities are at most two. -/
+theorem indegree_le_four (Q : OctagonIncidence) (hQ : Q.PairSparse) (a : Vertex) :
+    Q.indegree a ≤ 4 := by
+  have hsum :
+      (∑ b ∈ Finset.univ.erase a, Q.pairMultiplicity a b) ≤
+        ∑ _b ∈ Finset.univ.erase a, 2 := by
+    exact Finset.sum_le_sum fun b hb => hQ (Finset.ne_of_mem_erase hb).symm
+  rw [Q.sum_pairMultiplicity] at hsum
+  norm_num at hsum
+  omega
+
+/-- There are exactly 32 selected incidences in an octagon witness system. -/
+theorem sum_indegree (Q : OctagonIncidence) :
+    ∑ a, Q.indegree a = 32 := by
+  classical
+  simp only [indegree]
+  rw [Finset.sum_comm]
+  calc
+    (∑ v : Vertex, ∑ a : Vertex, if a ∈ Q.targets v then 1 else 0) =
+        ∑ v : Vertex, (Q.targets v).card := by
+      apply Finset.sum_congr rfl
+      intro v _
+      rw [Finset.sum_boole]
+      norm_num
+    _ = ∑ _v : Vertex, 4 := by
+      apply Finset.sum_congr rfl
+      intro v _
+      exact Q.card_targets v
+    _ = 32 := by norm_num
+
+private lemma eq_of_bounded_sum
+    {α : Type*} [Fintype α]
+    (f : α → ℕ) (k : ℕ) (hle : ∀ a, f a ≤ k)
+    (hsum : ∑ a, f a = Fintype.card α * k) (a : α) :
+    f a = k := by
+  classical
+  have ha : a ∈ (Finset.univ : Finset α) := Finset.mem_univ a
+  have hrest :
+      (∑ x ∈ (Finset.univ.erase a), f x) ≤
+        (Finset.univ.erase a).card • k :=
+    Finset.sum_le_card_nsmul _ _ _ fun x _ => hle x
+  have hsplit := Finset.sum_erase_add Finset.univ f ha
+  have hcard := Finset.card_erase_add_one ha
+  simp only [Finset.card_univ, nsmul_eq_mul] at hrest hcard
+  have hmul :
+      Fintype.card α * k = (Finset.univ.erase a).card * k + k := by
+    rw [← hcard, Nat.add_mul]
+    simp
+  have htotal_le :
+      (∑ x, f x) ≤ (Finset.univ.erase a).card * k + f a := by
+    calc
+      (∑ x, f x) = (∑ x ∈ Finset.univ.erase a, f x) + f a := hsplit.symm
+      _ ≤ (Finset.univ.erase a).card * k + f a :=
+        Nat.add_le_add_right hrest (f a)
+  rw [hsum] at htotal_le
+  rw [hmul] at htotal_le
+  exact Nat.le_antisymm (hle a) (Nat.le_of_add_le_add_left htotal_le)
+
+/-- Pair sparsity forces the four-in/four-out balanced incidence condition. -/
+theorem balanced_of_pairSparse (Q : OctagonIncidence) (hQ : Q.PairSparse) :
+    Q.Balanced := by
+  intro a
+  apply eq_of_bounded_sum Q.indegree 4 (Q.indegree_le_four hQ)
+  simpa using Q.sum_indegree
+
+end OctagonIncidence
+
+end Erdos97Octagon
diff --git a/LeanPool/Erdos97ConvexOctagon/LRAT/Elab.lean b/LeanPool/Erdos97ConvexOctagon/LRAT/Elab.lean
new file mode 100644
index 00000000..e5f07b47
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/LRAT/Elab.lean
@@ -0,0 +1,477 @@
+/-
+Copyright (c) 2022 Mario Carneiro, 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Mario Carneiro, Egor Lyfar
+-/
+
+import Lean.Elab.Command
+import LeanPool.Erdos97ConvexOctagon.LRAT.Format
+import LeanPool.Erdos97ConvexOctagon.MasterFormula
+
+/-!
+# Safe elaboration of the packed master LRAT certificate
+
+Adapted from `Mathlib/Tactic/Sat/FromLRAT.lean` (Apache-2.0).  The
+reconstruction reads typed project data, reconstructs unit propagation, and
+stores every retained nonempty addition as a stable internal theorem so later
+modules cross an ordinary imported-constant boundary.
+-/
+
+namespace Erdos97Octagon.LRAT
+
+open Lean Elab Command
+open Std
+
+/-- Fuel for decoding one generated list of at most 500 string literals. -/
+def embeddedCertificatePartFuel : ℕ := 640
+
+/--
+Exact maximum number of compiled expression nodes traversed while decoding a
+committed generated certificate part.
+-/
+def embeddedCertificatePartMaximumExpressionSteps : ℕ := 616
+
+instance : ToExpr Literal where
+  toTypeExpr := mkConst ``Literal
+  toExpr
+    | .positive index => mkApp (mkConst ``Literal.positive) (mkRawNatLit index)
+    | .negative index => mkApp (mkConst ``Literal.negative) (mkRawNatLit index)
+
+/-- A proved clause in the elaborator database. -/
+private structure GlobalClause where
+  literals : Array Int
+  expression : Expr
+  proof : Expr
+
+private def buildClause (literals : Array Int) : Expr :=
+  let literalType := mkConst ``Literal
+  let empty := mkApp (mkConst ``List.nil [0]) literalType
+  let prepend := mkApp (mkConst ``List.cons [0]) literalType
+  literals.foldr
+    (fun literal clause =>
+      mkApp2 prepend (toExpr <| Literal.ofInt literal) clause)
+    empty
+
+private def buildProofStep
+    (database : HashMap ℕ GlobalClause) (newLiterals : Array Int)
+    (antecedents : Array ℕ) (context clause : Expr) :
+    Except String Expr := Id.run do
+  let mut finish :=
+    mkLambda `valuation default (mkConst ``Valuation) ∘
+    mkLambda `satisfies default
+      (mkApp2 (mkConst ``Valuation.SatisfiesFormula) (mkBVar 0) context)
+  let valuation depth := mkBVar (depth + 1)
+  let satisfies depth := mkBVar depth
+  let mut binderTypes := #[]
+  let mut remainingClause := clause
+  let mut depth := 0
+  let mut literalContext : HashMap Int ℕ := {}
+  for literal in newLiterals do
+    let literalExpression := remainingClause.appFn!.appArg!
+    remainingClause := remainingClause.appArg!
+    binderTypes := binderTypes.push
+      (mkApp2 (mkConst ``Valuation.falsifies)
+        (valuation depth) literalExpression)
+    depth := depth + 1
+    literalContext := literalContext.insert literal depth
+  finish := finish ∘ binderTypes.foldr (mkLambda `falsified default)
+  for identifier in antecedents do
+    let some referenced := database[identifier]?
+      | return .error s!"missing antecedent clause {identifier}"
+    let mut unitLiteral : Option Int := none
+    for literal in referenced.literals do
+      unless literalContext.contains literal do
+        if unitLiteral.isSome then
+          return .error s!"antecedent {identifier} is not unit"
+        depth := depth + 1
+        unitLiteral := some literal
+    let mut refutation :=
+      mkApp2 referenced.proof (valuation depth) (satisfies depth)
+    for literal in referenced.literals do
+      let binderIndex :=
+        match literalContext[literal]? with
+        | some binderDepth => depth - binderDepth
+        | none => 0
+      refutation := mkApp refutation (mkBVar binderIndex)
+    let some literal := unitLiteral
+      | return .ok <| finish refutation
+    let literalExpression := toExpr <| Literal.ofInt literal
+    let negatedExpression := toExpr <| Literal.ofInt (-literal)
+    let priorDepth := depth - 1
+    let propagation :=
+      mkApp3 (mkConst ``Valuation.propagateCases)
+        (valuation priorDepth) negatedExpression <|
+      mkLambda `falsified default
+        (mkApp2 (mkConst ``Valuation.falsifies)
+          (valuation priorDepth) literalExpression)
+        refutation
+    let domain :=
+      mkApp2 (mkConst ``Valuation.falsifies)
+        (valuation priorDepth) negatedExpression
+    finish := fun expression =>
+      finish <| mkApp propagation <| mkLambda `falsified default domain expression
+    literalContext := literalContext.insert (-literal) depth
+  return .error s!"antecedents do not refute clause {newLiterals}"
+
+private structure DecodedStringList where
+  strings : List String
+  expressionSteps : ℕ
+
+private def decodeStringListWithFuel :
+    ℕ → Expr → Except String DecodedStringList
+  | 0, _ => throw "embedded string list exceeds its structural bound"
+  | fuel + 1, .letE _ _ value body _ => do
+      let decoded ← decodeStringListWithFuel fuel (body.instantiate1 value)
+      pure {
+        strings := decoded.strings
+        expressionSteps := decoded.expressionSteps + 1
+      }
+  | fuel + 1, .mdata _ expression => do
+      let decoded ← decodeStringListWithFuel fuel expression
+      pure {
+        strings := decoded.strings
+        expressionSteps := decoded.expressionSteps + 1
+      }
+  | fuel + 1, expression =>
+      let function := expression.getAppFn
+      if function.isConstOf ``List.nil then
+        pure {
+          strings := []
+          expressionSteps := 1
+        }
+      else if function.isConstOf ``List.cons then
+        let arguments := expression.getAppArgs
+        if arguments.size ≠ 3 then
+          throw "malformed embedded string list"
+        else
+          match arguments[1]!, decodeStringListWithFuel fuel arguments[2]! with
+          | .lit (.strVal value), .ok remaining =>
+              pure {
+                strings := value :: remaining.strings
+                expressionSteps := remaining.expressionSteps + 1
+              }
+          | .lit (.strVal _), .error message => throw message
+          | _, _ => throw "embedded certificate part is not a literal string"
+      else
+        throw "embedded certificate data is not a string list"
+
+private def readEmbeddedParts
+    (declarationNames : List Name) : CommandElabM String := do
+  unless embeddedCertificatePartMaximumExpressionSteps ≤
+      embeddedCertificatePartFuel do
+    throwError "measured string-list expression bound exceeds decoder fuel"
+  let mut result := ""
+  let mut measuredMaximum := 0
+  for declarationName in declarationNames do
+    let information ← getConstInfo declarationName
+    let some value := information.value?
+      | throwError "embedded certificate part has no value"
+    let decoded ←
+      match decodeStringListWithFuel embeddedCertificatePartFuel value with
+      | .ok decoded => pure decoded
+      | .error message => throwError message
+    if embeddedCertificatePartMaximumExpressionSteps <
+        decoded.expressionSteps then
+      throwError
+        "embedded string-list expression exceeds its measured maximum"
+    measuredMaximum := max measuredMaximum decoded.expressionSteps
+    result := result ++ String.join decoded.strings
+  unless measuredMaximum =
+      embeddedCertificatePartMaximumExpressionSteps do
+    throwError
+      "embedded string-list expression maximum does not match its committed bound"
+  pure result
+
+private def literalInteger : Literal → Int
+  | .positive index => Int.ofNat (index + 1)
+  | .negative index => -Int.ofNat (index + 1)
+
+private def clauseLiterals (clause : Clause) : Array Int :=
+  clause.toArray.map literalInteger
+
+private def masterClauses : Array (Array Int) :=
+  RawIncidence.masterFormula.toArray.map clauseLiterals
+
+private def masterBaseReferences : Array ℕ :=
+  RawIncidence.masterReferences.toArray
+
+private def masterExcludedMasks : Array ℕ :=
+  RawIncidence.masterExcludedRowMasks.toArray
+
+private def certificateProofType (clause : Expr) : Expr :=
+  mkApp2 (mkConst ``Formula.Proves)
+    (mkConst ``RawIncidence.masterFormula) clause
+
+private def certificateClauseName (baseName : Name) (identifier : ℕ) : Name :=
+  Name.str baseName s!"_c{identifier}"
+
+private def certificateInitialClauseName (baseName : Name) (identifier : ℕ) : Name :=
+  Name.str baseName s!"_i{identifier}"
+
+private def requireTheoremWithType (name : Name) (expectedType : Expr) :
+    MetaM Unit := do
+  let information ← getConstInfo name
+  match information with
+  | .thmInfo _ => pure ()
+  | _ => throwError "imported certificate declaration is not a theorem: {name}"
+  unless information.type == expectedType do
+    throwError "imported certificate theorem has the wrong clause type: {name}"
+
+private def truthProof : Expr :=
+  mkApp2 (mkConst ``Eq.refl [1]) (mkConst ``Bool) (mkConst ``Bool.true)
+
+private def clauseReflexivity (clause : Expr) : Expr :=
+  mkApp2 (mkConst ``Eq.refl [1]) (mkConst ``Clause) clause
+
+private def checkedSourceProof (proof clause : Expr) : MetaM Expr := do
+  let inferredType ← Meta.inferType proof
+  unless inferredType == certificateProofType clause do
+    throwError "source-clause theorem did not infer the exact certificate clause type"
+  pure proof
+
+private def checkSourceMetadata
+    (clauses : Array (Array Int)) : Except String Unit := do
+  unless masterBaseReferences.size = 3224 do
+    throw "master reference count does not match its committed source metadata"
+  unless masterExcludedMasks.size = 39 do
+    throw "excluded-row count does not match its committed source metadata"
+  unless masterBaseReferences.size + masterExcludedMasks.size = clauses.size do
+    throw "source metadata does not partition the master formula"
+  let excludedRows := masterExcludedMasks.toList.map fun mask =>
+    RawIncidence.packedRow (UInt64.ofNat mask)
+  unless excludedRows == RawIncidence.excludedRows do
+    throw "excluded-row masks do not match the master formula order"
+
+private def additionIndices
+    (initialClauseCount : ℕ) (additions : Array Addition) :
+    Except String (HashMap ℕ ℕ) := do
+  let mut indices : HashMap ℕ ℕ := {}
+  let mut previous := initialClauseCount
+  for index in [0:additions.size] do
+    let some addition := additions[index]?
+      | throw "certificate addition index is out of range"
+    unless previous < addition.identifier do
+      throw "certificate addition identifiers are not strictly increasing"
+    if indices.contains addition.identifier then
+      throw "certificate contains a duplicate addition identifier"
+    indices := indices.insert addition.identifier index
+    previous := addition.identifier
+  pure indices
+
+private def neededStageClauses
+    (initialClauseCount start stop : ℕ) (additions : Array Addition)
+    (indices : HashMap ℕ ℕ) :
+    Except String (Array ℕ × Array ℕ) := do
+  let mut initialSeen : HashMap ℕ Unit := {}
+  let mut importedSeen : HashMap ℕ Unit := {}
+  let mut initialIdentifiers := #[]
+  let mut importedIdentifiers := #[]
+  for index in [start:stop] do
+    let some addition := additions[index]?
+      | throw "certificate addition index is out of range"
+    for antecedent in addition.antecedents do
+      if antecedent = 0 then
+        throw "certificate antecedent identifier cannot be zero"
+      else if antecedent ≤ initialClauseCount then
+        unless initialSeen.contains antecedent do
+          initialSeen := initialSeen.insert antecedent ()
+          initialIdentifiers := initialIdentifiers.push antecedent
+      else
+        let some antecedentIndex := indices[antecedent]?
+          | throw s!"certificate antecedent {antecedent} is not a retained addition"
+        unless antecedentIndex < index do
+          throw s!"certificate antecedent {antecedent} is not earlier than its use"
+        if antecedentIndex < start then
+          unless importedSeen.contains antecedent do
+            importedSeen := importedSeen.insert antecedent ()
+            importedIdentifiers := importedIdentifiers.push antecedent
+  pure (initialIdentifiers, importedIdentifiers)
+
+private def cacheInitialClauseProof
+    (clause proof : Expr) (clausePrefix : Name) (identifier : ℕ) :
+    MetaM Expr := do
+  let theoremName := certificateInitialClauseName clausePrefix identifier
+  let theoremType := certificateProofType clause
+  if (← getEnv).contains theoremName then
+    requireTheoremWithType theoremName theoremType
+  else
+    addDecl <| Declaration.thmDecl {
+      name := theoremName
+      levelParams := []
+      type := theoremType
+      value := ← checkedSourceProof proof clause
+    }
+  pure <| mkConst theoremName
+
+private def sourceInitialClause
+    (clauses : Array (Array Int)) (clausePrefix : Name) (identifier : ℕ) :
+    MetaM GlobalClause := do
+  if identifier = 0 ∨ clauses.size < identifier then
+    throwError "initial certificate clause identifier is out of range"
+  let index := identifier - 1
+  let some literals := clauses[index]?
+    | throwError "initial certificate clause index is out of range"
+  let clause := buildClause literals
+  if index < masterBaseReferences.size then
+    let some reference := masterBaseReferences[index]?
+      | throwError "master reference index is out of range"
+    let tag := RawIncidence.tagOfRef 0 0 reference
+    unless reference < 20659 ∧
+        RawIncidence.masterReferenceUsedB reference ∧ tag.validB do
+      throwError "master reference metadata is not valid and in range"
+    unless clauseLiterals tag.toClause == literals do
+      throwError "master reference clause does not match the certificate formula order"
+    let proof := mkAppN (mkConst ``RawIncidence.masterBaseClause_proves)
+      #[mkRawNatLit reference, truthProof, truthProof, truthProof, clause,
+        clauseReflexivity clause]
+    pure {
+      literals
+      expression := clause
+      proof := ← cacheInitialClauseProof clause proof clausePrefix identifier
+    }
+  else
+    let maskIndex := index - masterBaseReferences.size
+    let some mask := masterExcludedMasks[maskIndex]?
+      | throwError "excluded-row mask index is out of range"
+    let row := RawIncidence.packedRow (UInt64.ofNat mask)
+    unless mask < 256 ∧ RawIncidence.masterExcludedMaskUsedB mask ∧
+        decide (row ∉ RawIncidence.canonicalRows) do
+      throwError "excluded-row metadata is not noncanonical and in range"
+    unless clauseLiterals (RawIncidence.rowExclusionClause row) == literals do
+      throwError "excluded-row clause does not match the certificate formula order"
+    let proof := mkAppN (mkConst ``RawIncidence.canonicalRowClause_proves)
+      #[mkRawNatLit mask, truthProof, truthProof, truthProof, clause,
+        clauseReflexivity clause]
+    pure {
+      literals
+      expression := clause
+      proof := ← cacheInitialClauseProof clause proof clausePrefix identifier
+    }
+
+private def importedAdditionClause
+    (additions : Array Addition) (indices : HashMap ℕ ℕ)
+    (clausePrefix : Name) (identifier : ℕ) : MetaM GlobalClause := do
+  let some index := indices[identifier]?
+    | throwError "imported certificate identifier is not a retained addition"
+  let some addition := additions[index]?
+    | throwError "imported certificate addition index is out of range"
+  if addition.literals.isEmpty then
+    throwError "empty clause cannot be imported as an intermediate theorem"
+  let clause := buildClause addition.literals
+  let theoremName := certificateClauseName clausePrefix identifier
+  requireTheoremWithType theoremName (certificateProofType clause)
+  pure {
+    literals := addition.literals
+    expression := clause
+    proof := mkConst theoremName
+  }
+
+private def reconstructStage
+    (clauses : Array (Array Int)) (additions : Array Addition)
+    (start stop : ℕ) (clausePrefix finalTheorem : Name) : MetaM Unit := do
+  unless start < stop ∧ stop ≤ additions.size do
+    throwError "certificate stage range is invalid"
+  unless (certificateClauseName clausePrefix 0).isInternal do
+    throwError "certificate clause names must be stable internal declarations"
+  match checkSourceMetadata clauses with
+  | .ok () => pure ()
+  | .error message => throwError message
+  let indices ←
+    match additionIndices clauses.size additions with
+    | .ok indices => pure indices
+    | .error message => throwError message
+  let (initialIdentifiers, importedIdentifiers) ←
+    match neededStageClauses clauses.size start stop additions indices with
+    | .ok identifiers => pure identifiers
+    | .error message => throwError message
+  let mut database : HashMap ℕ GlobalClause := {}
+  for identifier in initialIdentifiers do
+    database := database.insert identifier
+      (← sourceInitialClause clauses clausePrefix identifier)
+  for identifier in importedIdentifiers do
+    database := database.insert identifier
+      (← importedAdditionClause additions indices clausePrefix identifier)
+  let context := mkConst ``RawIncidence.masterFormula
+  let mut derivedEmpty := false
+  for index in [start:stop] do
+    let some addition := additions[index]?
+      | throwError "certificate addition index is out of range"
+    let clause := buildClause addition.literals
+    let proof ←
+      match buildProofStep database addition.literals addition.antecedents
+          context clause with
+      | .ok proof => pure proof
+      | .error message => throwError message
+    if addition.literals.isEmpty then
+      unless index + 1 = additions.size ∧ stop = additions.size do
+        throwError "empty clause occurs before the final certificate addition"
+      addDecl <| Declaration.thmDecl {
+        name := finalTheorem
+        levelParams := []
+        type := certificateProofType clause
+        value := proof
+      }
+      addDocStringCore finalTheorem
+        "Unsatisfiability of the 3,263-clause master coverage formula."
+      derivedEmpty := true
+    else
+      let theoremName := certificateClauseName clausePrefix addition.identifier
+      addDecl <| Declaration.thmDecl {
+        name := theoremName
+        levelParams := []
+        type := certificateProofType clause
+        value := proof
+      }
+      database := database.insert addition.identifier {
+        literals := addition.literals
+        expression := clause
+        proof := mkConst theoremName
+      }
+  if stop = additions.size then
+    unless derivedEmpty do
+      throwError "final certificate stage does not derive the empty clause"
+  else if derivedEmpty then
+    throwError "nonfinal certificate stage derived the empty clause"
+
+/--
+Decode one contiguous range of the packed master certificate. Every nonempty
+addition becomes a stable theorem constant for the following stage.
+-/
+syntax "master_lrat_stage"
+  " initial_clauses " num " additions " num
+  " stage_start " num " stage_stop " num
+  " clause_prefix " ident " final_theorem " ident
+  " data_parts " ident* : command
+
+elab_rules : command
+  | `(master_lrat_stage
+        initial_clauses $initialCount:num additions $additionCount:num
+        stage_start $stageStartSyntax:num stage_stop $stageStopSyntax:num
+        clause_prefix $clausePrefixSyntax:ident
+        final_theorem $finalTheoremSyntax:ident
+        data_parts $parts:ident*) => do
+      let initialCount := initialCount.getNat
+      let additionCount := additionCount.getNat
+      let start := stageStartSyntax.getNat
+      let stop := stageStopSyntax.getNat
+      unless masterClauses.size = initialCount do
+        throwError "master formula clause count does not match certificate metadata"
+      let currentNamespace ← getCurrNamespace
+      let partNames := parts.toList.map fun part =>
+        currentNamespace ++ part.getId
+      let encoded ← readEmbeddedParts partNames
+      let bytes ←
+        match decodeBase64 encoded with
+        | .ok bytes => pure bytes
+        | .error message => throwError message
+      let decodedAdditions ←
+        match decodeAdditions initialCount additionCount bytes with
+        | .ok result => pure result
+        | .error message => throwError message
+      let clausePrefix := currentNamespace ++ clausePrefixSyntax.getId
+      let finalTheorem := currentNamespace ++ finalTheoremSyntax.getId
+      Command.liftTermElabM do
+        reconstructStage masterClauses decodedAdditions start stop
+          clausePrefix finalTheorem
+
+end Erdos97Octagon.LRAT
diff --git a/LeanPool/Erdos97ConvexOctagon/LRAT/Format.lean b/LeanPool/Erdos97ConvexOctagon/LRAT/Format.lean
new file mode 100644
index 00000000..55744dcd
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/LRAT/Format.lean
@@ -0,0 +1,266 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.LRAT.Semantics
+
+/-!
+# Versioned packed LRAT format
+
+Deletion records are omitted because retaining proved clauses is sound.  Each
+addition stores an identifier delta, signed literals, and backward distances
+to its antecedent clauses.  Natural numbers use unsigned base-128 varints and
+the resulting bytes use unpadded base64.
+-/
+
+namespace Erdos97Octagon.LRAT
+
+/-- Maximum number of bytes accepted for one packed natural number. -/
+def packedVarintByteBound : ℕ := 16
+
+/-- One reverse-unit-propagation addition. -/
+structure Addition where
+  /-- Strictly increasing LRAT clause identifier. -/
+  identifier : ℕ
+  /-- Signed DIMACS literals in the derived clause. -/
+  literals : Array Int
+  /-- Earlier clauses used for reverse unit propagation. -/
+  antecedents : Array ℕ
+deriving BEq
+
+/-- The current position in a packed byte sequence. -/
+structure Cursor where
+  /-- Complete packed certificate byte sequence. -/
+  bytes : ByteArray
+  /-- Zero-based position of the next unread byte. -/
+  position : ℕ
+
+private def base64Byte (value : ℕ) : Except String UInt8 :=
+  if value < 26 then
+    pure (UInt8.ofNat (65 + value))
+  else if value < 52 then
+    pure (UInt8.ofNat (97 + value - 26))
+  else if value < 62 then
+    pure (UInt8.ofNat (48 + value - 52))
+  else if value = 62 then
+    pure 43
+  else if value = 63 then
+    pure 47
+  else
+    throw "base64 value exceeds six bits"
+
+private def base64Value (character : UInt8) : Except String ℕ :=
+  let value := character.toNat
+  if 65 ≤ value ∧ value ≤ 90 then
+    pure (value - 65)
+  else if 97 ≤ value ∧ value ≤ 122 then
+    pure (value - 97 + 26)
+  else if 48 ≤ value ∧ value ≤ 57 then
+    pure (value - 48 + 52)
+  else if character = 43 then
+    pure 62
+  else if character = 47 then
+    pure 63
+  else
+    throw s!"invalid base64 byte {value}"
+
+/-- Encode bytes as unpadded base64. -/
+def encodeBase64 (bytes : ByteArray) : Except String String := do
+  let mut output := ByteArray.empty
+  for block in [0:(bytes.size + 2) / 3] do
+    let offset := 3 * block
+    let some first := bytes[offset]?
+      | throw "base64 encoder index is out of range"
+    let a := first.toNat
+    output := output.push (← base64Byte (a / 4))
+    if offset + 1 = bytes.size then
+      output := output.push (← base64Byte ((a % 4) * 16))
+    else
+      let some second := bytes[offset + 1]?
+        | throw "base64 encoder second byte is missing"
+      let b := second.toNat
+      output := output.push (← base64Byte ((a % 4) * 16 + b / 16))
+      if offset + 2 = bytes.size then
+        output := output.push (← base64Byte ((b % 16) * 4))
+      else
+        let some third := bytes[offset + 2]?
+          | throw "base64 encoder third byte is missing"
+        let c := third.toNat
+        output := output.push (← base64Byte ((b % 16) * 4 + c / 64))
+        output := output.push (← base64Byte (c % 64))
+  match String.fromUTF8? output with
+  | some text => pure text
+  | none => throw "base64 encoder produced invalid UTF-8"
+
+/-- Decode unpadded base64. -/
+def decodeBase64 (text : String) : Except String ByteArray := do
+  let characters := text.toUTF8
+  if characters.size % 4 = 1 then
+    throw "invalid one-character base64 tail"
+  let mut output := ByteArray.empty
+  for block in [0:(characters.size + 3) / 4] do
+    let offset := 4 * block
+    let some first := characters[offset]?
+      | throw "base64 decoder index is out of range"
+    let some second := characters[offset + 1]?
+      | throw "base64 decoder second byte is missing"
+    let a ← base64Value first
+    let b ← base64Value second
+    output := output.push (UInt8.ofNat (a * 4 + b / 16))
+    if offset + 2 < characters.size then
+      let some third := characters[offset + 2]?
+        | throw "base64 decoder third byte is missing"
+      let c ← base64Value third
+      output := output.push (UInt8.ofNat ((b % 16) * 16 + c / 4))
+      if offset + 3 < characters.size then
+        let some fourth := characters[offset + 3]?
+          | throw "base64 decoder fourth byte is missing"
+        let d ← base64Value fourth
+        output := output.push (UInt8.ofNat ((c % 4) * 64 + d))
+      else if c % 4 ≠ 0 then
+        throw "nonzero padding bits in base64 tail"
+    else if b % 16 ≠ 0 then
+      throw "nonzero padding bits in base64 tail"
+  pure output
+
+private def appendVarintWithFuel :
+    ℕ → ℕ → ByteArray → Except String ByteArray
+  | 0, _, _ => throw "natural number exceeds packed varint bound"
+  | fuel + 1, value, output =>
+      if value < 128 then
+        pure <| output.push (UInt8.ofNat value)
+      else
+        appendVarintWithFuel fuel (value / 128)
+          (output.push (UInt8.ofNat (value % 128 + 128)))
+
+private def appendVarint (value : ℕ) (output : ByteArray) :
+    Except String ByteArray :=
+  appendVarintWithFuel packedVarintByteBound value output
+
+private def readByte (cursor : Cursor) : Except String (UInt8 × Cursor) :=
+  match cursor.bytes[cursor.position]? with
+  | none => throw "unexpected end of packed certificate"
+  | some byte => pure (byte, { cursor with position := cursor.position + 1 })
+
+private def readVarintWithFuel :
+    ℕ → ℕ → ℕ → Cursor → Except String (ℕ × Cursor)
+  | 0, _, _, _ => throw "packed varint exceeds decoder bound"
+  | fuel + 1, multiplier, value, cursor => do
+      let (byte, cursor) ← readByte cursor
+      let payload := byte.toNat % 128
+      let value := value + multiplier * payload
+      if byte.toNat < 128 then
+        pure (value, cursor)
+      else
+        readVarintWithFuel fuel (multiplier * 128) value cursor
+
+private def readVarint (cursor : Cursor) : Except String (ℕ × Cursor) :=
+  readVarintWithFuel packedVarintByteBound 1 0 cursor
+
+private def literalCode (literal : Int) : Except String ℕ :=
+  if literal = 0 then
+    throw "zero is not a literal"
+  else if literal < 0 then
+    pure (2 * ((-literal).toNat - 1) + 1)
+  else
+    pure (2 * (literal.toNat - 1))
+
+private def literalOfCode (code : ℕ) : Int :=
+  if code % 2 = 0 then
+    Int.ofNat (code / 2 + 1)
+  else
+    -Int.ofNat (code / 2 + 1)
+
+private def appendLiterals
+    (literals : Array Int) (output : ByteArray) : Except String ByteArray := do
+  let mut output ← appendVarint literals.size output
+  for literal in literals do
+    output ← appendVarint (← literalCode literal) output
+  pure output
+
+private def appendAntecedents
+    (identifier : ℕ) (antecedents : Array ℕ) (output : ByteArray) :
+    Except String ByteArray := do
+  let mut output ← appendVarint antecedents.size output
+  for antecedent in antecedents do
+    if antecedent = 0 ∨ identifier ≤ antecedent then
+      throw s!"antecedent {antecedent} is not before clause {identifier}"
+    output ← appendVarint (identifier - antecedent) output
+  pure output
+
+private def appendAddition
+    (previous : ℕ) (addition : Addition) (output : ByteArray) :
+    Except String ByteArray := do
+  if addition.identifier ≤ previous then
+    throw "clause identifiers are not strictly increasing"
+  let output ← appendVarint (addition.identifier - previous) output
+  let output ← appendLiterals addition.literals output
+  appendAntecedents addition.identifier addition.antecedents output
+
+/-- Pack additions after the initial clause range. -/
+def encodeAdditions
+    (initialClauseCount : ℕ) (additions : Array Addition) :
+    Except String ByteArray := do
+  let mut previous := initialClauseCount
+  let mut output := ByteArray.empty
+  for addition in additions do
+    output ← appendAddition previous addition output
+    previous := addition.identifier
+  pure output
+
+private def readLiterals
+    (count : ℕ) (initialCursor : Cursor) :
+    Except String (Array Int × Cursor) := do
+  let mut cursor := initialCursor
+  let mut result := Array.mkEmpty count
+  for _ in [0:count] do
+    let (code, nextCursor) ← readVarint cursor
+    result := result.push (literalOfCode code)
+    cursor := nextCursor
+  pure (result, cursor)
+
+private def readAntecedents
+    (identifier count : ℕ) (initialCursor : Cursor) :
+    Except String (Array ℕ × Cursor) := do
+  let mut cursor := initialCursor
+  let mut result := Array.mkEmpty count
+  for _ in [0:count] do
+    let (distance, nextCursor) ← readVarint cursor
+    if distance = 0 ∨ identifier < distance then
+      throw "invalid backward antecedent distance"
+    result := result.push (identifier - distance)
+    cursor := nextCursor
+  pure (result, cursor)
+
+private def readAddition
+    (previous : ℕ) (cursor : Cursor) : Except String (Addition × Cursor) := do
+  let (identifierDelta, cursor) ← readVarint cursor
+  if identifierDelta = 0 then
+    throw "zero clause identifier delta"
+  let identifier := previous + identifierDelta
+  let (literalCount, cursor) ← readVarint cursor
+  let (literals, cursor) ← readLiterals literalCount cursor
+  let (antecedentCount, cursor) ← readVarint cursor
+  let (antecedents, cursor) ← readAntecedents identifier antecedentCount cursor
+  pure ({ identifier, literals, antecedents }, cursor)
+
+/-- Decode exactly `additionCount` packed additions and reject trailing bytes. -/
+def decodeAdditions
+    (initialClauseCount additionCount : ℕ) (bytes : ByteArray) :
+    Except String (Array Addition) := do
+  let mut previous := initialClauseCount
+  let mut cursor : Cursor := { bytes, position := 0 }
+  let mut additions := Array.mkEmpty additionCount
+  for _ in [0:additionCount] do
+    let (addition, nextCursor) ← readAddition previous cursor
+    additions := additions.push addition
+    previous := addition.identifier
+    cursor := nextCursor
+  if cursor.position = bytes.size then
+    pure additions
+  else
+    throw "trailing bytes after packed certificate"
+
+end Erdos97Octagon.LRAT
diff --git a/LeanPool/Erdos97ConvexOctagon/LRAT/Semantics.lean b/LeanPool/Erdos97ConvexOctagon/LRAT/Semantics.lean
new file mode 100644
index 00000000..9882f859
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/LRAT/Semantics.lean
@@ -0,0 +1,113 @@
+/-
+Copyright (c) 2022 Mario Carneiro, 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Mario Carneiro, Egor Lyfar
+-/
+
+import Mathlib.Algebra.Group.Nat.Defs
+import Mathlib.Data.List.Basic
+
+/-!
+# Stable propositional semantics for LRAT certificates
+
+Adapted from `Mathlib/Tactic/Sat/FromLRAT.lean` (Apache-2.0).  This
+project-owned interface deliberately contains only the definitions and
+soundness lemmas needed by the local LRAT elaborator.
+-/
+
+namespace Erdos97Octagon.LRAT
+
+/-- A positive or negative occurrence of a zero-based propositional variable. -/
+inductive Literal where
+  | positive : ℕ → Literal
+  | negative : ℕ → Literal
+
+/-- Translate a nonzero DIMACS integer into a literal. -/
+def Literal.ofInt (value : Int) : Literal :=
+  if value < 0 then .negative (-value - 1).toNat else .positive (value - 1).toNat
+
+/-- Reverse the polarity of a literal. -/
+def Literal.negate : Literal → Literal
+  | .positive index => .negative index
+  | .negative index => .positive index
+
+/-- A clause is a disjunction represented as a list of literals. -/
+abbrev Clause := List Literal
+
+/-- A formula is a conjunction represented as a list of clauses. -/
+abbrev Formula := List Clause
+
+/-- A single clause viewed as a formula. -/
+def Formula.one (clause : Clause) : Formula := [clause]
+
+/-- Conjoin two formulas. -/
+def Formula.and (left right : Formula) : Formula := left ++ right
+
+/-- Every clause in `smaller` also occurs in `larger`. -/
+structure Formula.Subsumes (larger smaller : Formula) : Prop where
+  property : ∀ clause, clause ∈ smaller → clause ∈ larger
+
+theorem Formula.subsumesSelf (formula : Formula) : formula.Subsumes formula :=
+  ⟨fun _ membership => membership⟩
+
+theorem Formula.subsumesLeft
+    (formula left right : Formula) (h : formula.Subsumes (left.and right)) :
+    formula.Subsumes left :=
+  ⟨fun _ membership => h.property _ <| List.mem_append.mpr <| Or.inl membership⟩
+
+theorem Formula.subsumesRight
+    (formula left right : Formula) (h : formula.Subsumes (left.and right)) :
+    formula.Subsumes right :=
+  ⟨fun _ membership => h.property _ <| List.mem_append.mpr <| Or.inr membership⟩
+
+/-- A proposition-valued assignment of all propositional variables. -/
+abbrev Valuation := ℕ → Prop
+
+/-- The assertion that a literal is false in a valuation. -/
+def Valuation.falsifies (valuation : Valuation) : Literal → Prop
+  | .positive index => ¬ valuation index
+  | .negative index => valuation index
+
+/-- The assertion that at least one literal in a clause is true. -/
+def Valuation.satisfies (valuation : Valuation) : Clause → Prop
+  | [] => False
+  | literal :: clause => valuation.falsifies literal → valuation.satisfies clause
+
+/-- A clause is satisfied when its literals are not all false. -/
+theorem Valuation.satisfiesOfNotAllFalsified
+    (valuation : Valuation) (clause : Clause)
+    (h : ¬ List.Forall valuation.falsifies clause) :
+    valuation.satisfies clause := by
+  induction clause with
+  | nil => simp at h
+  | cons literal remaining inductionHypothesis =>
+      intro hliteral
+      apply inductionHypothesis
+      intro hremaining
+      apply h
+      simpa using And.intro hliteral hremaining
+
+/-- The assertion that every clause in a formula is satisfied. -/
+structure Valuation.SatisfiesFormula
+    (valuation : Valuation) (formula : Formula) : Prop where
+  property : ∀ clause, clause ∈ formula → valuation.satisfies clause
+
+/-- A clause follows semantically from a formula. -/
+def Formula.Proves (formula : Formula) (clause : Clause) : Prop :=
+  ∀ valuation : Valuation, valuation.SatisfiesFormula formula →
+    valuation.satisfies clause
+
+/-- Membership in a formula proves a clause. -/
+theorem Formula.provesOfSubsumes {formula : Formula} {clause : Clause}
+    (h : formula.Subsumes (Formula.one clause)) : formula.Proves clause :=
+  fun _ satisfies => satisfies.property _ <| h.property _ <| List.Mem.head ..
+
+/-- The sound unit-propagation case split. -/
+theorem Valuation.propagateCases {valuation : Valuation} {literal : Literal}
+    (positiveCase : valuation.falsifies literal.negate → False)
+    (negativeCase : valuation.falsifies literal → False) : False :=
+  match literal with
+  | .positive _ => negativeCase positiveCase
+  | .negative _ => positiveCase negativeCase
+
+end Erdos97Octagon.LRAT
diff --git a/LeanPool/Erdos97ConvexOctagon/Main.lean b/LeanPool/Erdos97ConvexOctagon/Main.lean
new file mode 100644
index 00000000..039d4a6e
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/Main.lean
@@ -0,0 +1,23 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.Classification
+
+/-!
+# The convex-octagon case of Erdős problem 97
+
+The headline theorem exported by this entry module is
+`Erdos97Octagon.erdos97_convex_octagon`: among eight labelled points in convex
+position, some point does not have four other points at a common distance.
+
+The proof reduces a hypothetical counterexample to a normalized balanced
+incidence table, classifies its first row up to symmetry, and excludes all
+seven canonical masks with one regenerable LRAT certificate checked by a
+project-owned kernel-safe checker.
+
+This is the eight-point convex case only. It does not prove the general open
+problem.
+-/
diff --git a/LeanPool/Erdos97ConvexOctagon/MasterCertificate.lean b/LeanPool/Erdos97ConvexOctagon/MasterCertificate.lean
new file mode 100644
index 00000000..f8474a23
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/MasterCertificate.lean
@@ -0,0 +1,9 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.MasterCertificateStage02
+
+/-! # Kernel-checked master coverage certificate -/
diff --git a/LeanPool/Erdos97ConvexOctagon/MasterCertificateData0.lean b/LeanPool/Erdos97ConvexOctagon/MasterCertificateData0.lean
new file mode 100644
index 00000000..83be7f17
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/MasterCertificateData0.lean
@@ -0,0 +1,517 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.LRAT.Format
+
+/-! # Generated packed master-certificate data -/
+
+namespace Erdos97Octagon.RawIncidence
+
+/-- Packed certificate data part 0. -/
+def masterCertificatePart0 : List String := [
+  "AQdiIjEzQVJxBL4Z0BbTFsEVAQYyIkFSYXEFvxnaFtYW1xa+FQEHRBQxNVFkcQS/Gb4WvBa6FQEHVBQ0QUVhcQTAGcIWwR",
+  "a3FQEGRBQ0UWFxBcEZxhbFFsQWtxUBB1gYISk4YXEEwBmUFpUWqhUBB1gYKDE5YXEEwRmYFpkWqBUBBjgYKFFhcQXCGZwW",
+  "mxadFqgVAQcrERshOmFxBcIZuxmmFaUVhhYBBysRGyExSnEFwxm8GakVphWIFgEIMREbIDtAa3sEyRmkFYYXpRUBCFARGy",
+  "AxO0BKCMoZxRm+GYkXiBemFaUViBYBBzARGyBLUGsEyxmNF5AXpRUBB3ARGyAwS2sEzBmMF48XphUBBjoRG0phcQXIGcEZ",
+  "jhaNFqUVAQh7ERsgMEtrcQTOGaYVpxWSFwEHQBAhKzBrewTPGZ0XnBehFQEHeyErOkFhcQXLGcQZohWRFqMVAQZqKjE7QX",
+  "EFzBnFGZMWlRahFQEHQBAgMTtrewTSGaUXphehFQEGMBAgS2t7BdMZrBepF6oXoRUBBjwRHSFMcQXOGccZ+xWCFp4VAQgx",
+  "ER0gPV1gfQTVGZwVkRedFQEIIBEdLDBBTWAI1hnQGckZmBecFZYX/xWbFQEGLBEdPFFxBdEZyhmDFoQWmxUBBUwhPFFxBt",
+  "IZyxmAFv8VhhaWFQEGXh4hMT9BBdIZyxn2FfEVihUBBj4eIS9BYQXTGcwZ9RXzFYcVAQtBEB4gMT1NUV9vfQjbGdQZzRmX",
+  "FasXgxWEFfYVAQYuHkFRX2EF1RnOGfoV+BWEFQEFPjg8Q0UG2hnVGdQZ0BjLGIQVAQhlIjJBQ0VRcQfdGdYZ1RmAFfUW8x",
+  "bdFQEHYhYjJzJSZgneGdwZ1xnVGe8W7Bb9FPoUwhYBCGcWJkNRYWNxB90Z2BnWGfkUyxbJFsoVAQdyFiIyQ0d2CeAZ3hnZ",
+  "GdcZ9xb2FvsU+hTDFgEFZhZGU3MG3xnaGdgZxRbHFvgUAQU0IykwPgbgGdsZ2BnoGPcY9xQBBTojKTA0BuEZ3BnZGesY+h",
+  "j4FAEFNCMpMDwG4hndGdoZ+hjrGPkUAQU6Iyk0PAbjGd4Z2xneGNYY+hQBByMqLDM5Q0cH5RnfGd0Z3Bn7FIUVhBkBBS4m",
+  "KjM5BuYZ4BndGYQZjhn8FAEFZiMpYGQG4xnhGd4Z/BeHGPsUAQYzIjlSaXkG6RniGd8Z+BT5FPsWAQV2MzlwdAbkGeMZ4B",
+  "nbF+gX+RQBBkIYIig5UgrrGegZ5BnhGYYXgBf/FvoU+xS+FgEGUhgiOUJYCuwZ6RnlGeIZgBeHF4EX+xT8FLsWAQdCGCIo",
+  "MlNZCe0Z6hnmGeMZhheHF/oU+xTAFgEHMiMrS1JiewTuGfwW/xb1FAEHYi0yQ01SfQTvGf0WhxfsFAEJMyI5PUNNUml9Bv",
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+  "29Hbwdux26HbkduB23HbYdtR20HVgDPKIdhAG7F3+pA6YDtwHcGtYa1RqhBJ4anRq0F/gZ8Rn1GaoXAeEZhx3gGd4ZgBTi",
+  "FpMUZYUYnxquGP8XgxqPA4Ia6hiCG9UbpRbIDAEHQhEVFxsrOTrDHcIdwR3AHb8dvh29Hbwdux26HbkduB23HbYdtR2AAV",
+  "kEPaMdhQG8F6oDpwOiBPkZ8hn2GeIXqxcB4hXjFeYbnxrTGLYB3BrbGt0X4xaIHeEZ3xnZHPwWxBawA4cbgxv/F8wToBrW",
+  "G5gcpRasGMgMAQ4vERUXHikrLTk9Q01ffSXDHcIdwB2/Hb0dvB27HboduR24HbYd4xegF6wXvRfdGd8ZiwK3AYwC+hbYE8",
+  "wThxa9GIUaohyxFvIUkhqzFboakRitGJEduhunFgEKUhUXJykyOTo/XArCHbwduh1ougGsA6kDphjlFtscAQYrERUXGzkt",
+  "xh3FHcQdwR3AHb8dvh29Hbwdux25HbgdQIgBvxemHaUEAwetA6oD9xn5GfUZ/BlcrhcC5RniGeQZix2BFwHlFbMY7BbmFe",
+  "kbohqRE+YWrAGJG/kDAQZOERUXG0IGwx3lAssBnReaHJwXAQZjQUNLT28Dyha5FrUDAQtBERc5PkNLT2Zpbw7GHcMdwR3A",
+  "Hb8dvh3dE9wT3RypGAHUG+cbvRYBCTMRFRcbOU9dXzjKHckdyB3HHcYdxR3EHcMdwh3BHcAdvx2+Hb0dvB28F4wBwxeqHU",
+  "QEqQSOHYsdkR2KHd0WxRffFv4Z+hmHAaYX6RcP0RPdE+MZmBqnHNkYjBjoFKca6BvVG7MYwBrtGLIB2xqeFMYD/gPNGJ4M",
+  "AQlSERUXGzlPXV84yx3KHckdyB3HHcYdxR3EHcMdwh3BHcAdvx2+Hb0djQHEF6sdRQUBqgSPHYwdkh2LHeIa5RrhGt4Wxh",
+  "fgFhCJHPkb+xn/GacX6hfkGb4BmRq8FtsWjRi4A40aAvETjhvTE44WqByoGqIYngwBDDERFxs5O0BDTFNWWAvIHccdxB3D",
+  "HcIdwR3JE9QTghypHO8YAQhPERUXGzldXyvNHcwdyx3JHccdxh3EHcMdwh3AHb8djwHGF60dRwesBJEdjh2UHY0d4BbIF+",
+  "IWigGBGv0ZEqkX7BfmGZsajxgCuhgDwAHiGgQBkBuSG6UWAQZzQUNLTX0DpxaaFsoDAQxBERcbOTxDS012eX0OzB3IHccd",
+  "xh3FHcQd4xPiE+QcrhgBzBu3G6gZAQgzERUXGzldXznQHc8dzh3NHcwdyx3KHckdyB3HHcYdxR3EHcMdwh3CF5IByRewHU",
+  "oKA68E5xnrGe4ZlB2RHZcdCYkB6ResF+MW5RbjE54aghqEGt4YkRjXE6wcrRqDFLoY5QO4G8Ya8xjhGo4c9hO9A5QbhwSh",
+  "DAEIUhEVFxs5XV850R3QHc8dzh3NHcwdyx3KHckdyB3HHcYdxR3EHcMdBJMByhexHUsLAQqKAbAE6BnsGe8ZlR2SHZgd5x",
+  "roGuoXrRfkFuYWnxqDGoUa0AGPHP8buhYCnRbNA5MaphbeFKUU5BuVG4sYlBatHKEMAQwxERcbOTtAQ05TVlgLzh3NHcod",
+  "yR3IHccdzxOIHPUYrhzaEwEHXxEVFxs5XTDTHdId0R3QHc8dzR3MHcodyR3IHcYdxR2VAcwXsx1NDbIElx2UHZodkx3mFu",
+  "gWAgYM6hmMAe4Z7BevF6EahRqHGpQYyhgD0gEEAZcbmBvoHJYb+ROyGLsbAQhBERUXGzlCXTnUHdMd0h3RHdAdzx3OHc0d",
+  "zB3LHcodyR3IHccdxh0BlgHNF7QdDk4NkQG+A+4ZmQGzBOoZ8Rl0lR2bHbAXlxjtF4wXrxrpEYYaqRyOGcYR0AOAHOQY4g",
+  "PsGtMBmBeNGpQb6RytGMkaxBvlFqMMAQdCERUXGzldMNUd1B3THdEd0B3PHc4dzR3MHcsdyh3IHccdDpIBlwHOF7UdD08C",
+  "tATrGfIZdZYdnB2/A+8ZmgGNF9IXmBiHGgG6HL8c2hWDFYEc5RjtGq0W0QOYG6wYmBbLGgEKQREXGzk8Q1ZZXg3THdEdzh",
+  "3NHcwdyx3qE+kTwAPrHKITtxiCHAEFYicpZGoG0R3NHcwd4BviG5kYAQZKERsgKkAK2B3THcwdnBqfGpsajwSbG5wbsBkB",
+  "CzMiKj9DS01PUm99CNgd1B3NHZsXyBieGuoapRYBBl0RFRcbOSrZHdgd1R3UHdMd0h3RHdAdzx3OHc0dzB1UFJwB0xe6HZ",
+  "4doR2aHZsduQQHxAP0GfIZ8BmfAbYXnRiOGowaBQQCpRMB6gPwGssWnBqmFgEIWREVFxs5QUI52x3aHdkd2B3XHdYd1R3U",
+  "HdMd0h3RHdAdzx3OHc0dARVVnQHUF7sdFJgBwgO/A3ucHaIdmx26BLYatxqeGPUXkxeKGo4a9BmDGcgDwQHwEbAczRGIHO",
+  "sY8xrOAbETlBrvHJsbtRjQGu4bxBitDAEGWBEVFxtcCdcd1B3THdId0QHAA/wV/xv7FQEGQhEVFxs5Kdwd2x3aHdkd2B3X",
+  "HdUd1B3THdId0B0WmgGfAdYXvR1XFwOeHbwEoR2kHZ0dxAPBAwGQGrkXoBiVFwLCHMccyhWKHO0Y/xXxHNQc2hMBCkERFx",
+  "s5PkNWWVwN2x3ZHdYd1R3UHdMdwgOqE4scvxjxE/Ic8hMBCzMiKj1DS01PUm99CN4d2h3THdgYrBfwGqUa0BYBBTkRFRcb",
+  "Lt8d3h3dHdsd2h3ZHdgd1x3WHdUd1B3THdIdogHZF8AdvwQGxwPEA5MakRoElhqPGloaoB2nHYAB+hejGPkZ+xkDAgirE4",
+  "0cwRgB8APXHNEW7heiGgENWRgpKy80OEFPX2FvewnfHd0d+RewGsMUuxTXGtka4BYBDT4RFRcbKSwvQUJKT1004h3hHeAd",
+  "3x3eHd0d3B3bHdod2R3YHdcd1h3VHdQdpAHbF8IdnwECwQT8GfsZvgKaGpca/halFp4ZnhvbHNEc3gO+Ga8WphoBshqzGs",
+  "oB3hK3HKkQ4RaoHdMY7RugGN8bwhqqGNAMAQszERcbIjs9QlF7fQbiHdsd2R3fE/YasBYBDSIRFxgbODs9QlFZe30L4x3g",
+  "Hdwd2R0B/Rr8Gv4a8BjxGLMaAQxKERUXGyksL0FCT10m5B3jHeId4R3gHd8d3R3cHdsd2h3YHe0BxR0FpwHeF8QEmhqdGg",
+  "PfF88DqgGiGZ8Z8gHhAwGrFvgYmR3cE8gXkRz8HJAXnhe6HAEHPhEVFxtBSwnjHd4d3R3cHQbCAqkWwxnVHAEGKRgnOGd3",
+  "BuMd3R3cHakYqBi2GgEFUlRcZ2kG4x3eHd0dkxyVHKgYAQtNERUXGyktL0FPXSXoHeYd5R3kHeMd4h3hHeAd3x3eHdwd2x",
+  "3kF8kdCeIX0wODGv8ZrgHIBOYX9AKbGqwWkxmHGOMc2RzWA7ga0xPkE4sVrwGVHMEQAQkvERUXGylBQl0V6R3kHeEd4B3f",
+  "Hd0dyh0K4xcjpwHJBAGiGgUEnxfkF/cB1AOnGQEQRxEVFy0xP0FNT11fYmlvcSDqHekd6B3mHeUd4x3iHeEd4B2CEvAQ/x",
+  "afG5UblhvmF/MZ5BeJHMka2AOxFp4Yqx2tHbgdohX9D9MBoRyEG6UQAQgpERUXG0FCXTnsHesd6h3pHegd5x3mHeUd5B3j",
+  "HeId4R3gHd8d3h3MHQyuAeUXJakBywQCixqIGoka5heIF/cCpBqeGq8WlhncHOYc2QOoG7AX3hbHGdIBrxqcArwa1AEBwR",
+  "yzEOoUsR39GNQbqhiKHM0asBiADQEGLBEVFyAoB+sd5R3kHeMdox2wHbMWAQsvERUXGystQU1PXRXrHecd5h3lHeQd4B3p",
+  "F84dDtgDiBqEGusX+QKxFpgZmRveHNsD6gOpGgEHXREVFxtBQg7tHecd5h3lHbEBKAMCjwGsAQGkHbEdtRYBCC8RFRcbKU",
+  "FCLe8d7h3tHewd6h3pHegd5x3mHeUd4x3iHQHQHSnpFxDXA9QDFM8EnxqhGqMaphrtF4kazAKYGYgYsxasGd0D1gG/Gukc",
+  "3xzsA/IYqRSiFOoT5xqDG6QOAQszERcbIjs/QlFrbwbwHekd5x3jFoUb7RMBDSIRFxgbODs/QlFZa28L8R3uHeod5x0Bih",
+  "uLG4wb/xj+GMEaAQcpERUXG0FCKfId8R3uHe0d7B3rHeod6R3oHeYd5R0EtQHTHewXEyzaA9cDF9IEphqpGgOSGo8alwSe",
+  "GeADgAIBuRaGGaYd6hPdF6Acgxv/FMIVigQBBkERFRcbQinzHfId8R3wHe4d7R3sHesd6h3pHecd5h22AdQd7RcULdMEAQ",
+  "eUAcsayhoF2wPYA6MapxqlGpABth3xF40a0ALsFrcWsBnhA+Mc8AOvGgEMIhEVFxspLC8+Qk9dNfUd9B3zHfId8R3wHe8d",
+  "7h3tHewd6x3qHekd6B3nHQG3AdUd7hcVwgPDA7Ydux3UBI4ajxrRArQXqhqtGvoXuBbfHOID7hzkHPEV5xWDGMUaxhrxA7",
+  "YYkRW3GLAZzxbdGx7SGmDcDAEMWREVKSsvNEtPX2FxBvQd6BXkFe8a7hryGQELPhEVFxspLC9CT1029x32HfUd9B3zHfId",
+  "8R3wHe8d7h3tHewd6x3qHekdA7kB1x3wFxfEA8UD1gSQGpEa0wKsGq8auhbmHPAchRjzA9EWshm2G9MZuRoBxxrIGt8BAp",
+  "UbkxTPEeEcixfREq0c1RqCHN8W5AwBCiwRFRcbKS9CT10w+B33HfYd9R30HfId8R3wHe8d7h3tHesd6h0EugHYHfEXGMUD",
+  "xgPXBK0asBoBrRfyF4UC4gOOGr0BuxazGfMc9AO1G6cX+xaMG4QblBSJGawdxxrqFLUQvgHuGuQSAQlPERUXGykvQl0t+B",
+  "33HfYd9R30HfMd8h3xHfAd7x3uHewd6x0F2R3yFxnGA8cD2AQB9BfjA5Majxq+AfYXhAOrGrwWlxjzHOkcyBrzE/0X4xOW",
+  "FZsV5gOlHPAa/BaNG8YNAQZXFiZZaXkG9x3wHe8duhi5GOAaAQxZGCktOEtNT11fb30E9x2ZGJsVyhoBCEQRFRcbKUJdOf",
+  "wd+x36Hfkd+B33HfYd9R30HfMd8h3xHfAd7x3uHQi+Adwd9RccNckDygPmHNsEA5samBqZGvYXkBeHA7Qarhq/FvYc7ByA",
+]
+
+end Erdos97Octagon.RawIncidence
diff --git a/LeanPool/Erdos97ConvexOctagon/MasterCertificateData1.lean b/LeanPool/Erdos97ConvexOctagon/MasterCertificateData1.lean
new file mode 100644
index 00000000..76809d56
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/MasterCertificateData1.lean
@@ -0,0 +1,517 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.LRAT.Format
+
+/-! # Generated packed master-certificate data -/
+
+namespace Erdos97Octagon.RawIncidence
+
+/-- Packed certificate data part 1. -/
+def masterCertificatePart1 : List String := [
+  "GOkDpRn/Frob1xm+GrkYwR0BzBrNGuQBshyNGawRhxzzGroYjw0BB10RFRcbKUI6/R38Hfsd+h35Hfgd9x32HfUd9B3zHf",
+  "Id8R3wHe8dCb8B3R32Fx02ygPLA9wEAekYBJwamRqaGvcXiAO1Gq8awBb3HO0cgRjqA6YZgBe7G9gZvxqHFs0azhrlAa4U",
+  "5xGPG8Id9BvuE78YJrMcig0BBy8RFRcbKUIx/R38Hfsd+h35Hfgd9x32HfUd9B3zHfId8R3wHQEK3h33Fx435QPiAyLLA8",
+  "wD3QStGrEatBq0F/sX2gKXGsEWlhjtHPcczRr7E4wYsBS3FPoDwBr1GtgWihuRG7IOAQYpERUXG0I4/x3+Hf0d/B37Hfod",
+  "+R34Hfcd9h31HfQd8h3xHQvBAd8d+BcfOMwDzQPeBALmA+MDrhojshq1GgGeGpsatBeMAsIWqBn6HOwDvBumF4cV2RbOGu",
+  "UBkhubFLIdvBC5GqwcvhjnG7AU+BrOFQEFQhEVFxsQ/h34Hfcd9h3CAQzNA84DAROgATm2F8IdtR3GFgEJPhEVFzg9QUNN",
+  "CP4d+R34Hfcd3QLEFtMX+hwBDSwRFRccHiAiOEFDT10bgh6BHvwd+x36Hfkd+B33HfUd9B23GroauRr7F88dAb0X/BfsA5",
+  "gaxwHOE78ZvBmZG8IbhBcBCV0RFRcbKS9BTxeCHv0d+x36Hfkd+B32HQPFAfwXI+MdmBTiBAEaSLcaHf8X7QPIAdgTAQdG",
+  "FhgmOHd5CYEegB76Hfkd7xruGsMYwhjVGgEKIhEVFxspLC8+TzeFHoQegx6CHoEegB7/Hf4d/R38Hfsd+h35Hfgd9x0Fxw",
+  "H+FyXlHcsdxh3hAuQEnhqfGsgWuhq7Gr0avBqeF/Qc/hwC/hjSF7sElhvAGe4TgQTCG8AawBjoFYIc+xviGt8U3hfWGrMc",
+  "4RjtDAEJPhEVFxspLC9PLoUehB6DHoEegB7/Hf4d/R38Hfsd+R34HQbIAf8XJuYd4gLlBJ8aoBrJFrsavBq+Gr0anxf1HP",
+  "8cA9MXvAQuwRnvE4IEwRoBkxT4GMMQ/xq0HPAYnhiMHAEMMREVFxsrPT9NT119HYYehB6DHoIegB7/Hf4d/R38HfkdyhaB",
+  "GAeAGCfnHfEDnRrCF4Id8xOEFLMc/hOdG54buxTXFNYaAQlKERUXGyksL084iB6HHoYehR6EHoMegh6BHoAe/x3+Hf0d/B",
+  "37HfodAgjKAYEYKOgdTecEvRq+GsAaghjDF/IDnhrNAQUwAZUCnx3LG8wbjhjBF9cWxhrmHNca6xafFeoW8RvYFP8YnxuT",
+  "HIAY/xPmGvMMAQgsERUXGykvTxaIHoYegx6BHoAe/x3+HfwdCYIYKekd6ATBGsAaA8QXAb4XlgKEHcwWAQk+ERUXGykvTU",
+  "8uiR6IHocehh6FHoQegx6CHoEegB7/Hf4d/R38HQEKzAGDGCrqHeYC6QSkGqMazRaFGPkcgx34HO4DuRou3BfXF4cU9hOi",
+  "GDK3HNkamhj5FecYyBqBG5oVAQhNERUXGykvTyqKHogehx6GHoUegx6CHoEegB7/Hf4dC80BhBgr6x3qBAECiBiWA74avR",
+  "rOFoYY+xyFHfUD0AHUF80XiBT3E6kYM7cc2hrKFZIWyRrRAawUAQ4+ERUXHiktLzg9Q09dfSOLHooeiR6IHoUehB6DHoIe",
+  "gR7+HegCphqlGq8ahRjPFp8XhxjZHdwa3RpRzgHDFLoUgxuCG/ANmRT4GIgW9xjpGtMdzRgBC0QRFRcbKSsvMTpPNo0ejB",
+  "6LHooeiR6IHocehh6FHoQegx6CHoEegB7/HQINhhgt7R3PAdAWUtAXiB3sBP0c/BzWF74axBq9GuociRilHfcDoxrSAcgZ",
+  "vBf8GNUCkhirGMobnhvGGNwa/RuuFLkchhv+GsYMAQorERUXGykvMTpPN44ejR6MHoseih6JHogehx6GHoUehB6DHoIegR",
+  "6AHtEWAw6HGC7uHdAB/hz9HFPRF4kd7QTXF78axRq+GooYph34A6Qa0wHJGb0X/RjWApMYrBjLG58b3RoB+hisFa8ZmRyE",
+  "G/4bzhjIDAEJOhEVFxspLzFPLI4ejR6MHoseih6JHogehx6GHoUehB6DHoIegR4ED4gYL+8d0QHSFood7gT/HP4chRnAGs",
+  "YavxqLGPkDpRrUAcoZvhetGN4aAdYd1RqcAfgN/xvnEAEJIhEVFxspLzFPOJAejx6OHo0ejB6LHooeiR6IHocehh6FHoQe",
+  "gx6CHgUBEIkYMPAd0gHTFlXtGe8EwRrHGsAaxBoEjBjSF+oX+gOmGtUB1x3LGY0U/BOUGK4YnQGMBM0bphunG98aqBzSD+",
+  "4Y7RqAHOIc3QwBCDERFRcbKS9PJZEekB6NHoseiR6IHocehh6EHgYRihgx8R3TAVbwBMIayBrBGsUaAu4ZAYkYBY0Y+wPW",
+  "AcwZ/ROvGI0EzhvgGq0Dyw4BCCIRFRcbKS9POZIekR6QHo8ejh6NHoweix6KHokeiB6HHoYehR6EHhKLGDLyHdQBBwHxBM",
+  "MayRrCGlfGGu4CnwKOGOwX1Bf8A6ga1wHZHakdlhiwGN0T5xPVGLwVwRXWFO0Y/wPUGuEanwGpG6gb7xzVG+sY3QwBB08R",
+  "FRcbKS86kx6SHpEekB6PHo4ejR6MHoseih6JHogehx6GHoUeE4wYM/Md1QHyBAjEGsoawxpYxxoC7wKgAo8Y7RfVF/0DqR",
+  "qqHZcY7hiABNUa7BgBhRmoFIsY8BzWG8wY2AGmGeIWoBviGsMRnhyIG9MY6AwBCTERFRcbPUFLTQqRHoweix6KHtcW8RkU",
+  "NI8d5hcBCEERFRcbKSwvOZUelB6THpIekR6QHo8ejh6NHoweix6KHokeiB6HHgKOGDX1HdcBFawarRrOAbAa9ATHFqoUzR",
+  "rMGsoayxrWHdsd9xwBogLiF5sY0RqsHYIEkQSsF44WvRvVBO4WyxyjBK0Y5BrWGP0b8hqcG/IMAQ0zERUXGyksMT9LYW9x",
+  "K5UelB6SHpEekB6PHo4ejR6MHoseiR6IHtUWmRe/G8cbwBvLGRaPGIAE+gP1BM4azRrLGpAY8BaQGbQapxv+Aa4YoxSOGP",
+  "Icyh3eE9ocjxuHG6AXnBwBDVkRFRcbIikvMTI9RWEZlh6UHpEekB6PHo4ejR6MHoke2hYXBDf3HZIdrhqvGtAB8xmvGJIS",
+  "rhu5GZkcphMBCSIRFRcbKSwvMTiYHpcelh6VHpQekx6SHpEekB6PHo4ejR6MHoseih4DBRiRGDj4HdoB2xaBA68asBqzGv",
+  "cE2R3eHc4a0BrNGs8a1Ri1F/Qc1hvXGwKTHdUa1BoB6BrpGoAC2RjaGLsZpgSPGfUauhmAHPYMAQ5ZFRsjKSs7PUNHS01Q",
+  "XQeUHpEejh7hE6wZ3RyZFgEIMREVFxspLC8vmh6ZHpgelx6WHpQekx6SHpEekB6PHo0ejB7dFtwB+h06GgcFkxj5BLUasR",
+  "qyGtMB0RrPGtIa0Bq3F9kb2BsC4BanFM4d9hwElR0B6xqCAvQStBn4GuQNAQtZGCkvOFFdX29xfQSXHrMY6hbqGgEHLBEV",
+  "FxspLzOcHpsemh6ZHpgelx6WHpUelB6THpIekR6QHo8ejh7eAfwdPByVGPsECdQa0hqzGrQa1QEHAqkC3xvgG+Eb0xrRGs",
+  "IU8BTeGukXsx33GPgc2RjiHZwUAewa7RqtGa4ZqRsBCysRFRcbKS8xOj1ENp0enB6bHpoemR6YHpcelh6VHpQekx6SHpEe",
+  "kB6PHuAWCgHfAf0dPR2WGPwEjB20GrUa1gGZGLsdtR2YHYEEzhrMGkHvF8QXlhnGGbUY+RyuG4oE2hvsGtcY1xqwHK0VlR",
+  "vKHIYZ2AwBCkQRFRcbKS8xOj0vnR6cHpsemh6ZHpgelx6WHpUelB6THpIekR6QHgsC4AH+HT4elxj9BOEWuRq1GrYa1wGa",
+  "GJkdggTPGs0aQp4Z8BfFF8cZthj6HIsE2BixHAHjGuUdwQHLDwEJOhEVFxspLzE9OJ8enh6dHpwemx6aHpkemB6XHpYelR",
+  "6UHpMekh6RHuIWDAPhAf8dPx+YGP4Ejh22Grca2AGbGJodgwTQGs4aQ5gZxhfxF/0XyBm3GLAbjATcG+4aAfgXwRnSFJUb",
+  "shyKGf8N5BqHHLcd2wwBCUQRFRcbKS8xPTigHp8enh6dHpwemx6aHpkemB6XHpYelR6UHpMekh7jFgENBOIBgB5AIJkY/w",
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+  "+B3GB9cUhRnDGvEf8B8CrBuDGgGqHqgekxyRHLceAQpMEBUdIDtKUWt7GdQh0iHRIdAhzCHKIRhMjx5LDAGqH6sfEaUgnS",
+  "DyHIshFr0b8QeyG7Ab6yABFEMVFx0eIyktLzE8P0FESk1RXWBrGtIh0CHOIc0hzCHLIcohySHHIdIckRudFJsd8yDIB+0d",
+  "3AdNnB7oGoMgqhb6GrsFzyDBGgETXRUXGx0eIyktLzE8P0FESk1Rax7UIdMh0iHRIdAhzSHMIcshyiH4HdsC2AfVB/geyQ",
+  "cB9AarIIEb9CCdHu0VtB7AHNsU8x+rFs8eyx6vHAEOPxAVHR4gMTs8REpRa3so1yHVIdQh0yHRIdAhzyHNIcwhyiHJIQOF",
+  "CBtPRJIeTg/cAo4hAb4H/R2CHaIaoRqnIJ8g7h2DGoAdpx+wGsAftBrRIPwasRzMHgENHhAVHSAxOzxESlFrey/YIdYh1S",
+  "HUIdMh0iHRIdAhzyHOIc0hyyHKIUUcUASGCKQhkx5PEN0CAfId8R3zHZQbgB30Gq0gqB/+HfoahxyjGrYewhzNHs8elxrL",
+  "ILkctRqAIKYejREBDT8QFR0gMTs8REpRa3s02SHYIdch1iHVIdQh0yHSIdEh0CHPIc4hzSHMIcshAQWHCB1R4hu7G6Mhoi",
+  "GUHswHUBGoHd4C2xvbB5AhqSChIOUdpBqsGPsdhRrQHtEe0x/WH9Mg6hOlFrQe5h6BIPIc2ggBDEQQFR0gMTs8SlFreyLY",
+  "Idch1iHUIdMh0iHQIc8hzSHMIQaICB5SlR5REgLcG6ogoiCGGgHoHekd0CCKGYwZ2xuzHM8egB7VGeoHAQ5DFRceICMqMT",
+  "w/QUVNUSLbIdoh2SHYIdYh1CHTIdIh0SHQIc8hzSHtFYsaoAPUG1ITkiFTvCGXG/UXpxvyHfMd0yDVIJ8enh7QGkWrH7ga",
+  "AQopFR0jLS9FTU9gBtYhzweKGf4Y+R/zFAENPxAVHR4gMTs8SlFreyPbIdoh2SHWIdUh1CHTIc8hAwkhVUqYHqkhyRwVVI",
+  "sIAqogiB2lG8QH8x3/HdIa3wcBlCH5F9cgyRq6Gq8eAQweEBUdIDE7PEpRa3sb3CHbIdch1iHVIdQh0CFLBAoiVpkeFlUB",
+  "+B33HfkdmhurB4YdApUh+hf4F9QgAQ0pFR0jLTE/QUVRX2FyDt4h2CHXIdYh1CHRIY8aghSKHYgd7R7rHvAd1BwBCjkYKD",
+  "E7P1FfYWsE3CHlGoAbtB4BDz8VGx0fICMxO0FFTVFrex/fId4h3SHaIdch1iHTIeobmxurIaohnB7UB+0d8h1YsB3jB6wa",
+  "tBjeH9sfApghjRwBuB63HqAcnxzGHgEJKSMxPD5BRWJyC+Eh3yHaIdkh2CHXIZIa8B72HPYV0CABBjIxPD5BRQfgIdoh2S",
+  "HYIdYg2SCXGgELPBAVHSAxO0pRa3sn4yHiIeEh3iHdIdwh2yHaIdkh1yHWISgQXJ8eHFsKBp4bzQYD8h0B8x3UGpYZ5RuK",
+  "Hq8atxgCmyGhGtIg2h6ZGt8Z8B4BDmIQFR0eIDE7P0RKUWt7M+Uh5CHjIeIh4SHgId8h3iHdIdwh2yHaIdkh2CHXISkRAV",
+  "1Szhv0Avcb4SDtIKAesSG0HR1c2Ae5H8sF4hvqAoke/R21IK0gnCFpvh6ZFfYc2gXeHtwegyD/HM0arA0BDT8QFR0eIDE7",
+  "REpRa3sq5iHkIeIh4CHfId4h3SHcIdsh2CEqEgJeU/UC+BviIKEe3xu1HR5d2Qe6H+Mb6wKKHv4driCdIWr3HAGsGdcc+B",
+  "z5H9sFvBzNH74TAQ1TFRsdIyktNERWXGtzCuUh4iHfId4h3CH6HIogsxaHHd4eAQ5zEBUdHiAxMjtESlFrezPoIech5iHl",
+  "IeQh4yHiIeEh4CHfId4h3SHcIdsh2iECBCwUYFWHHoIegR6DHtEb9wL6G6Me4RvhILcdX8UavB+MHu0CpBufIb0gihsBlS",
+  "CQIPgegByuGfsfxh6HHb4NAQ0yEBUdHiAxO0RKUWt7Fugh4iHbIS0VYQWkHvgCIWC4HY0e3AfQBwEDhB6lG/ce+B7aHAEM",
+  "HhAVHSAxO0RKUWt7Eekh4iHgIVcGLhZi+QKlHmEB6hzQGsIZ5Bf2HgELRBAVHSAxO0pRa3sk6iHpIech5SHjIeEh4CEvF2",
+  "MHph7UG/oCI2K6HY8e8ALeB9IHoiEBnRmbGe0bggjiHogg5B67ILMglRXbGOYZ+B4BDXMQFR0eIDE7Q0pRa3s07CHrIeoh",
+]
+
+end Erdos97Octagon.RawIncidence
diff --git a/LeanPool/Erdos97ConvexOctagon/MasterCertificateData2.lean b/LeanPool/Erdos97ConvexOctagon/MasterCertificateData2.lean
new file mode 100644
index 00000000..aee1970c
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/MasterCertificateData2.lean
@@ -0,0 +1,517 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.LRAT.Format
+
+/-! # Generated packed master-certificate data -/
+
+namespace Erdos97Octagon.RawIncidence
+
+/-- Packed certificate data part 2. -/
+def masterCertificatePart2 : List String := [
+  "6SHoIech5iHlIeQh4yHiIeEh4CHfId4hAQgwGGRZxRuNHdUb+wL+G4sfiR+IH6ce5Ru7HdIFJGPfB8AfqBuQHpwahx6EHu",
+  "EFoyHoIIcd6xLBHuIeiiDXHNMNAQxDEBUdHiAxO0pRa3s17SHsIesh6iHpIegh5yHmIeUh5CHjIeIh4SHgId8hAgkxGWVa",
+  "xhvWG/wC/xuoHuYbvB0lZOAHwR+pG5Ee7RydGogehR6kIekgwh7DHsQe8BIB+h6QHYod7BLjHosg1hzVDQELHhAVHSAxO0",
+  "pRa3s27iHtIewh6yHqIekh6CHnIeYh5SHkIeMh4iHhIeAhWwoyGmYD5xvXG/0CgBypHtocvR0mZeEHwh+SHtUHAYwHmR2S",
+  "GxKlIYoY5yDLGsAewR7xEokZhxqMIPwe/h7kHqYc2Q0BC0MQFR0gMTtKUWt7Nu8h7iHtIewh6yHqIekh6CHnIeYh5SHkIe",
+  "Mh4iHhIQsBMxtn2Bv+AoEcyhu5Ibghqh6+HSdm4gfDH6sboRmfGZMe7xz+HY0gjCDoIMwaBJ8ayBumIcIelhzTHood/B7U",
+  "H5IdjQkBCzIQFR0gMTtKUWt7NvAh7yHuIe0h7CHrIeoh6SHoIech5iHlIeQh4yHiIQwCNBxo2Rv/AoIcyxu6Ibkhqx6/He",
+  "kgKGfjB8QfzRqiGaAZlB7yG40gjiDXBwGAH/4ewCC9IOsZ5h7WHPMUpyHDHpccjQkBCjEQFR0gO0pRa3s38SHwIe8h7iHt",
+  "Iewh6yHqIekh6CHnIeYh5SHkIeMhNR1prB4paAEN2huAA4Mc8RyVHvkg/CDXGsAd2AfkB8UfA/oduyG6IaEZoxnBIL4g/R",
+  "6PII4g7BmPGucelCDXHIkc2B7TH5AJAQ9vFRcbHSMtQUdNT1FVYWsa8SHvIesh6SHoIeQh7hqaHd0cvCGlHNAe2QePHowe",
+  "oRyWHoYaxxauG5wd8Qf/BoIf/h7dGAETPBAVHSMpLS8wO0FESk1RYWtxeyXyIfEh8CHvIe0h7CHrIeoh6SHoIeYh5SGOCL",
+  "IC6xtrzBzNHNUb6B5gRd4crxvIIAGJHo8bmR69GtEezhn7H8wW1xq6GYIfAQpEEBUdIDtKUWt7FfQh8iHxIQM4IGzKH8sf",
+  "zR+vHixr+QKrIQHdG5EI0BvSG4shARIpFRsdIy0wOzxBRU1PUWFrcXsa7yHuIe0h7CHqIZAI8xavG/8emB+dH7AetALOHG",
+  "ItmBT9H4Eg/B2tHNwHlx7SH9wfhh0BEG8VFx0nKC0/QUVNT1Fha3Ec8yHyIfEh7yHuIe0h7CHrIZ4doB3vG7AI3QeYHqgc",
+  "mh7EHKIggweYIOIahh3IHoshgh3VHOsU3R8BB1IyQmFrcXsE9iGGH4cf2xoBEjUVFxsdIycoLz9CUV9ha3F7fQz3IfAh7y",
+  "HuIe0h8RuyCOobAcMUhh/eEwEOHhAVHSAjMDs8RU1Ra3sq+SH3IfYh9SH0IfMh8iHwIe8h7iHsIeshZnG4As8f0h/QH/Ib",
+  "tB4xcEu1GwSwIbMIA48enRuVG58exhwBjiHvHu4c1hnuBaYgyx7aGAEPaRUdIy1BTWFia25xcnR7CvQh8yHyIfEh7yHWGo",
+  "sU4x+EINkaARVDFRgdIygtMzk7P0FNX2FrbnFydHsS+CH3IfUh8yHyIfEh8CGbH6YaAc0egyDPHoAg3BjQGOUc3x4BCjwQ",
+  "FR0gO0pRa3sy/CH7Ifoh+SH4IfYh9SH0IfIh8SHvIe4hKAsIQHS7AtUf0x/SH7ceNHMDthveG4UcxiHFIZcIgiGRIYgesy",
+  "HxHP0boh7LGM8YAckgiB/PGosdmB3lH9Ae3h7dGAELUhAVHR4gO0pRa3s2/SH8Ifsh+iH5Ifgh9yH2IfUh9CHzIfIh8SHw",
+  "Ie8hQXVqKQEMCbge6Rz2G+YbjAOPHNYf1B81dPUCoR6bB5UelB6YHvIF/RytGvUalCG0Ic8e0hjeGNoeqiCZHecc8x2KH+",
+  "ENAQoeEBUdIDtKUWt7N/4h/SH8Ifsh+iH5Ifgh9yH2IfUh9CHzIfIh8SHwIWsqAg0KQnbqHPcb5xuNA5Ac1x/VH7kedTai",
+  "HuUHAfYCyyCVHpkeoR2bH/4dnx+uGpUhtSFo6hqbHdIe0xjbHuUf6BzjDQEJOxAVHSBKUWt7If8h/CH7Ifkh+CH1IfQh8S",
+  "FDd7oedjcrA+gbDtgf1h8LAdobuRuEIZMhjR7/HO8asRnMIPoWlheLIAEKfREbHS06PEtRcQn7Ifoh9CHzIcQdqB6VHJEc",
+  "xR4BD0QVGyMrLzFDSkxSVGJkewyAIv8h/SH5Ifch9iHKIPYe6AKtGvMYjh8BDS8QFR0jKy0xSkxna3sagSL+Ifoh+SH4If",
+  "cheukClhzXGdsZZPUbzQKXGpkab4oGuhwB2xuUFscgjx929BgBBh4uMT1RXQX8IfUhoB6iHqAbAQ9EFRsfIysxQ0pMUlRi",
+  "ZHsMgyKCIoAi/CH6IfkhzSD5HusCsBr4GJEfARFDFRsfICMrLjFKTFJUYmR7fBqEIoMigiKBIv8h/SH8Ifsh+iH4IYQC7A",
+  "KsHgG1Gt4buiHKIJYW+x75GJIf7xu6Gs4b9CABDC0QFR0gIzFKTFFreyCFIoQigiKBIoAi/SH8Ifsh+iEHfu0CzR5omhzf",
+  "GdEC2xlrnRqbGqgfpCAEAwHUINcgkh+sGvoY/B4BDRcVGx0gIywxOkpMUXsnhSKEIoMigiKBIoAi/yH+If0h/CH7Ifohjw",
+  "ayHn7IHu4CtR6xHtEa0hrCHfcfhCCmH5gdpB+9IaUdwxyhGMwg5B7+IIIh8hyyHbAbsSABDGIVGx0jKzJdaGtucgWHIoIi",
+  "kCCVH9EWARFHFRsdICMrLDFBQ11rbnJ5ew2HIoMigSL/If4hpx21Gr8hrBwB2hmiHYogAQxDEBUdICMxSkxRa3s1iiKJIo",
+  "gihyKGIoUihCKDIoIigSKAIv8h/iH9IfwhBAuCAfECtR6BAYkCtB64HtUaxR3aHwN30yGVHIQZhyCEIAHPINMguhr9BsAh",
+  "yBykA5sWpx3JHOEevxqXH4Eh2xm1HYAf3QkBDDIQFR0gIzFKTFFrezWLIooiiSKIIocihiKFIoQigyKCIoEigCL/If4h/S",
+  "EFAYMBDPICth6CAYoCtR65HtUg2SDcIJMG1hrGHbEaeNsfhiGCIdQhlhyFGbQbth2IIJkfmh+FINwZyhSBH98ewSG/G+cZ",
+  "3QkBC0wQFR0gIzFKUWt7NowiiyKKIokiiCKHIoYihSKEIoMigiKBIoAi/yH+IfMCDYQB0x5ucQG7GwaLArYexx3XGtwfAt",
+  "Yg2iDdIJQGshp51SGXHIYZiSCYH4Yg3RnvGYIfjSD0HIoanh2bHfQemR6zIOAJARA1EBUdHiAjLS8xQ0RKUWt7MY0ijCKL",
+  "IooiiSKIIocihiKFIoQigyKCIoEigCL/IQ4ByRuFAXrUHvYGpB6lHqge1SCGHMwapxihHOYZ4hnYArIbth2CH6ogqyCOGf",
+  "wU/xj6Gv4eU5of7x+wII0h/wwBD0QQFR0eICMtLzFDSlFrezKOIo0ijCKLIooiiSKIIocihiKFIoQigyKCIoEigCICyhuG",
+  "AXsP9walHqYeqR7WIIcc1R63HawduhqiHOcZ4xnZAqsgrCD7GsYc/x4BhR+HH4YhiSH9FIAZeK4bgwb+DAEOQxAVHR4gIy",
+  "0vMUpRa3szjyKOIo0ijCKLIooiiSKIIocihiKFIoQigyKCIoEiEAPLG4cBfNYe+AamHqceqh6IHIUcoxzoGeQZ2gKxH6wg",
+  "rSD8GsccAaEW6BvvHs8c+hziHuYewxqHIYUfsx6wHboggA0BDV0VGx0jKy1BTU9RZ2kJiyKGIoUipRqsG6cavCC6INAcAR",
+  "IyFRcbIysvMTo+QUJPX2J2e3wNkCKOIooiiSKIIocihiKIIZ8foR+DGYAS7h8BDS8QFR0eICMtMUpRa3slkCKNIowiiyKK",
+  "IokiiCKHIoYiEwaKAX/ZHucZ3QLrGaYcA7AH3we0H68gsCDKHAL5B1i9HQGPE88Uix+IH5AZhBn0HwEMHhAVHSAjLTFKUW",
+  "t7C5MijCKFIgGyHrEerx6wHrwdvh3nHwEPMhUbHyMrMTo8QVJUYmR7DJMikiKRIosiiiKJIqEfiSGMIYgZyBqJHwEQXRUb",
+  "HR8jLTE6QUNKTWJkexSSIpEikCKNIowiiyKKIokiuR6SHdweqhoBwRrKGoUhgCG8Hd4b3SABD1IQFR0gIy0xQUNESlFrez",
+  "KWIpUilCKTIpIikSKQIo8ijiKNIowiiyKKIokiiCIXCo4BA90e4CHfIesZqhzhAu8ZiRy4HwGJCLMgtCD9B1yWHaMfihmL",
+  "H40f0hS7G8shqx6KIfAeigH3HK4dviCcCgEORBAVHSAjLTFBQ0pRa3sXlSKSIpAiiyKJIgQLjwEY3h7sGfAZihwC/gddAb",
+  "0brB70G44fkB+OGQENQxAVHSAjLTFBSlFrezSYIpciliKVIpQikyKSIpEikCKPIo4ijSKMIosiiiIZBQyQAd8e4iHhIe0Z",
+  "rBzjAvEZixy6HwOLCLUgtiD/B16YHQHSG/EbyBrpHK0ezSGTIYIBsgP8HdYctR3DIKUfjh6rCgEOUhAVHSAjLTFBREpRa3",
+  "szmSKYIpciliKVIpQikyKSIpEikCKPIo4ijSKMIosiBg2RARoB4yHiIeAe7iDpIO4ZrRzkAvIZjBy7H6UfqR+MCLYgtyCN",
+  "GY4fkB/VFK4aixzOIYAIX6odrAK7G8Qd9h+gCgEOMhAVHSAjLTFBREpRa3szmiKZIpgilyKWIpUilCKTIpIikSKQIo8iji",
+  "KNIowiBwEOkgEbAuEesRrjIeQh7yDqIO8ZrhzlAvMZjRyBCGC8H6gfvBvFHY0ItyC4II4ZjiGRIY8f+xzcFIgSzyGBH58K",
+  "AQpVFRsfM0RTX2R7BpkikyKSIsEdkhmSHwENRBAVHSAjLTFBSlFrexyaIpgilyKUIpMikiKRIpAiHQSUAQnjHvEg7CCPHP",
+  "EZA7Magwi+GwIBlR+/IN4Urx3RIQENUhAVHSAjLTFBSlFrezSdIpwimyKaIpkimCKXIpYilSKUIpMikiKRIpAijyIeARGV",
+  "AeQeCtcb8hmxHOgC9hnmIechkByuHrIerx6/H7oguyAF6iCpH60fwxqQFaAZkRlj+h+TH6Yhrh2FHfQe0iGxCgEMQRAVHS",
+  "AjLTFKUWt7NZ4inSKcIpsimiKZIpgilyKWIpUilCKTIpIikSKQIgsfEpYB5R7nIeghkRyyHOkC9xnzGcAfkQi7ILwgAbUa",
+  "hQhkAu8c3RTYG9Mhsx67HcUbuAOZIbwdih++G4gBrB/BIJIZsAoBDF0QFR0gIy0xSlFrezWfIp4inSKcIpsimiKZIpgily",
+  "KWIpUilCKTIpIikSIMASATlwHmHugh6SGSHPIfiAfzH8Eewx60GrYa+Bn0GZ0c2RuYH5QfyyDJILMerx6IIf0gkxmgGb0d",
+  "rB+FH4Eg1CGlBJEcogoBCy0QFR0gIzFKUWt7HaAinSKcIpsimiKWIpUilCIhFJgB5x75GfUZAWYNAokH9B+gHNobiSH+IK",
+  "AdlCG4F50XrCABCl0QHiAsMUFNT1ENoSKbIpoilCKTIt4dzR7bHfEfvRu3Hrseyx0BCU8QHiAsMUFNUQucIpsilSKUIgGJ",
+  "CM8eyx7NHccIux4BDUEQFR0eICMsMTpKTVEloSKgIp4inCKbIpoimSKXIpUiAZsBkAGiApoB5B7jHsEHux66Hr4elhvMHY",
+  "kGkBvZIb8Y3xzeHMEdvRiAH5shniHAHeAdwxuYBgEIfR5RXWFrcXsFnSKWIskYyxi6HgEQNRUXGx0xPT9WXV5hYmhrbwmg",
+  "Ip8inSKbIqUb9RyxINEgrRQBFkcVFxsdICMrLDEyOj0/Q01RXV5ha28ZpiKkIqMioiKeIp0inCKbItYcxB3uHeMdnxylAt",
+  "wh+R+ZG5MbAaEhzxu+F/QehB+jGQETXhUXGx0eICMsMTo9QEpNUV1hayCnIqQioyKgIp8iniKdIpwimSK9HsEexB6/Hu8d",
+  "oByeAfof9AedHQGFIfgcoiHQG6Ab+x71HpEGnxykGa8Uhh8BE10VFxsdHiAjLDE6QEpNUWFrcXsLoiKhIpsimiIEkQfUHg",
+  "GuCKMZwR4BCx4QFR0gIzFKUWt7NqkiqCKnIqYipSKkIqMioiKhIqAinyKeIp0inCKbIpYBCR2hASqoAqIcoAEG/B+SB/0f",
+  "9gcBkAhv0h6cHfMazRj0Gp4Gwh7JG+QbpCHjCMMY+hzOG4chnh/WIPoZkx22H64guh3bDgEOQxAVHSAjMUFKUV1ea3szqi",
+  "KpIqgipyKmIqUipCKjIqIioSKgIp8iniKdIpwiCgEeK6IBqQKhAfMh9CGiGaQZtRznHdgbnQi2Hrce1h7MH/Mb5BunIKQg",
+  "oiGfIbcfIfsZiRqfH6sgix3mFP4e0SDrCQEOMhAVHSAjMUFKUV1ea3szqyKqIqkiqCKnIqYipSKkIqMioiKhIqAinyKeIp",
+  "0iLAsCH6MBqgLyHvQh9SGjGaUZthzoHZ4Itx64HtceoyGgIc0f5RuoIKUgAbofgCG5H+0U9BbVHOEhoB+TH70dhh/rCQEO",
+  "NRAVHSAjMUFKUV1ea3szrCKrIqoiqSKoIqcipiKlIqQioyKiIqEioCKfIp4iAS0MAyCkAasCnhzrGuka8x71IaQZphm3HO",
+  "kdlyHiIZ8IuB7YHvQbvwLOH/Ubvx2pIKYggSG4H+schR/9GZQf2CDuCQENXhAVHSAjMUFKUV1rexisIqsipiKfIg0EIaUB",
+  "rAKkAaUZpxm4HLkeuh7nGwL2GwGlH6Qf/hmBGrkfARNDFRsdICMsMTo8QUpOXWtucnl7EKwiqyKqIqYipSKkIqMipQEl9i",
+  "DeGuQhvxamIZ4h4xoBDF0QFR0gIzFBSlFreyKuIq0iqyKqIqgipiKlIqQioyIwDwYjpwGuAvYepxmpGboc7B2iCNEfqSAC",
+  "rRquGq0cAfwgux//IIAa1RqlHwELQRAVHSAjMUpRa3sZqyKpIqYipSKkIjEQB6gBrwL3HqgZqhm7HKMI0h+tIKogAZcIrh",
+  "qvGtsg3SDvHAELYxUbHSMpK0NHa24IqyKpIqcipiKCGsodwx2yIAEQXRUbHR8jKy86Q0dNT2JrchSxIq8irCKrIqgipyKk",
+  "IrAcvRy/HqUIqB2yHL8fvwenIfsWuiC8II0XAQoxEBUdICNKUWt7N7MisiKxIrAiryKuIq0irCKrIqoiqSKoIqcipiKlIj",
+  "SrAfoeJwOGIJwHhyATsgIK/CH9Ie0brRm+HKsZnCGRIdEd6SECAZoIedwesRqyGrMcqB+rH+Ag3iDAH5QapRy4IJkfjB/5",
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+  "+RJL4hvSGmI9Mi/x8BvB6oIOEj7hEBCzUQFR0eICkyP1FrKb8lviW7JbkluCW3JbQlsiWxJQ1NIzisBLcEliOVIyeYI74L",
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+  "W1JbQlsiWFIke3BPckhCWgIJ8gvAu/C/4BmyCsHvEftSLXIagjkxnAHMsg0CIBE28VFxgbHSg5PT9BS1FYX2FrdHoQvSW6",
+  "JasEtR6VIr0LwAvpG5UcqSO2CcAhvgmMH40flCQBCy0QFR0eIDI1P1FrNsIlwSXAJb8lviW9JbwluyW6JbkluCW3JbYltS",
+  "W0JQNQJjsPrwS6BL4LwQuAAiqbI5kjjiXmC5YilSKiIKEgAv8huB9s1x/PCpsdAeUh2SHMI7cJhR/JHoAg0CKWJKIiiSCv",
+  "EAEKNRAVHR4gMj9Ray3DJcElvyW9JbwluyW6JbkluCW1JVEnPBCwBLsEwguBAiucI5ojjyXnCwG6BIAi0AqSIARt+SSWIp",
+  "cigCD/H6MgAtohzSOGH84gqyPvG7gYlyQBCSAQFR0eMj9Ray3EJcIlwSXAJb8lviW9JbwluiW2JbEEvARSkCUoPYICESyd",
+  "I5sj6AsB2iTZJIEi1x+7BMAfoB+5CfskiCWYIuEgsB7nI9shtyCQGp0aziPLHpgk6B4BD10VFxsdISkqMTU9S1FZcR7DJc",
+  "IlwSW/Jb0lvCW7Jbgl7h6AIZUg7x6sIesi6SKuH+AbkSWEHrkk7CTvIZQisgviHpAfkR/SCK8k7xkBET0VFxsdHiEpKjE1",
+  "S1FZaWtxF8MlwCW/Jb4lvSW8JbsluSW4Ja8f6iKiIoUeuQu6JAGtC/Yg5CGGAc4chyHrIQEOWRAVHR4pKjI1OD9RaWsTxy",
+  "XEJcMlVbQEA78EryEvuguEAo4jAe8LvCSSH5Mfyx+jJAELeh4hKSoxP0tRa3kGxAvHC4YCmR74IIgBAQ5eEBUdHiExNT0/",
+  "UVhpayjJJcglxyXFJcMlwiXBJcAlvyW+JbwluyWwC98h4SHmIckkhgLbJF7BBLYEiyHOH/gglSWzCeQb8CTtJJAjmSKKIM",
+  "gchCGwI/Mh1CD0GeIiAQ1pEBUdHikqMjU4P1FrKcolySXHJcYlxCXDJcIlwSXAJb0lvCVYBsIEtwSWJTLlGwOaIocCAoMi",
+]
+
+end Erdos97Octagon.RawIncidence
diff --git a/LeanPool/Erdos97ConvexOctagon/MasterCertificateData3.lean b/LeanPool/Erdos97ConvexOctagon/MasterCertificateData3.lean
new file mode 100644
index 00000000..25a0febe
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/MasterCertificateData3.lean
@@ -0,0 +1,517 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.LRAT.Format
+
+/-! # Generated packed master-certificate data -/
+
+namespace Erdos97Octagon.RawIncidence
+
+/-- Packed certificate data part 3. -/
+def masterCertificatePart3 : List String := [
+  "vyQB5x76IL8J6CHmIYoB8yCRI5se7yGVH5sgtCSFHakc3yIBDCoQFR0eKTI1OD9RaxvKJcclxCXDJcIlwSXAJVkHwwS4BJ",
+  "clM+YbAZoinCKyIc0LxwuWHpUeyCPXIOUi4iLMIAELOBAVHR4pMjU/UWs2zCXLJcolySXIJcclxiXFJcQlwyXCJcElwCW/",
+  "Jb4lCMQEuQRamCU05xsBiSKGIsEkyAvLC4oCoh7yIvAijSGHIZ8Bvwv3Ieoh8SSXH50gxwKIINYZtiTBIr0e5SPhItQc7y",
+  "OcIuIg5xIBBygbHR8gIisEyyWPJZAlwB8BD0EVFxseISYpKjI5P1FXaQ/NJcwlxiXFJcQlwyWKBYcCwQvnH/Qk4CDRGYQe",
+  "3iIBD28VFxshJipRV19haWtxewrNJcclxiXFJcocxx77IMQJ9STSGQERexAVFx4hJikqMDI5P0tRaWsX0CXOJc0lySXFJc",
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+  "0yIhAccE/gcL4yfuJ9UmBpoj5CLMJY4omCOgD7AlqyiuKIYjkyWBIoQi9yGTJ/4l1B2GINUlAQwjEBUdID9BSkxRZGs1iC",
+  "mHKYYphSmEKYMpgimBKYAp/yj+KP0o/Cj7KPoocUT5BYAIAYQPhw/IJdIo0SjqB5EklSPjIpEj6iKQJ5Inhwn7DpglmSWd",
+  "IZ8hqiaBJv4ljiijD4Yg0R+gA9sllCbrJqYkyCOfEQELZBAVHSA/QUpMUWs2iSmIKYcphimFKYQpgymCKYEpgCn/KP4o/S",
+  "j8KPso+gVFgQgCcoUPiA/JJdMo0ijrB5Yj5CKSI+siiAn8DpklmiWrJqEijyiCJv8lhyAB/wu8A7AhriPXJ5EniifXJfkj",
+  "qiS/Hewm+hABCyMQFR0gP0FKUWRrNoopiSmIKYcphimFKYQpgymCKYEpgCn/KP4o/Sj8KPsFAUZzgggDhg+JD8olxCTtIt",
+  "Qo0yiTJOUikyPsIvEOtyWSJ5Qn/Q6bJeUgrCbEIt8nkCilD4MmgSb6I6kmogPnHu4lsifII58RAQxZEBUdID9BQ0pRZGs1",
+  "iymKKYkpiCmHKYYphSmEKYMpgimBKYAp/yj+KP0o/AUCAXRHgwgEhw+KD8sl5CHFJIEMvgPVKNQomCPmIpQj7SLyDrglzi",
+  "P+DpwlsSK4J60mxSKcJpEogibqILYh5iWMJ+8l+hABC0MQFR0gP0FKUWRrNowpiymKKYkpiCmHKYYphSmEKYMpgimBKYAp",
+  "/yj+KP0FAwJ1SIQIBYgPiw/MJeUhxiSCDL8D1ijVKJkj5yKVI+4i8w65Jf8OnSWyIq4mxiKdJpIohSaDJusgtyGNJwHaJb",
+  "Qn9CH8EAEKZBAVHSA/QUpRazeNKYwpiymKKYkpiCmHKYYphSmEKYMpgimBKYAp/yh2SYUIBv4F1yjWKIkPjA/NJZoj6CKW",
+  "I+8ijAmAD50lniWvJpMoBMciiyOGJoQmA8ADgwyyI5UnjicB4if4JPkk5R2gD6Am6CX7EAELQyIzP0FNT19icX0EjSnnIf",
+  "4jnyYBCUEQFR0gP0pRay6OKYwpiymKKYkpiCmHKYYphSmEKYMpgSl4S4cICNgogAaLD44PzyXxIpgj6iKcI4IPoCWfJY4J",
+  "sSaVKALkIMIDhQy0I98glCfJHOsJAaMmoSafJJ0k3SUBCWQQFR0gP0pRaziQKY8pjimNKYwpiymKKYkpiCmHKYYphSmEKY",
+  "MpgikBTIgICXnkJvkN4yb3Cekm2ijZKJAjyiKCBvkn7iePD9AlviHyIpkjnSOcIsoPhyaJJqAlmCeaJ48JqCK3ItIj1SjZ",
+  "H8Mb9yW4J84jkREBCCAQFR0/SlFrMJEpkCmPKY0pjCmKKYkpiCmHKYYphSmDKUx6TYkI2igC5Sb6DeQm+AnqJssigwb6J+",
+  "8nkA/RJb8hmiOeI50iyw+hJZAJjyO4IgHmIKIm1ijGH+El4CXUI+8jvicBDCMVGx0hKy1BRVFrewqRKYopiSmHKZAfwyHr",
+  "IN0Jnib5IQEOJhYbHR8iMz0/Rl1iZ2sHkimQKf4l/CXNHaQmihsBEEMWGx0hIistMzk/QVFdZGsbkSmOKY0pjCmLKYopiS",
+  "mGKckhvyF9hiPfCdIkhyO3JpMPhw/PJZgokyOmJYMksicBwCKuCgENLRUbHSErMz9BSkxRayiTKZIpkSmPKY4pjSmMKYsp",
+  "iimHKeAJft8o3ij3B7gmuya9D4gj0ySID/IilCPwIqcllA+FIpwo8QkDAeMnvSG9KLUj8yHjJaQkryCzJwENIxUbHSErNE",
+  "FRXmt0exKVKZQpjymOKY0piymIKYsflB9/jCaOJoYi5yDHIaYloiaQIAEMbxUbISIrLDRRXmt0EJUpkimPKY4pjSmMKYAB",
+  "hyKiI40muSi8KIUfsiG0Ib4nAQlMEBUdP0FKUWs4mCmXKZYplSmUKZMpkimRKZApjymOKY0pjCmLKYopkAhUigERB+Io4S",
+  "j6BwPGJcIl9SKXI/Mi2CXjIQIBiw+kJagluya/Jp8orQ/XH5InjhzmJ+knqyaqJt8iqCSGH6ckwSi6J44mryTjEAEKYhAV",
+  "HS0/QUpRazeZKZgplymWKZUplCmTKZIpkSmQKY8pjimNKYwpiykSCIIBkQgBVeQJ4yjiKIwjvCa/JtgkjA+YD4kioiO2J7",
+  "cnpg72IpkjvSWgKKslkQbFHOYnwSEHrSarJsEoqSSHH6ckmhy8J48mpBEBCS0QFR0/QUpRaxaXKZQpkimPKRMJgwGSCFbl",
+  "Cb0mwCaND4oioyOnDvcioSgBwSCpJK0nAQo1ISwuMzo8P0FKC5kpkymSKZEpqA7ZIcAovSicBuMioQYBDjwVGx0hKywzP0",
+  "FKTVFrE5oplimPKcklyCWOAdYkmA/XJechqQ7DJo8PjCKnIwGTJpIm6iMBDW8VGx0hKyw9P0FRa3sdmymXKZYplSmUKZMp",
+  "kimQKY8pjwHXJfoi5yioI/sojSIFnSOvJZwjxiXoIZMmkh/CKL8ozCG3CrohARRkFRsdISs0OT0/QUNFUV9ucnd7fRedKZ",
+  "wpmCmWKZUpkynpIc8hsiOOD5EPlCbYJf0kjB8GWq8mrQ+fJ6YixyjSGAEIQRAVHT9KUWsvnimcKZspmimZKZgplymWKZQp",
+  "kymRKZcIW4gBGA7pKAcFA/oinyP8It8lApIPqyXxJMYmoQ+3AeohtA+XBt4fmSfMH+wn0CEB/CDBJKQnsCanIoom9BoBCG",
+  "IhIisuZGtuCJ4pmimoJ6onkw+mIqgiyCgBD2QVGyErLjM0OUNER1FrbgyfKZspmSmYKZcplimaJpYfAbAkuiSiJwEOOxUb",
+  "HSErMz9DR01PUWskoSmdKZwpmymaKZkpmCmXKZUplCndJd0iiwH7Ip4PhCOvI6sjlQ+yJfgkoCOSJLoBzyUB0R7EHrMmsC",
+  "S6JIAnliXPJ80njSEBFVUVGx0hKzEzNTg/Q01PUWJpa3F7fBOiKZ8pnCmbKZopmSmRH5wlmB+MAd4i6QfsKLQmpiCAJ4Ei",
+  "+iWVGwERLRUbHSErMz9DR01PUWJka3seoymiKaEpnymeKZwpmymaKZkpuCPvCY0B3iLfIgLqB/YksQ6iI8En0iGUKOIhAZ",
+  "kmyCS1Jr4kxifNHQEPbxUbHSErMz9DR01PUWt7HKMpoimfKZ0pnCmbKZopmCmUJI4B4CXfIuAi7iiwI5Uisg7TIZUo4yEB",
+  "xyjRJcoouAnwIZgdmiYBDHMVHR8xMzU/Q01PcByiKaEpnymeKZ0pnCmbKZopyiS4KJgjuSjgIu0BqA+iD54I2x+3I5Yn7S",
+  "XnJb4k7AeEKKQjB5APAQdKEBUdP1FrIqQpoymiKaApnymdKZwpmymQASBjnwgWCJAOjgrhIqcjhSiQKAXnJbQO1SGXKAKa",
+  "D/kkqQ/yIQGhJ6QnmxwBBUwxMzVOCqQpoCmfKZ4pnSlimALPJM4h9CcBETwVGx0fLTEzNDpBTFJfa299EqgppymmKaMpoS",
+  "mfKZ4pnCnRJZkimSi6IMEi3iG9Jp8mtSbyHwEPIxUYGx0rLThFS1JcYGRrG6kppymmKaQpoimhKaApnymdKYMh9iKOD88l",
+  "nQ/HJ8gnkwGJHPQotibOIYMj/yWBJugj6iOOJgENMRUbHSArMz9BS0xRayapKagppymkKaIpoSmgKZ0plAHlJfQo9SjoJa",
+  "cPqg/NJp4PmyK2I7Mjqgm9JQNl0iICqiO0KAHsD/Ao3gPSIP0e0iH7JY4m7CMBBkQzOUFMTgeoKaQpoimhKfsn8yfXIQEO",
+  "dxgoNDk9P0FLUV9kb30MqympKaQpoymiKZcI1R+BJpUipCajJschAQ4jFRsdICswP0FLUWFrbyWtKasppymmKaUppCmjKa",
+  "ApoiKXAYgl6CVq9yj4KOsluSO7Dp4irQ+tCcAlrCSLI4chwyO1KALCJMYDAYoIhyPlI7omkCbLJAEKbxAVHSA/QUxRazev",
+  "Ka4prSmsKaspqimpKagppymmKaUppCmjKaIpoSmYAWsIKKcIuCOfIrcj6SX4KPkouiOrD64PrgnBJQS8DoYnriOMI7YoAw",
+  "H0KOID1iHOI4Ef+yeLCP0luiLuH/EjwCaVJ5Qm0iSYEQELIxAVHSA/QUxPUWs2sCmvKa4prSmsKaspqimpKagppymmKaUp",
+  "pCmjKaIpAZkBbAkpqAijD/Ei6iW8I/ko+ijtJawPrw+vCcAl0iaJIYUhvQ66J7gnryOuJI0jtyipJqcmjh7EJNobhCjIA4",
+  "MmoCTuI9gnvxEBE0MWGB0iJykzPT9BS09RX2FreH0fsCmuKa0pqympKacppimkKaEk8yK8IpoBsSPlJLAjwiapCKIp3CXw",
+  "HyqOI/wJ0ya4KNwhlSaUJvQj8yP/JQEKTxAVHSA/QUxRayyxKa8primrKaopqCmnKaQpmwEDbisLqgilD/MiviP7KPwo7y",
+  "XsJbEJwiWuD7EP1Ca/Do8juSgC5QOoDNEjAYYo1CLpI5QmsxzEJsUmwSTCJIAmAQlMEBUdID9BUWsVrSmsKaYppSksDKsI",
+  "nAHwJe0lrw8Epg/VJsAOAcQlvyWmI7Ij3iUBCSMQFR0gP0FRazi0KbMpsimxKbAprymuKa0prCmrKaopqSmoKacppimdAQ",
+  "FwLQ2sCOsiVYAjySP9KP4o8SXuJbMJsw+/I+4kpw/AJeEl1iazIbIhkSO7KOEn3yetJqwmyCTMIYUhzAOHKNMm8SC5J4Ym",
+  "niWDEQEKdhAVHSA/QUNRaze1KbQpsymyKbEpsCmvKa4prSmsKaspqimpKagppymeAQFxLg6tCALoA6sM/ij/KPIl7yXsIp",
+  "coVoEjyiOYJrQPmSa0Cfcj7ySOIvgjwCODJpwP4iWdJ4YmqA+UJIUiwCK9J8YmmiTcEAEJQxAVHSA/QVFrOLYptSm0KbMp",
+  "simxKbAprymuKa0prCmrKaopqSmoKQOfAXIvD64ImChXgiPLI+0i/yiAKfMl8CW1CbUPwSPwJI8iqQ/CJeMl2CaTI70owS",
+  "IC6QOsDMcm0CMB9yOEJpwn4hybJsAnmiTcEAEIQRAVHSA/UWs5tym2KbUptCmzKbIpsSmwKa8primtKawpqymqKakpoAFz",
+  "MBCvCIApgSn0JfElsw+2DwTxJIMj7iLMI54PtgnkJcEllCOqD9kmvigBiijOHrIeiiKZJrwnuCedJs8hiCHKD4smhSbrIr",
+  "QlrybcEAEKIxAVHSA8P09Raze4Kbcptim1KbQpsymyKbEpsCmvKa4prSmsKaspqikBoQF0MRGwCIwnkSeLJ8AjxCP5Iu8i",
+  "wiOCKfIlgSm3CcgloCiVKOAl3yWNIZEhqCTmIdcm1iTNIeEFrSaxJsIn8g+5IJ8mmyf4I7wRAQk8EBUdID9PUWs4uSm4Kb",
+  "cptim1KbQpsymyKbEpsCmvKa4prSmsKaspdTISsQgCogHBI8Uj+iLwIsMjgynzJYIpjSeSJ4wnuAnJJaEolijhJeAlqSTn",
+  "IeIF0SLzD6koAa8M6BzwI64mwye6IN0k3R2bJpwnsREBCSMQFR0gP09Razi6KbkpuCm3KbYptSm0KbMpsimxKbAprymuKa",
+  "0prCkBA6MBdjMTsgiXI7ojjieTJ40nwiPGI/sixCOEKfQlgymiKJcouQnKJbkP6CHaJtsm2SbYJI8huSP0D8QnwiezJrEm",
+  "gh+KJuInrhy4EQEJWRAVHSA/T1FrOLspuim5Kbgptym2KbUptCmzKbIpsSmwKa8primtKQECBKQBdzQUswjuA7EMmCO7I4",
+  "8nlCeOJ8MjxyP8IsUjhSn1JYQp/iOjKJgo8QS6Ccslug/yI6skuiOVIp0m6CfMJq8ciiahJ8sipxEBCE8QFR0gP1FrObwp",
+]
+
+end Erdos97Octagon.RawIncidence
diff --git a/LeanPool/Erdos97ConvexOctagon/MasterCertificateData4.lean b/LeanPool/Erdos97ConvexOctagon/MasterCertificateData4.lean
new file mode 100644
index 00000000..c1fca57b
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/MasterCertificateData4.lean
@@ -0,0 +1,517 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.LRAT.Format
+
+/-! # Generated packed master-certificate data -/
+
+namespace Erdos97Octagon.RawIncidence
+
+/-- Packed certificate data part 4. -/
+def masterCertificatePart4 : List String := [
+  "uym6KbkpuCm3KbYptSm0KbMpsimxKbAprymuKQWlAXg1FbQIkCeVJ48nxCPII/0i8yLGI4Yp9iWFKbsJzCWkKJkouw+sJO",
+  "oh9g8CsgzzIwOZI98lliLNJgGMJo0m5CfnJ7AczCKkJ6kRARFkFiYxNT9ER0tNVF1iaWtucQq7Kboptym0KbMpxyeyJvEg",
+  "viCkJgERIxYxMzU/REdLTVRdYmlrbnoNuym2KbUptCmzKfshug+9DwHMIqYmpCboIwEIPBAVHSA/UWs5vym+Kb0pvCm7Kb",
+  "opuSm4Kbcptim1KbQpsymyKbEpAwh7OBi3CKgBrwKTJ5gnkif5JfwliCmJKdQjiyO+D74J7CWmKJsobMoj6AWvKPkPyyXq",
+  "Hfog1yIBtQzQJoEk4yTCIMknoSadJ4Ik7hABCCMQFR0gP1FrOcApvym+Kb0pvCm7KbopuSm4Kbcptim1KbQpsymyKQEJBK",
+  "kBfDkZuAidI5QnmSeTJ7AC+iX9JYkpiinVI4wjvw+/CaconCht4SW5JMsj4CbeJOEm+g+nD74h6yftJ7kmuCa2G6YmoyeA",
+  "JP4QAQcgEBUdP1FrKcEpwCm+Kb0ptym2KToafaoBuQj7JYopiym9D8APAgqaJ5UnmyL8JKgPBbECjSOoKJ0obvsPAbcM+C",
+  "PoItIm/CCSJpAmhCSCJKMmAQljHR8zOT0/YGQHvCm6Kbcp0SS1D9Un6SABB0EQFR0/UWs6wynCKcEpwCm/Kb4pvSm8Kbsp",
+  "uim5Kbgptym2KbUpAhysAX88uwj9JYAmlyWMKY0pvw/CD7YP6SazIssjziPQDtUloCPCI9sBAeAn4Sf5H60InyaFJNck6C",
+  "iCJRe1H+4n5ie5JuQZjyisJuQkzxEBDEwVGx0hKzM/QEtRay3DKcEpwCm+Kb0pvCm7KbopuSm3KbYptAKBJv4lrQGNKY4p",
+  "hSPQI8wjwA/DD6EorCi3D+wP6CahI8soI9QlwyO0JO8lmSHJGuYeySfVJvcMoiGDIJcmpiatIQEQPBgbHSEsMzpDR0tNUW",
+  "txfRXEKcIpvym9Kbwpuym6KbgprgHyJdIO8yHpJu4FtSi4D/AdgCGDIqEc1iYBC28VGyErLDREUVxrEcQpwSm+Kb0pvCm7",
+  "Ka8BtiLRI78mtB+7H+go6yjhIeMh7icBDiMVGyErOT1HS01RXGtuDcIpwSm/Kb4pxR+8H5MFug/yJ9Qi9B3MJ4UeAQlTFR",
+  "srMzlDR1wbyCnGKcMpwCm/Kb4pvSniJNgk8yGhI/YhuiOvD6wP6ye2H4wniyehJ4sLpimsCbEBvya4D8YiAQh0OT0/R01y",
+  "egXCKbEnryfID/YfAQY/EBUdUWsyySnIKcYpxSnEKcMpwinAKbwpswHCCJMpBwmGASNDhCaHJsYPyQ8GgSOWI98jsSimKA",
+  "XDJKcj6yWxDwS9D9sl7ibiAQIBA9sm2Q/jJMsnviX3J/Un5CPzKO0iAQsyGCE7PD5BZGt0exDJKcgpxynCKcEpwCnXKMEo",
+  "viiFIugHwCasJJ8mnibtIwEGRDEzQUpMB8gpxCnCKcEplSidKPghAQY1MTNBSkwJySnFKcQpwynCKQHzIfQkmygBDCMVHR",
+  "8hLS8xM0JvfRHNKcwpxinFKcQpjCKAIaEg/iDCI50gxCbaJsYIySHiIbUPAQw8FRsdISo+QUpMUWsrzinNKcwpyynKKckp",
+  "yCnHKcYpxSnEKcMpwinBA/cPjgr3JfYl/SW4AZgpkib2Jpoiwg+/IgQDAr0oxSaEIuEfmSjnDwH5KPki4g/yH+EmySeWGQ",
+  "EKYxYbHTM7PUZdawTNKZ4elSG1JgEKQxAVHSpBSkxRazfRKdApzynOKc0pzCnLKcopySnIKccpxinFKcQpwykHugGMAckI",
+  "lCaYJgKaKZsp4Aq6I+Mj9Cb3JuUo1ij7JfYlxA/8IcEimiiWKAGCIu8n7ieMHoQh8yPiJqQm8iSTJMcmxQjpD7wm6SLiEA",
+  "EJTBAVHSpBSlFrLdApzynOKc0pzCnJKcgpxynGKcUpuwGNAcoIlSaZJgicKQGjKJwooCj6IQPhCrsj5CP1Jvgm5ijXKPwl",
+  "9yXFD+oP0yPCIuodyCa6JLomlyHvJ4Uh+SeNHgEHTDU7P0JGTwTPKaEopyiTIwEOQxYYISoxMzVBSk1RZHQY0inRKdApzy",
+  "nMKcspyinJKcgp+ySAIoki2iWbJskmnCjwIb8muCa5Ju0L9yj4KJEjAQlHISIqMTVBQkoL0ynRKcwpyynKKeEf+yH4KP8o",
+  "pSicIwEQNRUWGB0fISoxM0FKTVFkdArSKc4pzSnMKZQiAgGjKKsokCMBDDwVGx0hKj5BSk1Ray3WKdUp1CnSKdEp0CnPKc",
+  "4pzSnMKcspyinJKckDlgrAAaEpoCmaJv0m/ibZD8oPoiLHIgwBzibFKM0mkSPpH4wipSTmJewlhCYJgSn4IuoP6SD0J+km",
+  "mhkBDWMbHR8zOz1DTU9gZGsF0imdIcsP6yf3IAEKYxsdMzk7PWBkawbTKdEpzinoJJ4h7CcBCiMhKjA0PkFHTU8N2CnXKd",
+  "Ip0SnQKc8p9w/fKO4o6h3yD/colyMBDEQhKjA0PkFCSk1iZA3aKdkp1ynTKdIpsCjSJtQmqygB7SbvJvskAQ0jFR0fISYq",
+  "LzA0Pk1pLNsp2inZKdgp1ynWKdUp1CnTKdIp0SnQKc4pow7hKJsK+Q/DBPko1AjeI4Am6wriAaUp7yPqJcUO6yXAD/8m3C",
+  "TrJKAmnyaMIfon/iOvJpwk7CToJokovxsBCEEQFR0qSlFrOd0p3CnbKdop2SnYKdcp1inVKdQp0ynSKdEp0CnPKdUIxgET",
+  "pimnKZgBoCakJgsG7ArGI+8jgCeDJ9AP4ijjAc0iBPsn+if/I4kdApcj7CXyJaoohSIBhCnxJu8mhyneI58e7STEJoAowy",
+  "TvEAEJORghMTU7VWt7Cdop1SnUKdMpvySYIrImsSaAJAEQYBAdHyIxMztAQ0dNT1JkewzfKd4p2SnXKdUp0g+mJ8Ui8Cb+",
+  "IPgk8icBDzUQFR0hMTtAQ0dNT1FrexzfKd4p3SnZKdgp1ynWKckBuSMW2AipKbokySO5JNUmAtMohiWeIgGEJ+wi4g/xJv",
+  "gklSDQJwEOPBAVHSE7QENHTU9Ra3sK3inZKdcp1ikXoAoBzyjXKI8iAQojISoxOUNHT1FxE+Ap2inZKdgp1ynwHYAlhieI",
+  "J5Qn/yj+KM8P1Q/aCJ4jywHqI8kKAQ05HR8hKjE9Q0dNT1FxBuEpAacB5SPPI4YpAQ8xFRsdISo7PT5DR01PUWsP3incKd",
+  "op2SnzCs0BiCfXD9QiAacDDIEogiiOHQELVhAVHSotSlFka2825SnkKeMp4inhKeAp3yneKd0p3CnbKdop2SnYKdcpCKAB",
+  "zgEb3QisJqgmzArODq8primfI+cjzijDKPklBOMjziMB9yP0Ctwm3ibqKOsB1SDKB+Uk/Q/2Jo0oiCmEIf4kDMIkxyaIEg",
+  "EKLRAVHSpKUWRrbzfmKeUp5CnjKeIp4SngKd8p3indKdwp2ynaKdkp2CnPARwJoQHeCK0mqSbNCs8OsCmvKaAj6CPPKMQo",
+  "+iUF5CPPIwL4I/UK3SbfJuso7AHWIMsH5iT+D/cmiSmFIf8kDQHKJJcjyCeKEgEHRBEdH0FCSgTjKbcouCilIwEHKhAVHU",
+  "pRazLmKeUp5CnjKeIp3yneKd0p3CnbKa8mqybRAR7gCLIpsSkLzwrRDqIj0SjGKKMBB9Ej+iP3Cp8G2CLfJuEmBO0o7gEC",
+  "gRCRJqgFjCmPKeog5yCQJMommSO2HrYmhijiIgENRBUbHR8rLTFKTFJifRPoKeUp4inhKd8p3imyKLooxCivKB20Cv0j9i",
+  "aAJ4ElsiDpIMcnAQs8FRsdKz5KTFFreh7pKecp5CnjKeIp4SngKd8p3SncKZImkSaYJqkK5g/cAdEK3SP9Jf4l+yCAIQGH",
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+  "EeMN+wyaKPsSuRPAKOMSAs4pgSuEKwGtJrsn+ymhFwELVhsdICNDSlFZaWs2/Sz8LPss+iz5LPgs9yz2LPUs9CzzLPIs8S",
+  "zwLO8sqwLmBAEtYwiyAakClQWeKp0qnCrYLNcskSjVKQaVB8EqwCrmEeQNmyiXDvQlsBO6E7gm/SfhKeIp/BLjKpApiing",
+  "J7Ak/SnAFgEKaRsdICNDSlFZazf+LP0s/Cz7LPos+Sz4LPcs9iz1LPQs8yzyLPEs8CysAucEAi5kCbMBqgKWBZ8qniqdKt",
+  "ks2CySKNYpB5YHwirBKucR5Q2cKNYo9SWxE7sTuSb+J/0S4SrkKpEpiynCKAGvJugo/im/FgEKVhsdICNDSlFZazf/LP4s",
+  "/Sz8LPss+iz5LPgs9yz2LPUs9CzzLPIs8SwDL2UKtAGtAugEAaAqnyqeKqsClwUI2izZLJMowyrCKugR5g3RKZcH1yj2Jb",
+  "ITvBP/Jv8nnSj+EoQrhyuSKYwp4ynDKOInrCvDFgEJShsdICNDUVlrOIAt/yz+LP0s/Cz7LPos+Sz4LPcs9iz1LPQs8yzy",
+  "LK4C6QQwZgu1AawCmAWhKqAqnyrbLNoslCiYB54oAtIpCcQqwyreK9cr5w3YKPclsxP/EoUriCvEKOcSBPEr6iaTKQGxJr",
+  "8n/ynCFgELVhsdICNDTFFZaWs2gS2ALf8s/iz9LPws+yz6LPks+Cz3LPYs9Sz0LPMsrwLqBAExZwy2AbsprQKZBb0Ciyii",
+  "KqEqoCr9EoAT3CzbLNYilSjZKY4SxSjFKvEFmQfkKucq6BKsKa4r+CW+E/cnnyjfJ+YplRcBCmkbHSAjQ0xRWWs3gi2BLY",
+  "At/yz+LP0s/Cz7LPos+Sz4LPcs9iz1LPQssAIC6wQyaA23AbwprgKMKJoFvgKjKqIqoSr+EoET3SzcLNcijxKWKNopxijG",
+  "KvIFmgflKugq6RKtKfklvxP4J6AoAbMm7CiCKpQXAQlMGx0gI0NRWWs4gy2CLYEtgC3/LP4s/Sz8LPss+iz5LPgs9yz2LP",
+  "UssQID7AQzaQ64Ab0prwKNKJsFvwKkKqMqoir/EoIT3izdLNgikBKXKMcoxyrzBZsH6hKuKfolwBP5J6EoAdUpiyuIK9Ad",
+  "giqwK+YnlhcBD1YWIycrMzk9Q0VLTVlcaQuBLf8s/Cz7LPos+SzdJpQo6SmxK8AdAQlpGx0gI0NRWWs4hS2ELYMtgi2BLY",
+  "At/yz+LP0s/Cz7LPos+Sz4LPcsswICBe4ENWsQugGxArwmmifUJqYEwCTCKb8pwQLQIp0FpCrgLN8shA3JKucokhKEE5ko",
+  "kCfCE+sq6CrJKJ0HkSneJgG2Ju8ohSqzFgEJVhsdICNDUVlrOIYthS2ELYMtgi2BLYAt/yz+LP0s/Cz7LPos+Sz4LLQCAw",
+  "YB7wQ2bBG7AbICvSabJ9UmpwTAKcICkCjRIp4FpSqmKuEs4CyFDcoqhROTEpoo2CmRJ8MTyiieB44rkimLK98msyvqKeMn",
+  "thYBCCMbHSBDUVlrOYcthi2FLYQtgy2CLYEtgC3/LP4s/Sz8LPss+iz5LPAEN7UCbRK8AZ8FswKoKqYqpyqbKOIs4SyfB6",
+  "UoAbgmhyqKKoYqB7sQwwKRKNwigxOGE5QSyyrLKP4l7hIC2SmMK8YnBMImhyiYKbYWAQhBGx0gQ1FZaxiALf4s/Sy2AvEE",
+  "OAFuE70BtAKgBbsH/g/jLN0isyXLJ6IOhBOHE80ozCjqCwEKLRsdIClDSlFZazeJLYgthy2GLYUthC2DLYItgS2ALf8s/i",
+  "z9LPws+ywCtwIB8gQ51A38Jm8UvgH/D7UCzSrwDfIRoQXGE8wn/ybjLOEogCa8E+Up5CmZKOImiBOcKZ8n7intKc0o8BK2",
+]
+
+end Erdos97Octagon.RawIncidence
diff --git a/LeanPool/Erdos97ConvexOctagon/MasterCertificateData5.lean b/LeanPool/Erdos97ConvexOctagon/MasterCertificateData5.lean
new file mode 100644
index 00000000..81ee692d
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/MasterCertificateData5.lean
@@ -0,0 +1,517 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.LRAT.Format
+
+/-! # Generated packed master-certificate data -/
+
+namespace Erdos97Octagon.RawIncidence
+
+/-- Packed certificate data part 5. -/
+def masterCertificatePart5 : List String := [
+  "K9MhhyqRK6oo7RYBCSkbHSBDSlFZax6KLYUtgi2ALf8suAIC8wQ6cBW/AQO2As4qzSrzEaIFgBDiKMcTmijNJ4kTzijxEr",
+  "cr+SSJDQEBCTQpKy9LT19kdASJLYIqgSqHJQEOZBYmKy81Oz9EX2JqdHkLii2JLYYtgi2BLZUrlyuBKson8yn/JAEHWRsd",
+  "IENRayWNLYwtii2FLYQtgy2CLQa7AvYEPXMYwgHAB4MQuQKlBdAn6CydKAXRKtAq5SjKE4wT5ibyKfEpA8kCyimaEswjmS",
+  "KeKgEOXREdHycpKzM6QUpRUlgbjS2LLYotiS2GLYUthC2DLYItrSa9As8pzim4K7UriyGrJacD1CjCA9cruSWCKpUsoQ0Z",
+  "2hMBDlIRHR8nKSszOTpBSlFYD4stii2HLYYthS2ELQG6K7crjCGoA4cKuiXNJtgrAQlgGx0gKUNKUWshkC2OLYstiC2HLY",
+  "YthS2ELYMTGwN2xQH5BEC+ApsnddQqqAW8Ao8NuyWkKOsspieGENApAaoOxCb6HZMqAQlKGx0gKUNRa3EtkC2OLY0tiy2K",
+  "LYktiC2HLYYthC3GAfoEQb8CHAS9AnfsLKkF6yylKIcQAbkq6SjOE8QT+A36EZAT6ia2J9Uo3ynGI9In+Sr1KfQp7yKiKt",
+  "YkvinCIwEKYBsdIClDS1FcayGSLZAtjS2KLYktiC2HLYUTxwH7BELAAh0FvgJ4zgKqBcwp+RKaKZ0n1iqmKI4TkRPXLNco",
+  "iyPmA7orvSuPIQEOLRgnKSszOT1FS1hrbn0Ljy2NLYstiS2ILbIn4SnNJNUnoiidKwETUhgdJykrMzQ5PUNLUVhha25xfR",
+  "eTLZAtji2MLYstii2JLYct/QTCAtETqCjAAtgoAb8poxPiKaIopSq2KKAilSsBCVkUKSstRF1pawSTLdQkkirMJAEIcRsd",
+  "IClDUWs5li2VLZQtky2SLZEtkC2PLY4tjS2MLYstii2JLYgtCf8EywEhRsQCfK4FwgKqKPAs8SyMEAXQKdMp0gKVE6MS2i",
+  "j9EgTTE8go8CjvJgK5KO0khii5K5UqliqGBqcptyirJ88k5CmbK9cnkxYBBykbHSBDUWslly2TLZItjy2OLY0tjC2ABcwB",
+  "IkfFAn2vBcMCqyiNEAoBkxPaKuIN0SnSKcIlCJYN3hGiJ4oT8ST+Eoco3yu6KLorgR4BCVkWOTs9Rl1pawSVLcsk1iT9KQ",
+  "EJXRsdIENKUWtxKJktlS2SLZEtkC2PLY4tiy2CBc4BJEkCxwJ/sQXMB7EHxQK3KBLzLLgm3SjsKZgT1CnxKKYS4BGME90q",
+  "pCeYDaspmSiPIOIrjQyXJAEJPBsdIENKUWtxOJotmS2YLZctli2VLZQtky2SLZEtkC2PLY4tjS2MLQGDBc8BJUoDyAKAAY",
+  "ETwinHKcApf6cS2Q2yBc0HsgfgC8YCjSeQJ98ojROjKLgouSq7KhP0LKsp+CvFK8Ir7intKd4dmCqkK4QpwhcBCHEbHSBD",
+  "SlFrOZstmi2ZLZgtly2WLZUtlC2TLZItkS2QLY8tji2NLYQF0AEmSwTJAoEBswXOB7MHxwK5KLsquiq8KhT1LPYs7ynuKQ",
+  "ECghPGK8Mr/QubKJoNxCmmJ+AojhOEEvkr8yjOE5Eo2R2lK/4p9yfgFgEHShsdIENRax6cLZgtlC2SLZEthQXRAUwFygKC",
+  "Ac8HtAfIArooFfYs8CkBmBPfKucN1ymbDeMRkiinJ+ErjxOdIgEIdBsdIC1DUWs5nS2cLZstmi2ZLZgtly2WLZUtlC2TLZ",
+  "ItkS2QLY8thgXSAShNAQbLAoMBtQWeKpsq0AfXKdop6yboDZAn2QK1B8kCnCr2Jr8ovCq+KhacE4UrgyuqErsG9yzxKeEo",
+  "2yfFI4QTxSuQE64p9yizFwEHLRsdIENRazqeLZ0tnC2bLZotmS2YLZctli2VLZQtky2SLZEtkC2EAYcF0wEpAgfMArYFyg",
+  "L4LPksTtEH2CnbKekNkSfaArYHsye8KBe+Kr8qvSqdE6sS8inxKeIohRPGK8krAfonoCqUKeIqjgbQKKgriCmzFwEHdBsd",
+  "IENRazqfLZ4tnS2cLZstmi2ZLZgtly2WLZUtlC2TLZItkS2IBdQBKgMIzQIBhQG3BaAqnSrVLMsCniqWDJ4N+CbBKPks+i",
+  "zCKNIH2SncKaon2wKrJxi+KpsTnhOHK4UrrBKSE6sp8ynHKuMo3SePBscr0RYBBkMbHSBRazugLZ8tni2dLZwtmy2aLZkt",
+  "mC2XLZYtlS2ULZMtki0ChgGJBdUBzgKXDJ8NzAKrJ/ss+iyTEyu4BQEE3ALdKfoo2imsJ60S4yqQBp8TrCndE8Ep+SbBKA",
+  "nTB7gHlSjAKhn0KfMpyCvLK/wnqiuKKdEWAQd4MTU/cXJ6BpotmC2XLYcrhCuiJAEKcRsdICkqOEpRayahLZ0tnC2aLZkt",
+  "mC2XLZYtlS2LBdcB0AKIAQKZDOUpqQjpKboFzgLKD/oouwOqA5UTySWHAZgQtCeiH5IeuRPnJL8rrirLIKEoxykBDyMRHR",
+  "8pLTM1P0FCRVlhcA2iLZwtmy2aLZktmC22KMcfryrHKLQomx2TKwEJNRsdICkqSlFrJ6EtoC2fLZ4tnC2bLZotmS2YLY0F",
+  "2QGKAdICBJsM6ymWJ9AC/iz/LMwPrAO9A8slmhACsw6JAeMNlxPIHwH1KfQpjyKuK5Ap4ieLKgEIKRsdICpKUWsSnS2cLZ",
+  "stmi2OBdoBiwHTAgXRAgG9BbkomxDND60DzCW+AwEOTBsdICo1R0pRUllrcXYzpi2lLaQtoy2iLaEtoC2fLZ4tnS2cLZst",
+  "mi2ZLZgtjQ6PBdsBjAHUAgYBnQzpKa0I7SmYJ9IC8Cv3K+os3SyALYEt/ij8KfspmROkJIsBryevKc4nuCeNE4gqjSv0IY",
+  "4oxCueFgENdhsdICo1R0pRUllrcTSnLaYtpS2kLaMtoi2hLaAtny2eLZ0tnC2bLZotmS2QBdwBjQHVAgcCngzqKa4I7imZ",
+  "J9MC6yzeLIEtgi3/KP0p/CmaE+sqjAGwJ8ADuScByynlJtAg2CCOE4kqxSuPKLIooSqgFgEMRxsdICo1SlFSWWtxNagtpy",
+  "2mLaUtpC2jLaItoS2gLZ8tni2dLZwtmy2aLZEF3QGOAdYCCAOfDOsprwjvKZon1ALsLN8sgi2DLYAp/in9KZsT7CqNAbEn",
+  "wQO6JwGkJJEm5yeOKJQq8iu3KbQqzCnZINUrohYBC3MbHyMpMzU7P3B7CKItoS2gLZ4tkyTNKLoomSsBCjUbHSAqSlFZa3",
+  "Eoqi2oLaYtpS2kLaItoS2gLZ8tni2dLZMF3wGQAdgCCgWhDO0p8SmcJ9YC7izhLIQtgimAKp0T7iqPAbIDwwO8JwLIKqko",
+  "zynbINMgyCsBC0wWIycvQUJKVm98Eagtpy2kLaMtoi2hLaAt9Sv8K/krrRPTJ40qpySRKMYokCsBCVkbHSAqSlFrcSusLa",
+  "otpy2mLaQtoy2iLaEtoC2VBZIB2gIMB+EBowzvKbMI8ynYAvAs4yyHLYQpnxPwKpEBxQO0A74nAsQFvCjpIgHQKdkroimq",
+  "KpsikyjXJMUrAQhxGx0gKkpRaw+pLagtoS3wKfQp2wKWBQjZAoctAYQqgSqAKs8nAQtnGx0gKjVKTFFSazauLa0trC2rLa",
+  "otqS2oLactpi2lLaQtoy2iLaEtoC2XBZQB3AIOCeMBpQzxKbUIAfUplQ6gJ9oC/yv4K/wr8izlLNYnsBPAJ6ssiC2JLZUo",
+  "yiiaKpwqoRPWKYMqhSqEKroqzSbSKNorlBYBCkwbHSAqNUpRUms3ry2uLa0trC2rLaotqS2oLactpi2lLaQtoy2iLaEtlg",
+  "6YBZUB3QIPCuQBpgzyKbYIAvYpoSfbAoAs+Sv9K/Ms5iyxE8EnrCyJLYotlAHXKYQqhiqFKqITziaFJbsq0yjKKAGRKrkr",
+  "lyiUFgEJUhsdICo1SlFrOLAtry2uLa0trC2rLaotqS2oLactpi2lLaQtoy2iLZYB3gIQC+UBpwzzKbcIA/cpmQWiJ9wC9C",
+  "znLLIT8yrCJ60sii2LLbgDyQOVAYUqhyqGKqMTAdIp4SCLJe4m3CeXE5IquiuYKNIjqiqXFgEKUxsdIy8zP1FhawamKJoF",
+  "3wKYE90CiyUBD10bHSMnLzM5QUJHUVJhaxCxLastqi2pLagtpy2bBeAC3gKIJdoqvirAKKwdzSiiKwEHShsdICpRayyzLb",
+  "ItsS2uLa0tqy2qLaktqC2nLaYt+imZARPoAeECqgy6CJwF3wIO9yzqLAa1E8IO9iryDZgBuwOmEwIDywUB2ynfJ8gTrR2/",
+  "Ks8o0yLCKLQrAQhgGx0gKSpRay20LbMtsS2wLa8trS2sLastqi2pLaYtpxMBFOkB4gKaAasMuwidBbwn+CrgApkBrgGDJ4",
+  "4tqhCDLJInyCjDKfsRuSy4DLUniSjFKMsT+STAKsco2iiSI9crAQxiKS1FS01SWVxka24JsC2vLastqi2/K70r9SfiK+Uh",
+  "AQo8Gx0gIykqUVlrN7YttS20LbMtsi2xLbAtry2uLa0trC2rLaotqS2oLZwBFp8FAuQC6wGuJwOtDL0IySjKKJsB4gLRE/",
+  "UNwxKQLZEtkCnAJ+8p+SrCKZksnSymBrUTySaLKAHIKLcrhSrHKOkjsCqeK54o6BUBCVkbHSAjKSpRax+3LbYtsi2xLa8t",
+  "ri2sLastyiidARegBQPlAuwBBK4M4wKuJpEp+iqPKbYT/CkBtSjDKsko1yL8JLgrAQgjGx0gKSpRayK4LbcttC2zLbAtry",
+  "2uLa0trC2eARihBeYC7QEFzCjkAtAFki0BiSqIKsooySjEKt4oBJIpkiX7KtsrkCmWI/0pAQ0+ERsdJykvQEJLWVxuIrgt",
+  "ty21LbQtsi2xLbAtry2uLastxynGKdIp/CexJ50TqROsE/Amly3xKO4BnwGhLIASpiXmK8kokCXRBcsqjijdKLMqAQ9ZER",
+  "sdHycpLzA7QEJLXG4gty22LbUttC2wLa8t/SeVLaETnhOqE60T8ij3KfMpsQy5EwHUJ8Qn0gWdLKEsqgaPKOYnnCr8J8Ir",
+  "kSXnK4chAQ04ERYYGyInKTM7QlFYD7otuC23LbMtsS2wLYsqjCr8J/0nnSqZI84qzyrGKAEKWSkrL1Nfdnl7fAa1LbQtsS",
+  "3IKJYkoysBBykbHSAqUWsyvS28LbotuS24LbcttS20LbMtsi2xLbAtCqYF8gHrAqMBHbQMxAjpApctmC0FsxC3AYArgSu0",
+  "JpUpvBOCKoEpAwLQE68nlCWbI/oTzyrLKIsq/yfHK9sTnyqyIukn5SkBCFkbHSAqQVFrOb4tvS28Lbstui25Lbgtty22Lb",
+  "UttC2zLbItsS2wLaQBHgunBQHsAvMBtQzFCIIt9SzqApgthCeYKZktjSeKLLETjSzWJaMB2CWcJ4USzSn3Kc0OjSO/J70T",
+  "1gWUKpMq6yu8KJMoyyi4KtwrpCi5FgEHQRsdICpRaya9Lbstui24Lbctti21LbQtsS0MqAUC7QL0AaUBH7YMxgiDLesCmS",
+  "2FJ5kpjieLLLITjiykAZ0nhhLOKcAnAZYqoyPnK+IrxiEBDmgRGB0jJygtMzlCUmFuDb8tvC26Lbgtty22LbUtkirOKMwq",
+  "3CjgIsErARBZERgdHyMnKC0vMzlCYW56JMAtvi28Lbstui25Lbgtty22LbUt0SizJ7ETwBMBmSrQKM0q3Ci/KJ8rvB/LK4",
+  "Eo4CyMKoQqhiqcLZspxialKsMs9iTLJ7EGAQYqGx0gUWs7wi3BLcAtvy2+Lb0tvC27LbotuS24Lbctti21LbQtyQi5DPcB",
+  "8AIiqAGrBe4CnC2dLQ8Fhi35LAOGK4Urmim5JvwTwROHKrQnhin/E6kTAZUqlirQKNEozirfKLco5SvQKYEO+SamLPgkzC",
+  "ukKrYprhYBEC0RFBsdIykrMzVBQkVSVGscwi3BLcAtvy27LbotuS24LbUnuyeyBZ0tni3XIbwezyrnKNQovSqSKtEmriKp",
+  "KrYTux2oAYoS2ScBDl0bHSMpMzU/QUJRUmFrEsMtvS28Lbstui25La0F8gLwAp4p3QOaJewq0Cq8HdUo6Ci0KwELWRsdIC",
+  "YpQUVHUWslwy3ALb8tvS28LbotuC2uBQP6AasBJfMCuxDxAtko2CjdBYojAsQN0Ce4E+0qwROAKowSAawT8CnyK6IfsSm/",
+  "KuoooiXKKwEIKRsdIEFKUWsZxS3CLb4tvS28LbstrwUErAEm9ALyAqAtzgPfA+0lvBDaKIYgAZcqlirYKNco0ioBDF0bHS",
+  "A4QUpRUllgazXHLcYtxS3ELcMtwi3BLcAtvy2+Lb0tvC27LbotuS2wBQX8Aa0BJwH1AroT3wXfB/oH8wKsAdInoS2iLc8D",
+  "4APmJsYNnCqdKtsp2SmxJ5IO6inrKcMkxSSNKIcqrivBKtIoryjlK+QXAQx2Gx0gOEFKUVJZYGs1yC3HLcYtxS3ELcMtwi",
+  "3BLcAtvy2+Lb0tvC27LbotAvYCuxOxBQb9Aa4BKAHgB/sH9AKtAdMn4AWvE6Itoy3QA+EDxw2dKp4qsieTDo8SiCrQKdwn",
+  "kiz5IPEg5iuqKtMosCivK+YXAQtgGx0gOEFKUVJZazbJLcgtxy3GLcUtxC3DLcItwS3ALb8tvi29Lbwtuy28E7IFB/4Brw",
+  "EpA/cCrgHUJ+EF4Qf8B/UCyA3nBqMt0QPiA7MnlA6eKp8qkBKJKt0nArAT7inRKfog8iDnK9QoAa8otirDKugXAQxVGx0g",
+  "OEFKUVJZXWs1yi3JLcgtxy3GLcUtxC3DLcItwS3ALb8tvi29Lbwt+yazBQj/AbABKgEE+ALiBeIH/Qf2AqQtpS3SA+MDoC",
+  "XBJukm8iqfKqAqwSnWKtYp1ynME8YTlQ6nKNQr5SjSKIgnyQ3XEoQXAQtdGx0gOEFKUVJZazbLLcotyS3ILcctxi3FLcQt",
+  "wy3CLcEtwC2/Lb4tvS20BQmAArEBKwIF+QLjBeMH/gf3AqUtpi3TA+QDoSXCJuom8yqgKqEq1yrXKdgpzRPHE5YO5ijvKN",
+  "MoiSfKDdgSAfcrxSqLKIQXAQpSGx0gOEFKUVlrN8wtyy3KLcktyC3HLcYtxS3ELcMtwi3BLcAtvy2+LQb6ArUFCoECsgEs",
+  "5Af/B/gC5AWmLact1APlA6EqoioD9CrDJs4TyBOXDocqyw3ZEpMSAbMT9ymnJYonqSXWK+4jlijGKskr/SaHFwEQYBsfIC",
+  "MnKzAzNUFKU2JpaxbJLcctxS3ELcMtwi3AE+4q2CeyAcwNzCi0E7cnlBLVKZcsnSyaLP4g6yv2IAEJOBsdIEFKUVlrG8ot",
+  "xi3DLbcFDIMCtAEI/ALmBeYHgQj6AqgtpCoC2ygB9iqoJcoTmQ61E4kqzQ2VEsMoARBgERsdHyAjKzAzOUFCR1JrEM4txy",
+  "3FLcQtwhPjKNontAHnB84Nmg7lJ5YSzh/bKosCAQpzGx8jJysvMzlwCcktyC3GLcUt3ijrKMwTwCvBJAEIWRsdIEFKUWsl",
+  "0C3LLcktyC3HLcYtxC26BQ8xtwGGAgv/AukHhAj9AuoD2QMD4SgCyCb5Ks0TnA6MKtAN3hIB3SrdIqcl4CjSK/wplSEBB0",
+  "EbHSBKUWsb0S3QLc4tyi3JLcctgAO7BRAyuAH+AqwtAQyFCKYqpSqpKuEoxCfgKN4qvyPSKtEqrigBCi8bHSAjKUpRWWs3",
+  "0y3SLdEt0C3PLc4tzS3MLcstyi3JLcgtxy3GLcUtvAURM7kBiALmKMsngQMBxifeJ+co/wK8ErgslyuWK7oOvCzrBa4trS",
+  "2rKYYU0hPcKLYnlynfKuApkg73KOQosSuiKsIlgCzNKpMo6hYBCSkbHSAjSlFZaynULdMt0C3PLc0tzC3LLcotyS3GLeco",
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+  "DeMN0w3DDZMIIQ/ybLArYqvSrHLJYGqyO7L+cH6S+GLY0X9hHUFsAs2QjmFssWii2LMP0mAQkoERsnMDM7P1A46DDnMOYw",
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+  "DAMHzQIfF9MWzRbaL9cIrhKEEMUXAqMupC6VF80QtSrhLeAtmybzKc4onQ6VLdkWqy0BljCHLasq0y/7Lf0t4SjaKPcrxy",
+  "63LdUtkR8BCisRGycoMDM7RVA36jDpMOgw5zDmMOUw5DDjMOIw4TDgMN8w3jDdMNwwCA0EAc4CIBjUFs4W3gHsL4MthS3h",
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+  "DlMOQw4zDiMN0wDgUCzwIhGc8W3wHtL4Qt2QiGEMEqpi7oKQGPMI4tpCadJuoW9i6kLQEIRREbJzAzO1AR6TDkMOMw4TAP",
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+  "EsEspib2K7wSkhDTF9sQ9hbtLbAtgC+CLwHgLeIttSuoKsotAQcjERswMztQH/gw9jD1MPQw8TDwMO0w6jALG9wCLibmCJ",
+  "MQBZEttxGXLZMt/S+LK4wsB7Mu/CkBlTC7KuAvAwEHQREbIiYwUBL3MN0WC90CLyfnCJQQzyrZLKAwozAeuBGIEpwt0iz4",
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+  "6GJt8o4i3wLasqAQ0/ERUbISImMzQ5O2FxD/kw8zDyMOwv3xDfApYQpxfHKvItrSaiMKAwpDDcKgELLREVGyEiJi9hb3EQ",
+  "+jD2MPQw8zAl4AKXEK4m8yrGLKYw+xb2KbUthS+1JgEGOxEbMDNQO/0w/DD7MPow+TD4MPcw9jD1MPQw8zDyMPEw8DDvMO",
+  "ECMyvnFuEW6wjCEpgQ2RcQIAUEty64LuEQAwKWLf8vnC2YLZArAaQwpjCnLbotuS3yA8wU4iiDL4cTyy2LLI4u5S6PLoop",
+  "iyezL+gt4B4BCTURGyMnMDtBUCj9MPww+DD3MPYw9TD0MPMw8TDwMPYq4gI0LAHoFuIW7AjDEpkQ2hf0COYL1CrnKs0qqh",
+  "elLawt+hbJKbowty2cLZot6xboD68m6yDzLQEIQREbIycwO1An/jD9MPww+zD6MPcw9jD1MPQw8zAC6RbjFvcq4wI1Le0I",
+  "xBKaENsX9QjnC9Uq3ywBlDCRKo4S0y3jENgs9i33LcEtzCiNKtMooBcBDC0RGyEjJzU5O1BhdCP/MP4w/TD7MPkw+DD3MP",
+  "Yw9TD0MPIwvDC7Kb4w5AI26hbkFp8tni3uCLImnC3FEpsQ3BeEK+oP2yvCLfUt4yfYJ+Qt4yQBDlMjJys1OTs/QERLTU9Q",
+  "DP0w/DD5MPcwnizrFuUWmirrL/Ioty/XJAEJWTU5Oz9LT1BSB/0w+TD3MOMr7BbGL+woAQkrERsjJzA1O1A4gzGCMYExgD",
+  "H/MP4w/TD8MPsw+jD5MPgw9zD2MPUw+yrnAjkxBu0W5xYE8Qj6KsAw6wv5CL0uvi7IEp4Q3xfsKrcOsS2vLaEtny3nEOIs",
+  "3ivtDwIBxi/XLcEviy77KO0v+SWkF5AuwSu1HwEINREbIycwO1AghDGCMf8w+zD5MPgw7hYF6AI6Mge+Lr8u8gjsC/oI6B",
+  "CfEO0q3ysBBMQMuA7GLY4q+S3lK/gowi/XJAEOKxEbHiEjJzk7PT9PWF8ahDGCMYEx/jD9MPsw+jD3MMIw/SrpAvQIoS2U",
+  "EsoSoBDhF+Ms7w/ZLYQXuyetJ+gt5y39KAEMLREbISMnOTs9P1BhH4YxhDGBMYAx/zD+MP0w+DDCMIIwAgfqAjzwFuoWpC",
+  "2iLcAu9Ai4Jr0mmCrqEKEQ/C2KK5opkS/EL64oAQhTERsjJzA7UDmHMYYxhTGEMYMxgjGBMYAx/zD+MP0w/DD7MPow+TCk",
+  "LAMI/yrrAj01CvEW6xacMMEuwi71CO8L/QiZKusQAcwSohDjF9st2i29L5or9wmxLQKZK8cMyS36K44tkSrrL+8vvSjpLZ",
+  "Evoiz+HgEHIxEbJzA7UDqIMYcxhjGFMYQxgzGCMYExgDH/MP4w/TD8MPsw+jCAK+wCPjYL8hbsFvYI8Av+CM0SoxDkFwEJ",
+  "wi7DLuwQBJ0wmiqbK9wt2y3LL8Yv+AmAKeUv7C+OLgKyLZorA8gMyi2PLbMhki+VLsYrgB8BCDURGycwO0xQKIkxiDGGMY",
+  "UxgzGAMf8w/jD8MO0CPwH4CDcM8xbtFs4SpBDyKuUX8Qv/COQrtRe3LcQphRfDLv0Bwi2eKvYW+Ra2LPMPhirQL+In6y0B",
+  "B0ERGycwO1AbiTGIMYcxhTH+MO4CQAL5CDgN7halEOAq6izZKgGfMJkS4yzuEMwtgi6BLtco3iihLgEMKxsnLzU7P0BES0",
+  "1QDIcxhjGSK+8C9RbvFvIvhCmIKc8vwS+TKQENNREbISInMjk7QFBhcRuKMYcxhDGDMYIxgTHHKfACQvsIggn2FvAWpxD1",
+  "KvAQ5yu4F4ACAbAwoSq+JoEu7Sv0JMovAQcrERsnMDtQOo0xjDGLMYoxiTGIMYcxhjGFMYQxgzGCMYExgDH/MAMF8QJDEP",
+  "wIO/cW8RbHLsguhCv1C4MJ0hKoEOss8RAB7CzpF4wXojD9Fp8qoCv9CZQtrzCRBZsn6i+ELoUuhSnyKMsvoi6lLOsu7y3P",
+  "K7QfAQgpERUjMTk6PAaGMYUxhDGDMagXpCUBBicRGzA7UCaPMY0xjDGLMYcxhjGFMYQx8wI9RRL+CPkW8xb3C4UJqhAFyS",
+  "7KLvMQBwIDpDCiK/8J1AGWLYsr/xazMJkqhi6dJ7kp8y8BCDURGyMwO0FQKY8xjjGMMYsxijGIMYcxhTGDMfQCPkYT/wj6",
+  "FvQW+AurEOYq+SryK98qvBe+LbctjBfbKckt/RbGJsAmhS7xK/gkzi+gLsYp4y39INcv7iABB0ERGyMwO1AhkDGPMY4xjD",
+  "GJMYgxhjGFMfUCP0cUAoAJ9RasEOcq8SwBpjCgEvUQ6iyILokukBfTLd4o2yzlKKEurjDHKQEQUxEWHSEmKTU5P01PVWRq",
+  "fQ6PMYwxijGJMYgxhzHGKoIX+i35Lf0t/SDTJ5svARNkERYdISYpNTk7P0RLTU9QanR9FZExkDGOMY0xizGKMYkxiDH9Fv",
+  "cWgxeILvQrAdEviyn8Lf0t/iCcL84iAQ1TIyk5Oz9AREtNT1BUC5AxjzGMMYkxpyz+FvgWyi+tKowp/i8BFC4RHR4hIyYs",
+  "NTk7P0BES01QanR9DpMxkDGOMYwxhzGzLbAwgwnaEgKdLgHYLxMBCGI5P0dNT2RqBZAxoS+fL4YXrigBCCsRGyMwNTtQOZ",
+  "cxljGVMZQxkzGSMZExkDGPMY4xjTGMMYsxijGJMfsCRU0IBtEu0i4agRf7FoYJgCuOK/sQwxf1LPYs/wuNCbIQ3BLDLeMq",
+  "hxf5KwKeLZsq+Cr+L/MvgRCLBPcrnS/rLZ8p+CukLtsvryyEHwEILhEbIzA1O1A5mDGXMZYxlTGUMZMxkjGRMZAxjzGOMY",
+  "0xjDGLMYoxAfwCRk4JB9Iu0y4bghf8FtgMhwmBK7cttC22LbQw/BDEF+IsgAzPJsgmsxDdEpwr5CqXF/oroS+jLwKNLvQt",
+  "gS6CMIMurCnWK6UusR8BDygRGyEjJiovOTtARE1QYSeXMZYxlTGUMZMxkjGRMZAxjjGLMbYw/QJPgxf9FtAmySa9LbstlC",
+  "u0KogJsC2bF5gX9S+0LYIWyCz9EPEsHK4wji6iL6Qv+iv6JdcvAQ9OERshIykvOT9ARFBha30jlzGWMZUxlDGTMZIxkTGQ",
+]
+
+end Erdos97Octagon.RawIncidence
diff --git a/LeanPool/Erdos97ConvexOctagon/MasterCertificateData6.lean b/LeanPool/Erdos97ConvexOctagon/MasterCertificateData6.lean
new file mode 100644
index 00000000..c8ca04e8
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/MasterCertificateData6.lean
@@ -0,0 +1,517 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.LRAT.Format
+
+/-! # Generated packed master-certificate data -/
+
+namespace Erdos97Octagon.RawIncidence
+
+/-- Packed certificate data part 6. -/
+def masterCertificatePart6 : List String := [
+  "MY8xjjGMMYEw9i+KCoMW+SySK/4CUKsrhBf+FuUqiQmxLd8ttCukKp4qlCqmL6Qo2C+BLsggAQhWERsjMDU7UDmbMZoxmT",
+  "GYMZcxljGVMZQxkzGSMZExkDGPMY4xjTEEA/8CSVEMCtUu1i6FF/8WHooJhCv/EMcXgwyRCbYQ4BLnKgL9K4Muhi6CLtQw",
+  "tSvtFs8Oxy3dLfUrAZ8r2S+OLNAo6S2jL6wsjh8BBzURGyMwO1AsnDGZMZcxljGUMZMxkjGRMZAxjzGAA0pSDQvWLtcuhh",
+  "eAFx+LCYUrhAySCbcQ4RL3KwUEAcgXA9Uw0A7ILd4t9isCoCuUKYYunyGkL7wlAQ5FERUjKSs5Oz9AS0xQWAyZMZgxlTGU",
+  "MZIxjQqHF6ongTCVKdMv8iQBBysRGyMwO1A6njGdMZwxmzGaMZkxmDGXMZYxlTGUMZMxkjGRMZAxAoIDTA8NiBeCF1Qhsz",
+  "CNCZUr2C7ZLoYMlAnjErkQghH8LP0ssCr6F7ErnReOF44KpS25MAGVLpYuhjD7L4MplimGLoUuuCi2LOwtqy7HHwEMLhEb",
+  "ISMqNDs9UGF0FZ4xnTGXMZYxlDHfDIMDiiuDF1Ui1ibPJo4JEJUuli67MLMprSevLgEGIxEbMDtQLqAxnzGeMZ0xnDGYMZ",
+  "cxljGVMRGEA06KF4QXViOPCZYJ5RK7EAIEtTCvErMrhBEP2y6QCgGnLZwrkBe9MKoqli6XLq4nhDCILIguhy7yJK8usC61",
+  "LAEJKxEbISImOTs/Bp8xhQOYK8owxjCCKwEFOxEbMFAwojGhMaAxnjGcMZsxmjGZMZgxlTGUMYYDUIwXhhdYkQm9ECWKDJ",
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+  "LN8w9S+jEwHOAk3wLMQqxzOxMOoUsTOhL9Ys8jIBDSMVFx0hKjAzPEFQYXEZqjSpNKQ0ozSiNKE08SxJkBqWGsUqsjPAL8",
+  "QasQ7bKeIpxy2UGAGnLuAB+C2+JaUxAQooGy0wMzs8UFNqN600rDSrNKo0qTSoNKc0pjSlNKQ0ozSiNKE0oDSfNJEGA+wU",
+  "T5EaogGXGtECmhqdGvEw7zDQAvwx+DGbL/kz9zMBsg/XM6ot2i/EKtMl3y64MrMyszOAMeMyszGJL7svvzHQLIoxrQv3LK",
+  "kgAQw4FRcbISkwMzxBYXESrDSrNKY0pTSkNLQzkgb6M9ExBMUqAuoakhqYGtUz1DPBLQEPLhcbKSotMzk7P0FQU2J7Hq40",
+  "rDSrNKg0pzSmNKU0pDShNLYPxxrDL78vkwaTGpka0wLeLOEu0gL7M/kzzTCfL8ExvS+aK/0wjDHxLgEJahstMDM7PFBTGr",
+  "A0qzSqNKc0pjSkNJ0aoBoG7xRSpQGaGtQC8jDTAv8x+zEDAp4vAckuuTK2MpovAQhNGyErPUFLXQiVBsQu0jDSC9MDsBqe",
+  "GuswARAoFRcbISIqNTk7P0FTXWtxIbA0rjSsNKs0qjSpNKg0pzSlNKQ0lC6ML9Yz3DPVM5YG/jPCKpsu3wOGMYUxni2wJN",
+  "QukS/JMNkw+S3fCuMumjKyKwEIUxstMDM7PFAaszSxNLA0qzSqNKk0lwbXAv4xgjIJ8hRVlxqoAdYC/zEHA74m8ChABbkz",
+  "3TPKKgEJYhsoLTAzOzxQOLQ0szSyNLE0sDSvNK40rTSsNKs0qjSpNKg0pzSmNJgG2AL/MYMyClaYGqkBnhoB1wKAMoA0/j",
+  "OcGPMUCN4zuQ/IMcUxyyrmLroz+DLCL98snhOGMaQayzCSL7Yn9i2vLr4yqzH3MNsw/iyvIAEIKBstMDM7PFA1tTS0NLM0",
+  "sjSxNLA0rzSuNK00rDSrNKo0qDSnNAKZBtkChDILV5kaqgGfGtgCgTKBNP8znRgB6ynXKd8zug/nLvkyzCq7M8QvhzHDL5",
+  "IvyDGsMeAsgy/cMOYunTKSMbItpRrMMPIjARJiFRcYHSEjMjk7P0FCTVhhZGsKtTSyNK40qzTEMfMDoi2EMYoxxy8BCEwb",
+  "LTAzOzxQObc0tjS1NLQ0szSyNLE0sDSvNK40rTSsNKs0qjSpNN4w3zACmwbbAoIyhjINWQSsAaEaiC3aAoMygzSfGIE0Cc",
+  "otqS7LL5Mx0zDPGtUw1jDmLKIX6S7dAYMvqy2pLfowgDOFM8gxgS29MZQxxiEBBy0bMDM7PFA6uDS3NLY0tTS0NLM0sjSx",
+  "NLA0rzSuNK00rDSrNKo0nAbcAoMyhzIOWpwarQGiGtsChDKENII0BaAYAwrLLaouzC+TMZQx1DDQGtYw1zDnLPsuoxcBhi",
+  "/eAawtqi37MI0zyTGjK5UxmiyvMYMtxiEBBGAbH1AUtDSzNK80rjSmGqwanRqjGp0G3QLcAtEtyiupLdYy1zLPK/wy/TL5",
+  "LgEGMxswOzxQO7o0uTS4NLc0tjS1NLQ0szSyNLE0sDSvNK40rTSsNBCeBt4CXIYyhTKJMp4arwGkGt0ChjSENALoMPoP5j",
+  "Bvvw7gGgysLs4v1C7hM6IY6Sz3KLgkiDG5K8gv+y6iMpcxiDDuLbAxsjGOJNEw2BmsLawhAQkjFxstOURQYXQPuTSzNLI0",
+  "sDSfBt8CnxqwAd4C6imyMbAxzyycL6MYAQgoGy0wOzxQajm8NLs0ujS5NLg0tzS2NLU0tDSzNLI0sTSwNK80rjQCoAbgAl",
+  "6IMosyhzISoBqxAaYarBrIM9EzzDPfAoAx/jCeLpcviDSVL6YTAfwawQ/mM+kv7i65LeIlkDHyMpwvxzLHL8AlizPjMIMz",
+  "hi21IAEHahstMDs8UDS9NLw0uzS6NLk0uDS3NLY0tTS0NLM0sjSxNKoarRqhBuECX4wyiDIToRqyAacaA+ACgTH/MM0z0j",
+  "PJM4k0li+YLwH4LMcqAv0a4zPWLtcuxDCLMZAzji2iLaQy0jHfKb8ylCYBClkXGzE1OUFLUFYKuTS2NLU0tDSzNJ8v4gKC",
+  "M+EC4iUBEiMVFxgdHiEqLTI5Oz9BUGFrcRm+NL00uTS3NLY0tTS0NLI09SmELaMaqRqRAswxzzGnGJot9SzRLeYwvhrbM7",
+  "oupC3zAQEHIxUXISo6PAy9NLg0tzS2NM0ZhS2yDoUC2yq4M9gapy4BCk4VFxshIys7PUEF9QGlBtQumS6+GAEKLxYbIygr",
+  "OTtBUBm/NL40vTS5NLg0tzSmGrcBrBqmBuYC5QKvE4s02i3BLIUzhjP/M8kkqzGsMYEvgi+UMQEHYhstMDs8UDrDNMI0wT",
+  "TANL80vjS9NLw0uzS6NLk0uDS3NLY0tTQJpwbnAmWPMpIyGacauAGtGgbYM9MzzzPmAo4ynS+lLo80BNwxgxvYMRH+LM0q",
+  "6TPdLpMC2jDLMs0yvi7FJ+owlC3pEYYxni+4MfctozGlIAEHbxstMDs8UDrENMM0wjTBNMA0vzS+NL00vDS7NLo0uTS4NL",
+  "c0tjQKAagG6AJmkDKTMhqoGrkBrhrZM9Qz0DPnAo8ypi6QNPop5imEGwcSsC3OKv8s6jOKEN4u8S+tL5IxlS3rMMMakjDi",
+  "GYwzwjCSL/oyszGnIAEGLRswOzxQLcU0wjS/NL40vTS8NLs0ujS4NLc0C6kG6QJnkTKUMhupGroBrxraM9Ez1TPoApAypy",
+  "4BtRrhMNwwwC7sMAL7KYUbE88qgC2WLfIKwzCLEI8tri+rMgENUxcbKS80OENLUFlrcRLENMI0vjS9NLs0+S2qGrsBqgbq",
+  "AvAo6QKSNJUxxSu8Mb4xni8BBTAbOzxQJsc0xTTENME0vzS+NL00vDS6NLwBsRqrBusCHWnqApYykzKTNA2vD9wz0zMCfP",
+  "UwhxDMDoIt7jP9LOEuoS8Ryy3ZL8gyiSgBCmEVHSEjLTE5Oz8QwjTANL803gL+KfcpxDP2Cc0t0DL3L6gR9wnAE5I0agEH",
+  "ahstMzs8UCbJNMQ0wzTCNME0wDS/NL00vDS7NLYauRqtBu0CH74BsxqtGmsC7AKNMYsxkzTnKmHhGvgv5DDvGsQukTLwMK",
+  "Ytry2ULZMtsjIBCGEbIy0zOzxQOco0yTTINMc0xjTFNMQ0wzTCNME0wDS/NL40vTS8NAMBrgbuAiC/AbQarhpsji3tAoAq",
+  "ljSUNOUq+SmqEbEu5S3jMOUwuDPwGrIYxS7eL88tkjKYGrEV8TCcMZkwzzDtLKczwifAMbIy+y2rMc8gAQg4GyMtMzs8UD",
+  "nLNMo0yTTINMc0xjTFNMQ0wzTCNME0wDS/NL40vTQEAa8G7wICIcABtRqvGm2PLb4aEpQykTLuAqMJlzTmKrIu6TDnM4Et",
+  "vS2xGNAw1zHeL98smzGBM/QBtS+nL8Mxty+jL6oxjjHTGJUt3yEBByMbLTM7PFA6zDTLNMo0yTTINMc0xjTFNMQ0wzTCNM",
+  "E0wDS/NL40AwWwBvACIsEBthqwGm6QLe8CmDSWNOcqAeQa4C+zLuct5TDnMLQYxy7zMAKVMpIygS2nLdQY2DHSK5ww3iWe",
+  "MZAziy/eKbQyqzHfMsor0CABAx0WGgbMNMUTkQH8CbMbsRsBBi0bMzs8UCvONMw0yjTJNMc0xjTFNMQ0wzTANAeyBvICJM",
+  "MBuBqyGnDxAuwqjS2aNJg0Avgz9DPhLbYYBeklhDP3AdkmwRqXMpQylydCtC63MOkwnDHaJwEFMxs7PFATzTTHNMY0xTTE",
+  "NCXEAXEI8wLyAu0qAY8Q1A72M+Mvpwm2LgEKKBcbIioyOEFQaxfPNM40zDTINMU0+jOUNPMztBq0BvQC8wK4D5MOnDSBMK",
+  "UxpzGmMWrmMecx2y8BBDERFRs90TTQNM80zjTNNMw0yzTKNMk0yDTHNMY0xTTENMM0lhY47BO1BvUCrzT/Ca0bvhrBGoQy",
+  "zg36MdMazRryC5wVlzHYD+Mu+TD+Lf0xwQ3BLskxxzG2LIIqmDSVNO8r1zKTK7gvzjLBMrUxrRO1M9Qv7y7rMN4XyzOHIg",
+  "ENKBcbIyotMTk/QVBvcSbRNNA0zjTNNMo0yTTINMc0tgb2AscBvBq2GvUC6AL3MZ40ly3uM9kwzi6GAhIDojC+LdEapjHk",
+  "Je0tljO4GK0t4TH1J4MtnymZMwEGIxstOzxQK9M00jTQNM80zjTMNMs0yjTJNMg0xTQEDCnIAb0atxp1twb3AvYCnzSdNO",
+  "4qzTPJM+kCC8YanDKZMr8tAYktuS7xMLwwoTHmL+MxnSiXM6gpAQIWGgfTNMwTB5gBojSkNK0bAQc/Gy07PFBqOtU01DTT",
+  "NNI00TTQNM80zjTNNMw0yzTKNMk0yDTHNA65BvkCAgYrygG/Grkad8IaxRr4ApkxlzGEMKE0nzTaD/sz8zCRLYcv/y/PM5",
+  "0yri+wL9Ut0QSRG8oxiC7vMesxR6Qx1zLzLpYv7i/8MOUhAQZqGy07PFAs1jTUNNM00jTRNM80zTTMNMs0yjTINMMaugb6",
+  "AgMHLMsBwBq6GngP+QKaMaI0oDQB9TDMM5kO8TD8GrEvkC3RLp4yszO+M4A0kRujKsoxty+aMwEHOBstOzxQYRzXNNA0yT",
+  "QBuwb7AhAECMwBwRq7Gnn6ApoOozShNLcRhjDuMIgw0i6fMr4VpRo26i2TGwEHbxstOzxQYSzYNNY01TTUNNE00DTPNM40",
+  "zTTKNAERvAb8AgUJLs0Bwhq8Gnr7AqQ0ojQCuBHdLYcw/hrOM/MwoDKSLdMugjSTG6oxvxW5L7cvsy/RDc0xzSUBBmEbLT",
+  "s8UDHZNNc01jTVNNM00jTQNM80zjTLNAYSL84Bwxq9Gnu9Bv0C/AKjNKU0Acka9TDyMPAwijDULqEypxrAFQLaM7ETvy6L",
+  "L5Qb3i2rMdYryiy2MbYzwy/hMv0nzzHKJgEEPhEVGzbZNNg01zTWNNU01DTTNNI00TTQNM80zjTNNMw0oRYJ9RNBvgb+Aj",
+  "/dM7g0iArfM9wzthvzMPQw+TD1MMca7S6GMNcN8C6cMewu/zCHLtIx0DG/LIsqnjShNPgr+i7gMqgx1S2CL5svvjEBBjgb",
+  "LTs8UCXbNNg01zTTNNI00TTQNBQMCAIx0AHFGr8afb8G/wLVM8gazhoipDIL/gLnKp4OpzRg4jDuLawxwxjYJKIzoDO2Lw",
+  "EBGgjbNAjUE6EWebA0xwy0GwEELTs8UDDdNNs02jTZNNc01jTVNNQ00zTSNNA0zzQBwQYWDgSBA9IBxxrBGn8zyhrQGiSm",
+  "MqMygAOpNAIKnwH8MPgw0zPYLpEtly2EMYc0jy+kLqYz1g0fliSwMQEKeR8nKStDRUtPfAnXNNQ00zQCny/dGr4rxTK6Kw",
+  "EENBEfMgQDwwblDMMFAQVZOzxQbzzgNN803jTdNNw02zTaNNk02DTXNNY01TTUNNM00jQExAYDGRE2hAPVAcoaxBqCAZUB",
+  "jjGMMaAQgwPnEKw0qjTlDsYu5zCPMNoz5BOpMqYy+yrfK+wqhzSjL6EvvTGiL8ov/TLiJKMxqDP+GdMyri/2MdQhAQRvOz",
+  "xQIuE03jTdNNs02TTYNNc01jTUNAXFBhoSN4UD1gHFGoMBhAOtNAHJGASWAY8xoRDmDugQxy6QMNszsjGqMt4kAQM7PFAw",
+  "4jThNN803jTdNNw02zTaNNk02DTWNNU01DQGxgY4hgPXAcwaxhqEAYUDrDQB0hrVGv4w+zD5MBuTMKoysTATpTEJkDGtLq",
+  "4uzDP7LcoY5w7ILtwz/Sr5Ma8pAQNvPFA+4zTiNOE04DTfNN403TTcNNs02jTZNNg01zTWNNU0B8cGATmHA9gBzRrHGoUB",
+  "qTHwGaoxqDGGAyOvNKgCrTSnDNUOuxOBK5Uvny3NE4Y0kjDqMKwyqTL1KuAr2zPCLyXLGJkztzG3LOAkijGqM+AY1jLWMf",
+  "gx4SABBDQRHzgECMgG/AyvBAECPFA/5TTkNOM04jThNOA03zTeNN003DTbNNo02TTYNNc0CckGiQPaAc8ayRqIAwLVGtga",
+]
+
+end Erdos97Octagon.RawIncidence
diff --git a/LeanPool/Erdos97ConvexOctagon/MasterCertificateData7.lean b/LeanPool/Erdos97ConvexOctagon/MasterCertificateData7.lean
new file mode 100644
index 00000000..b90c7223
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/MasterCertificateData7.lean
@@ -0,0 +1,517 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.LRAT.Format
+
+/-! # Generated packed master-certificate data -/
+
+namespace Erdos97Octagon.RawIncidence
+
+/-- Packed certificate data part 7. -/
+def masterCertificatePart7 : List String := [
+  "AzusMaoxhwGxNK80gTH+MPwwJfIZljCtMqoCqQzLLuAujzSgG7MajDGXL4MrsC2vLYwSmC7aJY8p3ivaMdsxtzHtMuYy6C",
+  "riIAEKTBEfLENOYWlvcwngNN402zTZNArKBtYNkDGvJgEGUzM5O1BUCuI03zTcNAvLBvcvAssanTP0LAEILR8jMztBUGEa",
+  "5zTmNOM04DTfNN00DMwGjAMD0hrMGt0BiwPnL4sxnirRLoAulyqsM+ca4THZJ5kt9DEBBiMWKzA7UDHpNOg05zTmNOQ04z",
+  "TiNOE04DTfNN403DTbNA3NBo0DBNMazRreAYwDuDL/LtIu1hOyNO8MgS7oLoEN/S8CrDOtMyeENP4w+SjnLpMx3BmpL/gv",
+  "pyzMMdsEhDDZKPUxAQkuFyIsMzs/QVAw6jTpNOg05jTlNOQ04zTiNOE04DTfNN403TTcNA7OBo806RSqEIw0jgMF1BrOGp",
+  "ktjQPFLoQu+RXbM/sstjSIK4gxhjG2MuQulDH8LuIG7C2sLvsxqDGzM+Un8C25MQEILhcjKkFQVVki6zTmNOQ04zTiNOA0",
+  "3zTdNA/PBvIPqxCPAwbVGs8ajjGOA+0a6hqDLrc0iTGKMf0t5S79JbIxrzHzGIgRoS23MqgKAQdLFiswO1BqOuw06zTqNO",
+  "k06DTnNOY05TTkNOM04jThNOA03zTeNBDQBgOQAwfWGtAa4QHZGtwajwO7Mrcygi//LtUu2ROWMYQNtTTyDIQu6y7+LgWv",
+  "M7Az3CiAMv8x/Sn7L/ov7jLfGbErry/kMZE00jHWMestuhwBBmoWKzA7UCXtNOw06DTnNOU05DTiNOE0EdEG2hqRAwjXGt",
+  "EakAO8MtYu2hOFDfMMhS4GsTMBqzHfBOsu5REE3ieAMv4xzCyPMO8y/ikBBSsWMDtQPO407TTsNOs06jTpNOg05zTmNOU0",
+  "5DTjNOI04TTgNBLSBpIDCdga0hrjAZEDvTK6MrkyhC/XLtsThg23NPQMhi7tLgexM7IzAaoKrCzAMO0a4RmPMYIwsS/JMZ",
+  "M0+S68KfYy8zKCMv8xmS3XMbcz0S+zM7scAQcuFyMqOTtQEuo06DThNBPTBq8QkwMK2RrTGpIDuTSOMYEu1xj9LIMtpTMB",
+  "By4XIis5O1AY7jTrNOk06DTnNOY04jQU1AaUAwvaGtQa5QGTA4YvujSVNI8xgi7YGP4s+iimMwEHIxgfKjA7UDPxNPA07z",
+  "TuNO007DTrNOk06DTnNOY05DQV1QY4lQMM2xrVGuYBlAPAMrwy2i67NIkuiQ33DAqFMLUztDMJsRCONIEpYa8s5BnDMfAa",
+  "mzGwL/8vvzDvLtQxuTONMKIt/TEBBBYwO1AY8DTtNBbWBpYDDdwa1hqVA98T2y6KLrs0+AyKDQQLtTMByRTzLpY0mTTdFw",
+  "EILhciKjk7QVAg8TTwNOw06jTpNOg05TQX1wb4D5k0+g+zEJcDDt0a1xqiLaUvljGTL5YD8hrbGL00kjHdJ9AxhiqvKd0v",
+  "nBcBCy4VHyEjMTo+QVRhGfI07TTrNOo06TTmNBjYBpkymzK9NKgJhzGJMfYa8BoP2Bq/LU7zLewx1C+uLecZAQYoKzA4O1",
+  "A79TT0NPM08jTxNPA07zTuNO007DTrNOo06TToNOc0GdkGmQMQ3xrZGuoBA8AymAPEMsEyiy/dD94uvzTBNIsthi36M8sx",
+  "zDHKMbkz0y/eKPoPnjTSL+wxwy/hL58xhy/AKIwx8hiNDPIt0jHsMoYyzSzKIQEGRyswODtQO/Y09TT0NPM08jTxNPA07z",
+  "TuNO007DTrNOo06TToNBraBgGaAxHgGtoa6wEEwTKZA8UywjKML+Iv3g/fLsA0wjSlLYwthy37M7IbujPfKAzCKI0xxRj6",
+  "E9Qt9Sv1Gu0xlzHgL/MYjgzUMY4whzLOLLUhAQUrMDg7UDz3NPY09TT0NPM08jTxNPA07zTuNO007DTrNOo06TQb2wabAx",
+  "LhGtsa7AEFwjKaA8YywzKNL98P4C7BNMM0jS2ILd8YuzMCAfwz4CgNpDTDKNcx2DGOMeAv4ifhL4Isxhj7E/YatTHuMYAz",
+  "mDGMMMMztyEBBkMRTmFjaQfwNO00HNwG7inoDe8pAQlnER8nKTU9YWMJ8TTwNO807jQd3QaFKtYE/yUBCCMXKjM7P0FQKf",
+  "k0+DT3NPY09TTyNPE08DTvNB7eBp4DFeQa3hrvAZ0DkC2LLesz4y7GNL8t4hi+Mw/2LmaXNNIsxiywLYYy2DHbMYsw4y/m",
+  "L8kx8THYLwEFLjA4O1A8+zT6NPk0+DT3NPY09TT0NPM08jTxNPA07zTuNO00H98GBJ8DFuUa3xrwAQm7EJ4DyjLHMsYynj",
+  "HjD+QuxTTHNPoajC2RLZkxmjGXMb8z4xj1LgGeNKE0qi3mJ9gxvS/HLOUvyjGEM78x/S37C/ArjjKGIgEEODA7UCz8NPo0",
+  "+TT4NPc09jTzNPI08TQg4AagAxfmGuAa8QEKnwPLMsgy5A/GNMg0ki2NLeQYwDMBohv4LgVoAqA0ozSrLdQsyCzZMb0vyz",
+  "GAFNovhjMBDGgRHykrNTtVY2ZqexH8NPk09zT1NPQ08jQh4QbYNNs0/zLAG6Iw2gShL94vyzEBCCMXKjk7QVBhHvw0+zT2",
+  "NPU09DQi4gaiAxnoGuIa8wGhA+cuyDTDLQ+kG5AuauYYuimMLdwx3zHTGucv6i/SLPUxAQYuIyswO1A7/zT+NP00/DT7NP",
+  "o0+TT4NPc09jT1NPQ08zTyNPE0I+MGowMa6RrjGvQBDQOiA8oyzjLLMugulS/ELck0yzQ+mjSbMZ4x+S6TMJEuqTHnGJEv",
+  "jS21M8svtS2HGfMtjSbfMdMz4DGFMpIqiDONMrUrnCIBCUwRHzxDTmlqcwv6NPg09TTzNCTkBqcx8A3tGvAaySYBBSMrMD",
+  "tQJ4E1/zT7NPk0+DT2NPQ0JeUGBaUDHOsa5Rr2AQ+kA9AyzTLqLpcvyzQCpxuTLukYjy3WGkD7Lq4wiC+rMfEaiRnNL8op",
+  "si34MQEFZBEfYmgG/DQmizOKM/ktnzMBCmERHyEpLWNkZmsJ/TT7NPo0+DQn5wb6LbkohDMBBmgRH2JmawX+NCiJM/stnT",
+  "MBBEAfQkQHgTUp6QbuM+0zvC7sMwEEKzA7UB6GNYQ1gTX+NP00/DQq6gYUCqoDIfAa6hr7AakD1TLSMpwv0DQFFqwb5y6Y",
+  "Lq807hiULZApvDMBBDQyPnAIhDUr6waJG4Mb/TP+M5kvAQNQMDs+iDWHNYY1hTWENYM1gjWBNYA1/zT+NP00/DT7NPo0LO",
+  "wGrAMj8hrsGv0BlxarA9cy1DLxLhbUNNI0AgwKFa4bhC/5M5ourzSsNPAYty2WLb4zdNwsxCnlMfEvyS//MdYxqzDWL6Ev",
+  "oTKQGYUZsjHWMO4y9iEBCT8fJysvNWVnbwUtli+UL+ABrSwBB2cfMDRja28IhzUu7gbvCJANsSyNNM8sAQJQMA+LNYY1/z",
+  "QvgAKvAwPWMtoy1zKtBNEx0DHSMdkwAQVFFR9ASwUw8AbYLs0u/A0BAjBQAQIBBTgVHzI7B4s1MvIG0Q7wLog06S4BB3Yf",
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+  "CAM+MxxTTDNIEs7ALXMvA07zSWLf41qjWFK9YLsRO7M/AdvDPYHZY0tTLaHIY0xxCyIgEHOxUfITNGSzDxN/A37zfuN+03",
+  "7DfrN+o36TfoN+c35TeWA9YJjwKgDaEC3x3iHZU1mTX0He4dgRmTD70CvTCgNJo09DaKEPIO/DGHHr423C6jMOw13CfoNI",
+  "oxjDCVM5k2pRuDNfQ1sCkBBTMUFihZPPM38jfxN/A37zfuN+037DfrN+o36TfoN+c35jflN5cD1wmQApYGdOIPAgQnPLYe",
+  "pQHaEs4HgjPlMYMzjzOTNcU0sjKBM9Y04jPuArcwpDHyNPM0mC2ANqw12AuHK7MTnzHaHb0z8h2YNKcb3By6NOQ2tyIBBF",
+  "kUFigu8zfyN/E38DfvN+w36zfqN+k36DeYA9gJkQKXBnXjDwUDKD23HtsSzweRM5AzAZUD1TLfK7s0myrXNLMyxjTUMo8z",
+  "gzXhM5UP8TSlMOQQjQinNbkogjcBAygUFir0N/M38jfxN+037DfrN+o3mQPZCZICKT6YBnbkDwa4HqcBAck0yDSAM4Qzlg",
+  "PUMtUy8DQE3BLQB5IzhDWNKqYw5RDcGMsQjgioNboogzcBCyMRISgrNTlDS2FpHPU39DfwN+437TfsN+s36TeaA9oJkwLo",
+  "MaY1ozWXD8EY8h3mEKQ0uTGRN7so/DKDNfctd+UP0TcBCGcRHyEpOWNrGfQ38zfvN+437TfsN5sD2wmUAqUN0jd4Ks4H+A",
+  "mLM5gD/iiBCIU3zRD0CfIC+S3cNgEFYRQWJ1Y8+Df3N/Y39Tf0N/M38jfxN/A37zfuN+037DfrN+o3nAPcCZUCmwZ5Awks",
+  "QecPqzWlNfAxszCqAag1ux76HfQdmQMBhzPaNN00uTKiMMY08wL6NPs0+TSIM5Az4QnOEJkP/Db7NugQ9SrnMrgTojHfHa",
+  "0iAQRWFBYnPfk3+Df3N/Y39Tf0N/M38jfxN/A37zfuN+037DfrN50D3QmWApwGegQKLULoD/ExtTC0MKsBvB6aAwKIM9s0",
+  "3jS6Msc0iTMBhjaoMKMw9AL7NPw0+jSRM+IJzxD9Nr40/DboMukQmg+KMvYq2QKLNKMxryIBAycUFj76N/k3+Df3N/Y39T",
+  "f0N/M38jfxN/A37zfuN+037DeeA94JlwKdBnsFCy5D6Q/yMbUwrAGbAwOJMwG9MrYwvR7INLsyiDPdNOkzD4010zHjCfw0",
+  "/TT7NNAQ/Tb+Nr80pgGHNuky6hCbD4sy+S7aAow0pjGxIgECFBYa+DfzN/I38TfwN58D3wmYAp4GAXwGDC9ErQHqDwTlNN",
+  "IHjzP8CZwDhS72Av0tAQdnFjFBWWl5I/k39zf1N/I38TfwN+43oAPgCZkCujK8MgHjNOA0qg2rA74y6R3sHekW3jOjNfgw",
+  "9DD+Hfgd8QiONMcw+TX2LsI0wDTMLQEFOxEVM0YV+Tf4N/E3oQPhCZoCmBejA6sN6h3fAv0Ong+qNfoQkjK/NNYz5zbZNr",
+  "8xAQZiFh8gKDg1/jf9N/s3+jf5N/g39zf2N/U39DfzN/I3ogPiCZsC8wiiCQOsDcc36x3uHcQe1TTUNNM0uB72MNE1gB76",
+  "HdQ15R3JMAKJNqcB3DLJGP0X+C77Nb0y4zSqNpwztDKMNb80rTHhMew2wCoBBTgWHyAoNf83/jf9N/w3+zf6N/g39zf2N/",
+  "U39DfxN6MD4wmcAvQIowkErQ3IN+wd7x3FHrkegR77HdU1yjABmzPWNNU09zCbNuYd1DSMM4oz/DW+MuQ0qzadM441gjGT",
+  "NLEv9ha7KrUy9jTxB80yAQlNFR8yO0dLcXse/Df6N/k39jf1N/M38jekA+QJnQLyArICrg3JN5MykTK3MdEt3TDtHfAdrD",
+  "SmNM40pDWVMvkwhxOPNIEyAQppFh8gIygzWWJnN4E4gDj/N/43/Tf8N/s3+jf5N/g39zf2N/U39DfzN6UD5QmeAo8xwTKl",
+  "CQYCrw3KN5Ez8zHuHfEdxx7mM/kw1zXaNegdrTbjM6kB+BbHNMM0xTSIE9At4S+bMOU01Tb4NMg25jDDMcwwgzecHwEHRR",
+  "EVGCEpOCn/N/43/Tf8N/o3+Tf4N/c39TemA+YJnwKdF8kZsQOQLtgxsA3qEs4x5jbvHfIdtAHyEK811i30LYMu+TH+HdI0",
+  "rDawNrA02C79MJEZ6DSJN5ouAQxfFh8gIygzQVZZYmc1gziCOIE4gDj/N/43/Tf8N/s3+jf5N/g39zf2N/U3pwPnCaACAq",
+  "cJCASxDcw3kzP1MUfwHfMdjDbVNKszrAGBMZEzsDaPNbgwoTOpAdk15zTLNsQ0wTT1B6ku5jLYLoU3mDSZMtsfAQtWFh8g",
+  "IygzQVliZzaEOIM4gjiBOIA4/zf+N/03/Df7N/o3+Tf4N/c39jeoA+gJoQKoCQkFA7INzTeUM/YxSI021jTxHfQdrQGSM5",
+  "A1uTCiM9o16DTnMqoBxTTCNPYHAesdsDbTMJkwijWwNIMY/BS/MdsfAQhZFR8gKDI5Yh+FOIQ4gTj/N/g3qQPpCaICtwL6",
+  "CLMNzje0A/Id6jOONtc0rgHpM9g1gR7QGIQY/y6TNZI1hDDsHa4xszGzNAEKQRYfICMoM1liZzeGOIU4hDiDOII4gTiAOP",
+  "83/jf9N/w3+zf6N/k3+DeqA+oJowKqCQsHtA3PN5Yz+DFK8x32HQWPNtg0rwGUM5I1uzCkM9w1AsUygTHtHbs21TDtNYs1",
+  "hR7+LoUYmjSYNJEtrTTdBJsynCABCSMWHyAoM1liZxKHOIY4gzirA+sJpAIMCLUN0Df0Hc0eAeA12jXsM+sz2TQBClMWIy",
+  "crOUFnaXYThTiCOIA4/jf9N/s3rAPsCaUCpTMN7DS2DfUd4y/mLLA0tjSfMAELQRYjJyszOVhnaXkjiDiGOIQ4gziBOIA4",
+]
+
+end Erdos97Octagon.RawIncidence
diff --git a/LeanPool/Erdos97ConvexOctagon/MasterCertificateData8.lean b/LeanPool/Erdos97ConvexOctagon/MasterCertificateData8.lean
new file mode 100644
index 00000000..fd98a327
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/MasterCertificateData8.lean
@@ -0,0 +1,506 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.LRAT.Format
+
+/-! # Generated packed master-certificate data -/
+
+namespace Erdos97Octagon.RawIncidence
+
+/-- Packed certificate data part 8. -/
+def masterCertificatePart8 : List String := [
+  "/zf+N/w3rQPtCaYCmDPHMpcz+zEOtw32HfkdAZU1vjCnM+005RbwHbM2njDmLeAEjDflLL8uszQBCkcnKSszOUFnanEdhz",
+  "iGOII4gTiAOP83rgPuCacCtTD9NPwxsTAg9x36HeQYD601hjFO2Tb3Fp8yiRihLeEEjDeXMgEJTBYfICgwMzxnOIs4ijiJ",
+  "OIg4hziGOIU4hDiDOII4gTiAOP83/jf9N68D7wmoArM0sjS5NK8JEAyACbkN1DfWAqcz+B37HeIE0R6NNwTkNeE13jTfNM",
+  "kymTOZMQLNNM80khPWMLEulTKCNYE1nzCyNpc19zOgHwEIPBYfICgwM2c5jDiLOIo4iTiIOIc4hjiFOIQ4gziCOIE4gDj/",
+  "N/43sAPwCakCsAkRDYEJug3VN9cCqDP5Hfwd4wTSHo43BeU14jXfNOA0yjKaM5oxA4MXzjTQNJMTljIB5y+dMtgx8DTfNu",
+  "gW8zWyNIU1qTOgHwEHMBYfICgzZy6NOIw4iTiIOIc4hjiFOIQ4gziCOIE4gDj/N7ED8QmqArEJEg6CCbsN1jepMwb6HdMe",
+  "4DThNOY14zXLMpszAeksBIQX0zTPNJQTnzL+NvQ1sjSOMpw0+ikBBjMWHyAoZxmKOIY4hDiDOLID8gmrAg+DCbIJE6ozvA",
+  "3XN/sdB+E04jTMMgHJHpAeih6jHtkwAQh3FR8nKTEzZw6LOIU4hDizA/MJrALRMtAy2De9Dd40+zSrAb4CAQkpFSEnLTM5",
+  "Q0cNijiIOIY4hTi0A/QJrQJmvg25GqkznzOSNgEFZxYfICgukTiQOI84jjiNOIk4iDiHOIY4tQP1Ca4CtQmGCRYSvw3aN/",
+  "4dgR7XHq0zA8MCDOQ05TTMHs8ynzGKMe0v5DWTHo0eigPoBNwwxTCGNa0w9TSvM+wvjTHgNgEILRYfICgzWWI5kjiROJA4",
+  "jziOOI04jDiLOIo4iTiIOIc4hjiFOIQ4tgP2Ca8CtgkBhwkXE8AN2zeiM4Qy/x2CHpg2nTbYHvAyijH3M7sBwi++Nvkdpj",
+  "SkNOs16DWRMaMq9DOKNYQIqjDNLfU05jbpBNE05DCxNaIgAQlTFR8jJystWGUrkTiQOI84jTiMOIs4ijiJOIg4hjiFOLcD",
+  "9wmwArAzqjCRLoYyiTKLMgLBDdw35jTnNPg09TT6HRSAHoMe7zLzMrEzkTGLNTDwL5IxuDS7NKg0uy4BB2IWHyAoM1kolD",
+  "iTOJE4jziOOIw4iziKOIk4uAP4CbECA4kJGRXCDd03pDOBHoQemjafNtoe+TOMMfIyvQHtNeo1+x3ANvYzApMYuAH3NKww",
+  "vzGGCAELdxYuOUFSWWVmcXkbkjiQOI44iziKOIk4hzi5A/kJsgLUMhr6NMMNkS+CHoUepzS5HpMxqjTCNpQy7ATqLuQt0z",
+  "QBBlkWHyAoMymTOJI4kTiQOI44jDiLOIo4iTi6A/oJswIFiwkbF8QN3zemM4YeAqUzmDboNL8Bwi+VGLY1M+EYAfg0+TSu",
+  "MNc01DSICKwyqjLBMbw0AQ0tFh8jJyszOUFYZml5IpY4lDiSOJE4jziOOI04jDiLOIo4uwP7CbQCpjOlM4kyHMUNhB6iNg",
+  "SjNcwwqCqJCKEz7gTWNJo3qzK8NKwwwTaWMgELUxYfIycrL0FmcXknlTiUOJM4kjiROJA4jziOOI04iji8A/wJtQK4Nx3G",
+  "DZYulzDhN4UeGbo1ygIC7DSnM6M2tTO6Nv00+jS2M541lC/nNqc0ky37Me8EAQhZFR8gKDI5ZhaVOJM4vQP9CbYC4jeOCc",
+  "sCxw2GHoke/jObNp826zTCAcUvmBj9M5selR6tMgEHQREVLTI7TCWYOJc4lTiUOJI4kTiPOI44jTi+A/4JtwK1F8ADgQTJ",
+  "A8gNghNi8DGHHooezAHcNKET8zOpGa83wjTHMY81yy36Mv8v4TegNsAvAQYwFh8gKDM7mziaOJk4mDiXOJY4lTiUOJM4kj",
+  "iROJA4jziOOI04vwP/CbgCvwkgkAkKHAXJDeQ35gLuNO80iB6LHuEeqTOqM/E19DWmNvcyxAEEmhgDpzXGMP40gDW1Afgv",
+  "kzWZMYIe1TPHNPgt3DTaNJ43pzLrHwEFMxYfICg8nDibOJo4mTiYOJc4ljiVOJQ4kziSOJE4kDiPOI44wAOACrkCwAkhkQ",
+  "kLHcoN5TeOMokejB7iHgbvNPA0qjOrM6c2+DIBlTHXHu81nh6YHpk2xQGwMpsY0TCoNZswgx6rNMsxqDKbMfMEyjSUNfE2",
+  "ujD4HwEHJxUfITI7Ry+bOJk4mDiXOJU4lDiTOJI4kTiQOMEDgQq6AuY3zwKPA8sNih6NHsQ1wTWfHpkerBnZAugw4TSGHY",
+  "QZsTI6jDKRLtcxyjS7M5I1lTWbMr83hS79MsUyyTajNu80yScBCS4RFR4gJis9XS2eOJ04nDibOJo4mTiXOJY4lTiTOJI4",
+  "kDjCA4IKuwK5F50XxAOFBM0DyzHMDeUZuzS0MrMyix6OHvoewh7dNI4R4TXjN88tR5M1lDXFM5AygjfiDZkxhiuFNQEEKB",
+  "YfICifOJ44nTibOJk4lziWOJU4lDjDA4MKvAIkzQ3oN4wejx7lHg4D0QLDCZQJIAbzNNoemDHyNaEemx7qMJgD/zKqNtMw",
+  "lDXEKpYX2yoBDC0VHyMpKzEzR1hlcSCdOJw4mziYOJc4ljiVOJQ4xAOECr0CtDOYMuo3zg3pN/E0jR6uMcI1iDU9ujOULZ",
+  "IIkBGqM9805A2HHso2tTABCGkWHyAjK1lnKZ44nDiaOJk4lziWOJU4kzjFA4UKvgLhMgImmTK0M/00zw3qN4g1wAWOHpEe",
+  "3zKZMYgezTa2MKAYowGwNOQRnTGtMj6TCN80wDWZL4Y24i4BBTAQFiAmDJo4lzjGA4YKxQaPF9QCmBvtAgO6ELYzAQotFh",
+  "8gIyszWWJnN6M4ojihOKA4nzieOJ04nDibOJo4mTiYOJc4ljiVOMcDhwrAAgKWMigE0Q3sN5sytjO3M5Aekx6sNukewgXy",
+  "NAG0M681zzD8MfY1vCr6BK0zlQjhNIwdtzLJNKEyuDC3NM82ozHiMps1pSABCUwRFSktLzM7QCKkOKI4oDieOMgDiArBAi",
+  "e/F2zKA4sE0wOUEdIN1gHmMec1kR6UHow3Xas0/zKCMose6zfRMcwysRuaNYswwi+qNgEKVhYfICMrM1liZzelOKQ4ozii",
+  "OKE4oDifOJ44nTicOJs4mjiZOJg4lzjJA4kKwgICKgYEpBikF9MN7je4M7kznTL0NK42A5IelR7EBYw1tjOIM7E10TD+Mf",
+  "g1yAGjMYwezhTPNNE09TKnAbQ03DHmNOM06h8BCWIWHyAjKzNZZyymOKU4ojihOKA4nzieOJw4mziaOJk4ygOKCsMCKwfU",
+  "De83uTO6M54ykx6WHuwexQUEBfU0tzOyNdIw+TUDpRgBoTHlMo0ezxSNNtI0ni+KMOU0AQ4uFR8hKzM0OT0/QEdLeyWnOK",
+  "Y4pTikOKM4oTifOJ44nTicOJo4ywOLCsQCTvE38DebA0TtHtUw9DWHA9E08jCeNZ81nC7JN8w3wjCFMYgx9TS1MYk1xDAB",
+  "CFkWHyAjKzNnHqc4pTigOJ84njidOMwDjArFAgktvDOgMtYN8TeVHpge7h7HBQYCqzHBM0WLMP8Eljf4LYIZvCwBBi0RK0",
+  "RGSxClOKQ4nTjNA40KxgJxvjKgMoY3/TaLC+g0gjS9MqseAQdnFh8gIyszLqo4qTinOKY4pTijOKI4oTigOJ84njjOA44K",
+  "xwILL74zojLYDfM3yQWXHpoe8B4IAvs0+jToMrszkTWlMZEeljRH/TXEM9Q23Sq/MIEF6TSpGOUzoi+RNgEIcRYfICMrM1",
+  "k5qziqOKk4qDinOKY4pTikOKM4ojihOKA4nzieOJ04zwOPCsgCMAwB2Q30N74zvzOjMpgemx7xHpM1kTWVNQnqMs01+jRI",
+  "ozG9M4QywzOSHrY2/TDgNpA2sjXPAaoYvzS9NJ8tnQjSNLUy6jSqIAEHQRUfITAzSiyqOKk4qDinOKY4pTijOKE4oDifOJ",
+  "440AOQCskC2g31N/cCmR7tNPA06jTEEM81ngiuHrsZ9zDAMq432TTBHr4Fli+5MkOmNuYx+jLQMr40ojWBL4kwgDUBCV8W",
+  "HyAjKzNdcTitOKw4qziqOKk4qDinOKY4pTikOKM4ojihOKA4nzjRA5EKygICAw4ywTOlMtsN9jfFMf00/jSVNZM1lzWaHp",
+  "0e8x6+M78z5zb/MAu4Nrk1zzXWM4kzhjKlNQ2sGMcB2TS2NJYylh3sNPQfAQhdFh8gIyszcTmuOK04rDirOKo4qTioOKc4",
+  "pjilOKQ4oziiOKE4oDjSA5IKywIDBA8zwjOmMtwN9zf+NP80ljWUNZg1mx6eHvQevzPAMwy5NtA1ijNLyDOHMgHYNsMwrR",
+  "jIAYAx2jT+MuEq7zTtNPExvTTtHwEHcRYfICMrMyOuOKw4qziqOKk4pzilOKQ40wOTCswCBRA0wzOnMt0N+DeXNZk1nB6f",
+  "HvUeDdE1TMkzAZYeBIA1wTO6Nq0x2jYBBisWHyAjMyqwOK84rTisOKk4qDimOKU41AOUCs0CETXEM6gy3g35N/YezwUOBp",
+  "Y1AYM2sh6sHsQy+zCvGKovqjaYNe8ygTXCM9wwvDWvMM4wlx6HBd8xAQd9Fh8gIzNZOrE4sDivOK44rTisOKs4qjipOKg4",
+  "pzimOKU4pDijONUDlQrOAgESNrgTqBfEM6kyxTPfDfo3nh6hHvc08zT1NPce0AXhL+MvwzL8MMIyD+stuja8Ntk0gS6YNa",
+  "kx7zKlA4Q2oRGZN902qDWXMbsyvh8BBlkWHyAjMzuyOLE4sDivOK44rTisOKs4qjipOKg4pzimOKU4pDjWA5YKzwICEze5",
+  "E6kXxTOqMsYz4A37N58eoh74NPQ09jT4HtEF4i8Q7C2CLpk1pgOFNq0DmDEB5C+7Nr02lDSqMZc2mR7eNoszqCqgN8E0xT",
+  "K7HwEFIxYfIDM8sziyOLE4sDivOK44rTisOKs4qjipOKg4pzimOKU41wOXCtACOBT8N+ENqzLHM/keoB6jHgP5NPU09zSq",
+  "F7oTAYM1hDXFM9IFEeMvvjbxMsQzmjWuMZoe0TDdNs8wmC6nA4Y2qjWuA4gxlzChN9o09TG2HwEHdytBR0tNcRGvOK44qD",
+  "inONgDmArRApQx/zHJMjniDfM0xzLhNOA07jMBDCcWISsvOT1HS01Sex6yOLE4rzioONkDmQrSAuI36zLWD8oyxjI63jTj",
+  "DYEyoh6lHrIx4jXZNZc1oheAA7Yw/jdhiDWJNegbAQxfFh8gKy0wM1ldZ3c1tji1OLQ4sziyOLE4sDivOK44rTisOKs4qj",
+  "ipOKg42gOaCtMCtzI7FwOBA84x5A3/N6wbzhCjHqYe/B75Mvcy+DLGM482jDbeMyzWMo0FuDe8CN8arzWsNcsziC7JNfQ0",
+  "qAjcLqggAQk7FhghMTNDR0sjtTizOLE4rzitOKw4qjjbA5sK1AKOMjzlMOYD5Q2kF6Qepx7bNbMexhnYD7ozpxHlNN80wT",
+  "KRAY8NeeMH3TfhMbExiDUBC2IWHyArMDNZX2d3Nrg4tzi2OLU4tDizOLI4sTiwOK84rjitOKw4qziqONwDnArVAgU9GYMD",
+  "rhvmDYE4+jLQEPsy+TLhGqUeqB7+HsgztjGRNo42yTXMNdYB4DMuArcYmzOwNYou+TT2NKoImTLeLro37B8BCl8WHyArMD",
+  "NZZ3chuTi4OLc4tDixOLA4rziuOK043QOdCtYCBj4ahAOvG+cNgjjREP8ekjbXAdExA7gYAcoxsjWvNZYqiy73NAEJdxYf",
+  "ICswM1lnOLo4uTi4OLc4tji1OLQ4sziyOLE4sDivOK44rTisON4DngrXAgc/G4UDsBvoDYM4/DLSEP0y+zKnHqoegB/KM5",
+  "M2kDbYATABxxv9Lfs0+DSsCIgz9DOUGYI3vDHDNss1rjSkL7w3zjTQMusfAQhnFh8gKzAzWRe7OLo4uDixOLA43wOfCtgC",
+  "CEAchgOxG+kNhDjTEP4ygR+UNpE2MZ81AQEHMBYfICszWTq8OLs4uji5OLg4tzi2OLU4tDizOLI4sTiwOK84rjjgA6AK2Q",
+  "IJHUGHA7Ib6g2FONQQ/zKpHqwegh/MM5U2kjaYNZc1AaE1njXCNr425zDjMM812gG9K783vjeLLtIy+jSuCLQVuxjOMsU0",
+  "6DawNOwfAQgnFiErLV1lcSi8OLs4uji5OLc4tTi0OLM4sjjhA6EK2gK0MukxQu0NqheTAaoehjj3HuA14TXfLaMw7C1a7A",
+  "LvAogDljK1NZ8wnzXDNtUzmTPONZA1zTMBCycWISotMzk7Q0dLIb04vDi6OLk4tji0OLM4sjjiA6IK2wLcM0Mu7A2rHq4e",
+  "8AGANasXwTOHOOE3uzHqM6Ue6jHTCpE1kDXOM80zzzUBBjsVHyEyRyC+OL04uji3OLY4szjjA6MK3AKJOIg48QKxA4Uf7w",
+  "2sHq8e5jXjNcEeux77AoM10zIirjLaN+g3wzG9LrkvzDUBDCcRFRgeKS0vMzg7QCq+OL04uzi6OLk4uDi3OLY4tTi0OLM4",
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+  "AnAQJFXTf+Ov06/Dr7Ovo6+Dr3OvY69TrzOvE6owbjDJwF3wHcAck6yzreIa8Q7CDvIHYswAHPAQEOvTfAN8M3lTWOHOg0",
+  "1DaWOus1zCDmG9Y5+TScNyjgNKg64DPNNfwz3DeNM5Y4lTihNqA29TcBAV1AgDv/Ov46/Tr8Ovs6+jr5Ovg69zr2OvU69D",
+  "rzOvI6pAbkDJ0F4AHdAco6zDrfIbAQ7SDwIHctwQHQAQECvjfBN8Q3D5I1ljXpOd452znaOY8c6TSwNfo01TadN5c6KaEy",
+  "qTLhNKk6I4I5hjnSN+EzkBf8OP02+DfSJwEBTBaAO/w6+zr1OvQ6pQblDJ4F4QHeAcs6zTrgIbEQAS2sN6Y3zgGXNZM1wz",
+  "cBATwH/Dr1OgIBrzeoN7kBAQFLF4I7/jr9Ovc69jqnBucMoAXjAeABzTrPOuIhsxADAgGWNcI3yTeUNaw3mDUBABeDO/86",
+  "/jr4Ovc6qAboDKEF5AHhAc460DrjIbQQBAIBwjfFN8g3ljWaNa03",
+]
+
+end Erdos97Octagon.RawIncidence
diff --git a/LeanPool/Erdos97ConvexOctagon/MasterCertificateManifest.lean b/LeanPool/Erdos97ConvexOctagon/MasterCertificateManifest.lean
new file mode 100644
index 00000000..efb416e5
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/MasterCertificateManifest.lean
@@ -0,0 +1,87 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.LRAT.Format
+
+/-! # Generated master-certificate manifest -/
+
+namespace Erdos97Octagon.RawIncidence
+
+/-- Packed certificate format version. -/
+def masterCertificateFormatVersion : ℕ := 1
+
+/-- Number of initial clauses. -/
+def masterCertificateInitialClauses : ℕ := 3263
+
+/-- Number of retained LRAT additions. -/
+def masterCertificateAdditions : ℕ := 4294
+
+/-- Number of omitted LRAT deletion records. -/
+def masterCertificateDeletions : ℕ := 3145
+
+/-- Total number of actions in the generated LRAT text. -/
+def masterCertificateActions : ℕ := 7439
+
+/-- Number of packed bytes. -/
+def masterCertificatePackedBytes : ℕ := 316443
+
+/-- Number of base64 characters. -/
+def masterCertificateEncodedCharacters : ℕ := 421924
+
+/-- Number of generated data modules. -/
+def masterCertificateDataModules : ℕ := 9
+
+/-- Number of sequential proof-stage modules. -/
+def masterCertificateStageModules : ℕ := 3
+
+/-- Maximum retained additions reconstructed in one proof stage. -/
+def masterCertificateMaximumAdditionsPerStage : ℕ := 1432
+
+/-- Retained additions reconstructed by each sequential proof stage. -/
+def masterCertificateStageAdditionCounts : List ℕ :=
+  [1432, 1432, 1430]
+
+/-- Zero-based addition boundaries of the sequential proof stages. -/
+def masterCertificateStageBoundaries : List ℕ :=
+  [0, 1432] ++
+    [2864, 4294]
+
+/-- Maximum measured bytes used by one packed natural number. -/
+def masterCertificateMaximumVarintBytes : ℕ := 2
+
+/-- Decoder byte bound for one packed natural number. -/
+def masterCertificateVarintByteBound : ℕ := 16
+
+/-- Maximum string literals emitted in one generated data part. -/
+def masterCertificateMaximumStringsPerPart : ℕ := 500
+
+/-- Maximum measured compiled-expression steps used by one generated data part. -/
+def masterCertificateMaximumStringListExpressionSteps : ℕ := 616
+
+/-- Structural fuel used to decode one generated string-list part. -/
+def masterCertificateStringListFuel : ℕ := 640
+
+/-- SHA-256 of the generated DIMACS formula. -/
+def masterCertificateCnfSha256 : String :=
+  "08c463f6ab9db9cc6925f59fe09a5db880c0b8e4acbecb36258b2e92572c3ae4"
+
+/-- SHA-256 of the normalized LRAT text. -/
+def masterCertificateLratSha256 : String :=
+  "e793eacb1b67901daad1a61d11e9c6f20ccc7ad832b67d16fe7550c1ea292e83"
+
+/-- SHA-256 of the packed certificate bytes. -/
+def masterCertificatePackedSha256 : String :=
+  "55a6fad508976f2ccb1a0ee412ca941564df743a4d6cf4552be1bd3c3360ccae"
+
+/-- Pinned CaDiCaL source commit. -/
+def masterCertificateCadicalCommit : String :=
+  "c60730422e758ef1cebe7aeddf2dda31c996bf04"
+
+/-- Pinned drat-trim source commit. -/
+def masterCertificateDratTrimCommit : String :=
+  "2e3b2dc0ecf938addbd779d42877b6ed69d9a985"
+
+end Erdos97Octagon.RawIncidence
diff --git a/LeanPool/Erdos97ConvexOctagon/MasterCertificateStage00.lean b/LeanPool/Erdos97ConvexOctagon/MasterCertificateStage00.lean
new file mode 100644
index 00000000..1a164f18
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/MasterCertificateStage00.lean
@@ -0,0 +1,41 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.LRAT.Elab
+import LeanPool.Erdos97ConvexOctagon.MasterCertificateData0
+import LeanPool.Erdos97ConvexOctagon.MasterCertificateData1
+import LeanPool.Erdos97ConvexOctagon.MasterCertificateData2
+import LeanPool.Erdos97ConvexOctagon.MasterCertificateData3
+import LeanPool.Erdos97ConvexOctagon.MasterCertificateData4
+import LeanPool.Erdos97ConvexOctagon.MasterCertificateData5
+import LeanPool.Erdos97ConvexOctagon.MasterCertificateData6
+import LeanPool.Erdos97ConvexOctagon.MasterCertificateData7
+import LeanPool.Erdos97ConvexOctagon.MasterCertificateData8
+
+/-! # Master-certificate proof stage 0 -/
+
+namespace Erdos97Octagon.RawIncidence
+
+master_lrat_stage
+  initial_clauses 3263
+  additions 4294
+  stage_start 0
+  stage_stop 1432
+  clause_prefix masterCertificateClause
+  final_theorem masterFormula_unsatisfiable
+  data_parts
+    masterCertificatePart0
+    masterCertificatePart1
+    masterCertificatePart2
+    masterCertificatePart3
+    masterCertificatePart4
+    masterCertificatePart5
+    masterCertificatePart6
+    masterCertificatePart7
+    masterCertificatePart8
+
+
+end Erdos97Octagon.RawIncidence
diff --git a/LeanPool/Erdos97ConvexOctagon/MasterCertificateStage01.lean b/LeanPool/Erdos97ConvexOctagon/MasterCertificateStage01.lean
new file mode 100644
index 00000000..2e8a48dc
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/MasterCertificateStage01.lean
@@ -0,0 +1,32 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.MasterCertificateStage00
+
+/-! # Master-certificate proof stage 1 -/
+
+namespace Erdos97Octagon.RawIncidence
+
+master_lrat_stage
+  initial_clauses 3263
+  additions 4294
+  stage_start 1432
+  stage_stop 2864
+  clause_prefix masterCertificateClause
+  final_theorem masterFormula_unsatisfiable
+  data_parts
+    masterCertificatePart0
+    masterCertificatePart1
+    masterCertificatePart2
+    masterCertificatePart3
+    masterCertificatePart4
+    masterCertificatePart5
+    masterCertificatePart6
+    masterCertificatePart7
+    masterCertificatePart8
+
+
+end Erdos97Octagon.RawIncidence
diff --git a/LeanPool/Erdos97ConvexOctagon/MasterCertificateStage02.lean b/LeanPool/Erdos97ConvexOctagon/MasterCertificateStage02.lean
new file mode 100644
index 00000000..bdf0ae21
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/MasterCertificateStage02.lean
@@ -0,0 +1,32 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.MasterCertificateStage01
+
+/-! # Master-certificate proof stage 2 -/
+
+namespace Erdos97Octagon.RawIncidence
+
+master_lrat_stage
+  initial_clauses 3263
+  additions 4294
+  stage_start 2864
+  stage_stop 4294
+  clause_prefix masterCertificateClause
+  final_theorem masterFormula_unsatisfiable
+  data_parts
+    masterCertificatePart0
+    masterCertificatePart1
+    masterCertificatePart2
+    masterCertificatePart3
+    masterCertificatePart4
+    masterCertificatePart5
+    masterCertificatePart6
+    masterCertificatePart7
+    masterCertificatePart8
+
+
+end Erdos97Octagon.RawIncidence
diff --git a/LeanPool/Erdos97ConvexOctagon/MasterFormula.lean b/LeanPool/Erdos97ConvexOctagon/MasterFormula.lean
new file mode 100644
index 00000000..52a8f2db
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/MasterFormula.lean
@@ -0,0 +1,179 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.MasterFormulaData
+
+/-!
+# Master coverage formula
+
+The master formula combines the shared semantic clauses used by the certificate
+with the needed noncanonical first-row exclusions. It has 64 variables and 3,263 clauses.
+-/
+
+namespace Erdos97Octagon.RawIncidence
+
+open LRAT
+
+/-- Shared semantic-clause references retained in the unsatisfiable core. -/
+def masterReferences : List ℕ :=
+  (List.range 20659).filter fun reference =>
+    masterReferenceUsedB reference && (tagOfRef 0 0 reference).validB
+
+/-- The seven canonical first rows viewed as finite sets. -/
+def canonicalRows : List (Finset Vertex) :=
+  List.ofFn fun orbit : Fin 7 => packedRow (canonicalRowMask orbit)
+
+/-- Noncanonical first-row masks retained in the unsatisfiable core. -/
+def masterExcludedRowMasks : List ℕ :=
+  (List.range 256).filter fun mask =>
+    masterExcludedMaskUsedB mask &&
+      decide (packedRow (UInt64.ofNat mask) ∉ canonicalRows)
+
+/-- First rows excluded by the committed unsatisfiable core. -/
+def excludedRows : List (Finset Vertex) :=
+  masterExcludedRowMasks.map fun mask => packedRow (UInt64.ofNat mask)
+
+/-- A clause which is false precisely when row one equals `row`. -/
+def rowExclusionClause (row : Finset Vertex) : Clause :=
+  List.ofFn fun target : Vertex =>
+    if target ∈ row then
+      .negative (varIndex 1 target)
+    else
+      .positive (varIndex 1 target)
+
+/-- Retained shared clauses. -/
+def masterBaseFormula : Formula :=
+  masterReferences.map fun reference => (tagOfRef 0 0 reference).toClause
+
+/-- Retained noncanonical first-row exclusion clauses. -/
+def canonicalRowFormula : Formula :=
+  excludedRows.map rowExclusionClause
+
+/-- The single formula checked by the committed LRAT certificate. -/
+def masterFormula : Formula :=
+  masterBaseFormula ++ canonicalRowFormula
+
+/-- A valid in-range shared reference gives its clause directly from the master formula. -/
+theorem masterBaseClause_proves
+    (reference : ℕ) (hrange : decide (reference < 20659) = true)
+    (hused : masterReferenceUsedB reference = true)
+    (hvalid : (tagOfRef 0 0 reference).validB = true)
+    (clause : Clause) (hclause : clause = (tagOfRef 0 0 reference).toClause) :
+    masterFormula.Proves clause := by
+  subst clause
+  intro valuation hsatisfies
+  apply hsatisfies.property
+  rw [masterFormula, List.mem_append, masterBaseFormula, List.mem_map]
+  apply Or.inl
+  refine ⟨reference, ?_, rfl⟩
+  rw [masterReferences, List.mem_filter]
+  exact ⟨List.mem_range.mpr (of_decide_eq_true hrange),
+    by simpa only [Bool.and_eq_true] using And.intro hused hvalid⟩
+
+/-- A noncanonical in-range row mask gives its exclusion clause from the master formula. -/
+theorem canonicalRowClause_proves
+    (mask : ℕ) (hrange : decide (mask < 256) = true)
+    (hused : masterExcludedMaskUsedB mask = true)
+    (hnoncanonical :
+      decide (packedRow (UInt64.ofNat mask) ∉ canonicalRows) = true)
+    (clause : Clause)
+    (hclause : clause = rowExclusionClause (packedRow (UInt64.ofNat mask))) :
+    masterFormula.Proves clause := by
+  subst clause
+  intro valuation hsatisfies
+  apply hsatisfies.property
+  rw [masterFormula, List.mem_append, canonicalRowFormula, List.mem_map]
+  apply Or.inr
+  refine ⟨packedRow (UInt64.ofNat mask), ?_, rfl⟩
+  rw [excludedRows, List.mem_map]
+  refine ⟨mask, ?_, rfl⟩
+  rw [masterExcludedRowMasks, List.mem_filter]
+  exact ⟨List.mem_range.mpr (of_decide_eq_true hrange),
+    by simpa only [Bool.and_eq_true] using And.intro hused hnoncanonical⟩
+
+private theorem rowExclusionClause_satisfied
+    (Q : OctagonIncidence) (row : Finset Vertex)
+    (hne : Q.targets 1 ≠ row) :
+    (valuation Q.targets).satisfies (rowExclusionClause row) := by
+  apply LRAT.Valuation.satisfiesOfNotAllFalsified
+  intro hall
+  apply hne
+  ext target
+  rw [List.forall_iff_forall_mem] at hall
+  have hmember :
+      (if target ∈ row then
+          LRAT.Literal.negative (varIndex 1 target)
+        else
+          LRAT.Literal.positive (varIndex 1 target)) ∈ rowExclusionClause row := by
+    rw [rowExclusionClause, List.mem_ofFn]
+    exact ⟨target, rfl⟩
+  by_cases htarget : target ∈ row
+  · have hfalsified := hall _ hmember
+    simpa [htarget, LRAT.Valuation.falsifies, valuation_variable] using hfalsified
+  · have hfalsified := hall _ hmember
+    simpa [htarget, LRAT.Valuation.falsifies, valuation_variable] using hfalsified
+
+private theorem masterBaseFormula_satisfied
+    {p : Vertex → Plane} {Q : OctagonIncidence}
+    (hC : ConvexIndependent ℝ p) (hR : Realises p Q)
+    (hN : Q.Normalized) (hSparse : Q.PairSparse) (hBalanced : Q.Balanced) :
+    (valuation Q.targets).SatisfiesFormula masterBaseFormula := by
+  constructor
+  intro clause hclause
+  rw [masterBaseFormula, List.mem_map] at hclause
+  obtain ⟨reference, hreference, rfl⟩ := hclause
+  have hparts := List.mem_filter.mp hreference
+  have hchecks : masterReferenceUsedB reference = true ∧
+      (tagOfRef 0 0 reference).validB = true := by
+    simpa only [Bool.and_eq_true] using hparts.2
+  exact (tagOfRef 0 0 reference).satisfies hC hR hN hSparse hBalanced
+    ((tagOfRef 0 0 reference).valid_of_validB hchecks.2)
+    (tagOfRef_baseBranchValid Q (List.mem_range.mp hparts.1))
+
+/-- The canonical-row clauses are satisfied for one selected canonical orbit. -/
+theorem canonicalRowFormula_satisfied
+    (Q : OctagonIncidence) (orbit : Fin 7)
+    (hrow : Q.targets 1 = packedRow (canonicalRowMask orbit)) :
+    (valuation Q.targets).SatisfiesFormula canonicalRowFormula := by
+  constructor
+  intro clause hclause
+  rw [canonicalRowFormula, List.mem_map] at hclause
+  obtain ⟨row, hrowExcluded, rfl⟩ := hclause
+  rw [excludedRows, List.mem_map] at hrowExcluded
+  obtain ⟨mask, hmask, rfl⟩ := hrowExcluded
+  apply rowExclusionClause_satisfied
+  intro hequal
+  have hcanonical : packedRow (UInt64.ofNat mask) ∈ canonicalRows := by
+    rw [← hequal, hrow]
+    unfold canonicalRows
+    rw [List.mem_ofFn]
+    exact ⟨orbit, rfl⟩
+  have hmaskParts := List.mem_filter.mp hmask
+  have hmaskChecks : masterExcludedMaskUsedB mask = true ∧
+      decide (packedRow (UInt64.ofNat mask) ∉ canonicalRows) = true := by
+    simpa only [Bool.and_eq_true] using hmaskParts.2
+  have hnotCanonical : packedRow (UInt64.ofNat mask) ∉ canonicalRows :=
+    of_decide_eq_true hmaskChecks.2
+  exact hnotCanonical hcanonical
+
+/-- Every hypothetical normalized counterexample with canonical row one
+satisfies the master formula. -/
+theorem masterFormula_satisfied
+    {p : Vertex → Plane} {Q : OctagonIncidence}
+    (hC : ConvexIndependent ℝ p) (hR : Realises p Q)
+    (hN : Q.Normalized) (hSparse : Q.PairSparse) (hBalanced : Q.Balanced)
+    (orbit : Fin 7)
+    (hrow : Q.targets 1 = packedRow (canonicalRowMask orbit)) :
+    (valuation Q.targets).SatisfiesFormula masterFormula := by
+  constructor
+  intro clause hclause
+  rw [masterFormula, List.mem_append] at hclause
+  rcases hclause with hbase | hcanonical
+  · exact (masterBaseFormula_satisfied hC hR hN hSparse hBalanced).property
+      clause hbase
+  · exact (canonicalRowFormula_satisfied Q orbit hrow).property clause hcanonical
+
+end Erdos97Octagon.RawIncidence
diff --git a/LeanPool/Erdos97ConvexOctagon/MasterFormulaData.lean b/LeanPool/Erdos97ConvexOctagon/MasterFormulaData.lean
new file mode 100644
index 00000000..00c3f627
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/MasterFormulaData.lean
@@ -0,0 +1,111 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.RowSymmetry
+
+/-! # Generated master-formula core data -/
+
+namespace Erdos97Octagon.RawIncidence
+
+/-- Bitset of source-clause references retained in the unsatisfiable core. -/
+def masterReferenceWords : Array UInt64 := #[
+  65279, 0, 6054245457279494826, 12297664111594611348,
+  12290695751026430986, 12296235089538650794, 12106426295073286741, 3038248187879135910,
+  11721084945966473888, 11574961440274417160, 10961946942898741376, 2450558704720972168,
+  11694200616961870474, 11719078724732854313, 12297829382473034394, 6148914691237915306,
+  4701851469463158784, 45812984448, 12286945683374687568, 23090459312810,
+  12106426215079870545, 4611686018427423394, 2437239498081285, 12151418273816248840,
+  9808839989490943272, 4641568719538129032, 11676180718043533328, 289375150469161128,
+  9840365185804533776, 18320652080236200185, 58574344149794816, 156373316796416,
+  16140901380827756384, 15690541102385182062, 30751967071090, 135417298944,
+  477577216, 20731085583286272, 41049955237888, 2269880263614922752,
+  8004453240143872, 699183842149269504, 4613212140566759808, 1351079888211148837,
+  1836800, 70532112531456, 137791619776, 269156352,
+  11529250230441091264, 603501041765319696, 73325495764123650, 143282615091200,
+  5243034671172608000, 15472573364730818014, 15852630545700715455, 17437894875938807039,
+  4819694977254616062, 36100282415688704, 8560199916016631808, 9871764977258330315,
+  12819198254673535905, 17261909920381464790, 6902962401242775544, 8034395067448667035,
+  4232363302896645491, 14399133793503211605, 10093323258898857992, 2670565250079718758,
+  18085431369629774830, 15143710956201378379, 6393220096680036367, 1189216040921326938,
+  816721704146445073, 623570433608192, 14154657566601415466, 2307603894468616768,
+  306256536506597458, 5072302779683373827, 13898250291377119937, 1809901899135090950,
+  40134972199227520, 504403158266806272, 154618822656, 73606050007744512,
+  2247676679424651, 938112119106699456, 8075657957058021152, 2353412831224795138,
+  9223374753690048640, 37520935518278, 648518346341351442, 54043195533426712,
+  4415226380289, 576460821022900288, 8589950976, 292770259662815232,
+  2256197869633600, 4539611921514496, 67776, 17179869200,
+  65536, 144115188075872256, 1275716956061700, 4294967296,
+  34359738368, 34359738368, 137438953488, 0,
+  4398046511104, 1028, 0, 33554560,
+  2097152, 2600, 285873155342336, 144115188177051648,
+  5269283053779554304, 4503797222081552, 1153216356278075486, 9871894232631875852,
+  1362340264850507824, 70369281458192, 2427440336591651328, 5476377146882523145,
+  1125899911036928, 8589951056, 578712556697288720, 4398047035392,
+  18014400656967680, 0, 72198331534802944, 25165824,
+  8912057139328, 2256197860197376, 9223376778499719168, 2251937386856448,
+  0, 262144, 0, 0,
+  512, 20266473201074176, 17314086912, 0,
+  576465150350000256, 1024, 72060892572811264, 1073741824,
+  4503601775378432, 1585267068834516992, 17006598, 0,
+  131072, 1162210178838306945, 1126157604880416, 6917529027653666944,
+  21163399811432856, 1152921504640401408, 16777216, 0,
+  8796094070784, 0, 70368744177664, 18014401093173249,
+  0, 562949953421312, 1733885979187478528, 7,
+  14289926015827510789, 1081856, 0, 0,
+  0, 563499726012544, 4504166563053568, 0,
+  0, 0, 0, 196608,
+  17609365917696, 0, 2305843009213693952, 0,
+  1130847713361920, 0, 1125942856515616, 4611686019503228928,
+  17661711884352, 3497170457161891840, 1052736, 8796093022208,
+  0, 0, 0, 0,
+  9007199254740992, 0, 0, 0,
+  0, 0, 0, 0,
+  0, 2305843009213693952, 332802, 1152921504741072896,
+  9007243548819456, 35185462608132, 45035996282816512, 0,
+  0, 0, 0, 1188950301625810944,
+  0, 1024, 2048, 4611686035607257088,
+  4398046515200, 786480, 0, 9223654164934950912,
+  21111552, 18446744073709027328, 18446744073709551615, 7,
+  0, 0, 0, 0,
+  0, 0, 0, 18444492273895866368,
+  18446744073709551615, 18446744073709551615, 2047, 0,
+  18446744039349813248, 18446744073709551615, 18446744073709551615, 18446744073709551615,
+  18446744073709551615, 140737488355327, 0, 0,
+  0, 0, 0, 0,
+  0, 0, 0, 0,
+  0, 0, 0, 0,
+  0, 0, 0, 0,
+  0, 0, 0, 0,
+  0, 0, 0, 0,
+  0, 0, 0, 0,
+  0, 0, 0, 0,
+  0, 0, 0, 0,
+  0, 0, 0, 0,
+  0, 0, 0, 0,
+  0, 0, 0, 0,
+  0, 0, 0, 0,
+  0, 0, 0, 0,
+  0, 0, 0, 0,
+  0, 18446744073709551488, 18446744073709551615, 18446744073709551615,
+  18446744073709551615, 18446744073709551615, 18446744073709551615, 18446744073709551615,
+  2251799813685247, 0, 0, 0,
+  0, 0, 0
+]
+
+/-- Bitset of first-row masks retained in the unsatisfiable core. -/
+def masterExcludedMaskWords : Array UInt64 := #[
+  153122387330596864, 86168803613876256, 86151340276850688, 72903260267221536
+]
+
+/-- Whether a shared clause belongs to the committed unsatisfiable core. -/
+def masterReferenceUsedB (reference : ℕ) : Bool :=
+  bitSetB (masterReferenceWords.getD (reference / 64) 0) (reference % 64)
+
+/-- Whether a noncanonical first-row mask belongs to the committed core. -/
+def masterExcludedMaskUsedB (mask : ℕ) : Bool :=
+  bitSetB (masterExcludedMaskWords.getD (mask / 64) 0) (mask % 64)
+
+end Erdos97Octagon.RawIncidence
diff --git a/LeanPool/Erdos97ConvexOctagon/Obstructions.lean b/LeanPool/Erdos97ConvexOctagon/Obstructions.lean
new file mode 100644
index 00000000..6db8beaa
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/Obstructions.lean
@@ -0,0 +1,155 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.CycleStrip
+import LeanPool.Erdos97ConvexOctagon.EquidistantFour
+import LeanPool.Erdos97ConvexOctagon.Pentagon
+import LeanPool.Erdos97ConvexOctagon.Radius
+
+/-! # Erdős 97 convex-octagon formalization: Obstructions -/
+
+namespace Erdos97Octagon
+
+open scoped InnerProductSpace RealInnerProductSpace
+
+/-- A four-clique in one radius-labelled graph is impossible in the plane. -/
+theorem no_labelled_k4
+    {p : Vertex → Plane} (hp : Function.Injective p)
+    {Q : OctagonIncidence} (hR : Realises p Q)
+    {root a b c d : Vertex} (had : a ≠ d)
+    (hab : Q.LabelledEdge root a b) (hac : Q.LabelledEdge root a c)
+    (had' : Q.LabelledEdge root a d) (hbc : Q.LabelledEdge root b c)
+    (hbd : Q.LabelledEdge root b d) (hcd : Q.LabelledEdge root c d) :
+    False := by
+  obtain ⟨radius, hpos, hdist⟩ := exists_positive_radii hp Q hR
+  exact four_points_not_pairwise_equidistant (hp.ne had)
+    (dist_eq_radius_of_labelledEdge hdist hab)
+    (dist_eq_radius_of_labelledEdge hdist hac)
+    (dist_eq_radius_of_labelledEdge hdist had')
+    (dist_eq_radius_of_labelledEdge hdist hbc)
+    (dist_eq_radius_of_labelledEdge hdist hbd)
+    (dist_eq_radius_of_labelledEdge hdist hcd)
+
+/-- A hub and a five-cycle in one radius-labelled graph are impossible. -/
+theorem no_labelled_hub_pentagon
+    {p : Vertex → Plane} (hp : Function.Injective p)
+    {Q : OctagonIncidence} (hR : Realises p Q)
+    {root o a b c d e : Vertex}
+    (hoa : Q.LabelledEdge root o a) (hob : Q.LabelledEdge root o b)
+    (hoc : Q.LabelledEdge root o c) (hod : Q.LabelledEdge root o d)
+    (hoe : Q.LabelledEdge root o e) (hab : Q.LabelledEdge root a b)
+    (hbc : Q.LabelledEdge root b c) (hcd : Q.LabelledEdge root c d)
+    (hde : Q.LabelledEdge root d e) (hea : Q.LabelledEdge root e a) :
+    False := by
+  obtain ⟨radius, hpos, hdist⟩ := exists_positive_radii hp Q hR
+  exact no_unit_pentagon_centre (hpos root)
+    (dist_eq_radius_of_labelledEdge hdist hoa)
+    (dist_eq_radius_of_labelledEdge hdist hob)
+    (dist_eq_radius_of_labelledEdge hdist hoc)
+    (dist_eq_radius_of_labelledEdge hdist hod)
+    (dist_eq_radius_of_labelledEdge hdist hoe)
+    (dist_eq_radius_of_labelledEdge hdist hab)
+    (dist_eq_radius_of_labelledEdge hdist hbc)
+    (dist_eq_radius_of_labelledEdge hdist hcd)
+    (dist_eq_radius_of_labelledEdge hdist hde)
+    (dist_eq_radius_of_labelledEdge hdist hea)
+
+/-- A seven-vertex cycle-square strip in one radius-labelled graph is impossible. -/
+theorem no_labelled_cycle_square_strip
+    {p : Vertex → Plane} (hp : Function.Injective p)
+    {Q : OctagonIncidence} (hR : Realises p Q)
+    {root o x1 x2 x3 x4 x5 x6 : Vertex}
+    (e01 : Q.LabelledEdge root o x1) (e02 : Q.LabelledEdge root o x2)
+    (e06 : Q.LabelledEdge root o x6) (e12 : Q.LabelledEdge root x1 x2)
+    (e13 : Q.LabelledEdge root x1 x3) (e23 : Q.LabelledEdge root x2 x3)
+    (e24 : Q.LabelledEdge root x2 x4) (e34 : Q.LabelledEdge root x3 x4)
+    (e35 : Q.LabelledEdge root x3 x5) (e45 : Q.LabelledEdge root x4 x5)
+    (e46 : Q.LabelledEdge root x4 x6) (e56 : Q.LabelledEdge root x5 x6) :
+    False := by
+  obtain ⟨radius, hpos, hdist⟩ := exists_positive_radii hp Q hR
+  exact no_unit_cycle_square_strip (hpos root)
+    (dist_eq_radius_of_labelledEdge hdist e01)
+    (dist_eq_radius_of_labelledEdge hdist e02)
+    (dist_eq_radius_of_labelledEdge hdist e06)
+    (dist_eq_radius_of_labelledEdge hdist e12)
+    (dist_eq_radius_of_labelledEdge hdist e13)
+    (dist_eq_radius_of_labelledEdge hdist e23)
+    (dist_eq_radius_of_labelledEdge hdist e24)
+    (dist_eq_radius_of_labelledEdge hdist e34)
+    (dist_eq_radius_of_labelledEdge hdist e35)
+    (dist_eq_radius_of_labelledEdge hdist e45)
+    (dist_eq_radius_of_labelledEdge hdist e46)
+    (dist_eq_radius_of_labelledEdge hdist e56)
+
+private lemma common_circle_points_collinear
+    {A B q1 q2 q3 : Plane} (hAB : A ≠ B)
+    (hA12 : dist A q1 = dist A q2) (hA13 : dist A q1 = dist A q3)
+    (hB12 : dist B q1 = dist B q2) (hB13 : dist B q1 = dist B q3) :
+    Collinear ℝ ({q1, q2, q3} : Set Plane) := by
+  have hne : B -ᵥ A ≠ 0 := fun h => hAB (vsub_eq_zero_iff_eq.mp h).symm
+  have h12 : ⟪q2 -ᵥ q1, B -ᵥ A⟫ = (0 : ℝ) := by
+    rw [real_inner_comm]
+    exact EuclideanGeometry.inner_vsub_vsub_of_dist_eq_of_dist_eq
+      (by simpa [dist_comm] using hA12) (by simpa [dist_comm] using hB12)
+  have h13 : ⟪q3 -ᵥ q1, B -ᵥ A⟫ = (0 : ℝ) := by
+    rw [real_inner_comm]
+    exact EuclideanGeometry.inner_vsub_vsub_of_dist_eq_of_dist_eq
+      (by simpa [dist_comm] using hA13) (by simpa [dist_comm] using hB13)
+  have hfd : Module.finrank ℝ Plane = 1 + 1 := by
+    rw [finrank_euclideanSpace]
+    norm_num
+  letI : Fact (Module.finrank ℝ Plane = 1 + 1) := ⟨hfd⟩
+  have hfo : Module.finrank ℝ ((ℝ ∙ (B -ᵥ A) : Submodule ℝ Plane))ᗮ = 1 :=
+    Submodule.finrank_orthogonal_span_singleton hne
+  have horth : vectorSpan ℝ ({q1, q2, q3} : Set Plane) ≤
+      (ℝ ∙ (B -ᵥ A) : Submodule ℝ Plane)ᗮ := by
+    rw [vectorSpan_eq_span_vsub_set_right_ne ℝ (Set.mem_insert q1 _)]
+    rw [Submodule.span_le]
+    intro w hw
+    rw [Set.mem_image] at hw
+    obtain ⟨q, hq, rfl⟩ := hw
+    have hq_ne : q ≠ q1 := fun h => hq.2 (by simpa using h)
+    have hq_cases : q = q2 ∨ q = q3 := by
+      rcases hq.1 with hq | hq
+      · exact absurd hq hq_ne
+      rcases hq with hq | hq
+      · exact Or.inl hq
+      · simpa using Or.inr hq
+    rw [SetLike.mem_coe, Submodule.mem_orthogonal_singleton_iff_inner_left]
+    rcases hq_cases with rfl | rfl
+    · exact h12
+    · exact h13
+  letI : FiniteDimensional ℝ (vectorSpan ℝ ({q1, q2, q3} : Set Plane)) :=
+    Submodule.finiteDimensional_of_le horth
+  rw [collinear_iff_finrank_le_one]
+  calc
+    Module.finrank ℝ (vectorSpan ℝ ({q1, q2, q3} : Set Plane)) ≤
+        Module.finrank ℝ ((ℝ ∙ (B -ᵥ A) : Submodule ℝ Plane)ᗮ) :=
+      Submodule.finrank_mono horth
+    _ = 1 := hfo
+
+/-- Two distinct realised centres cannot share three distinct selected targets
+in a convex-independent planar family. -/
+theorem no_three_shared_targets
+    {p : Vertex → Plane} (hC : ConvexIndependent ℝ p)
+    {Q : OctagonIncidence} (hR : Realises p Q)
+    {a b q1 q2 q3 : Vertex} (hab : a ≠ b)
+    (h12 : q1 ≠ q2) (h13 : q1 ≠ q3) (h23 : q2 ≠ q3)
+    (ha1 : q1 ∈ Q.targets a) (ha2 : q2 ∈ Q.targets a)
+    (ha3 : q3 ∈ Q.targets a) (hb1 : q1 ∈ Q.targets b)
+    (hb2 : q2 ∈ Q.targets b) (hb3 : q3 ∈ Q.targets b) :
+    False := by
+  obtain ⟨ra, hra⟩ := hR a
+  obtain ⟨rb, hrb⟩ := hR b
+  have hcol : Collinear ℝ ({p q1, p q2, p q3} : Set Plane) :=
+    common_circle_points_collinear (hC.injective.ne hab)
+      ((hra q1 ha1).trans (hra q2 ha2).symm)
+      ((hra q1 ha1).trans (hra q3 ha3).symm)
+      ((hrb q1 hb1).trans (hrb q2 hb2).symm)
+      ((hrb q1 hb1).trans (hrb q3 hb3).symm)
+  exact three_collinear_not_convexIndependent hC h12 h13 h23 hcol
+
+end Erdos97Octagon
diff --git a/LeanPool/Erdos97ConvexOctagon/Pentagon.lean b/LeanPool/Erdos97ConvexOctagon/Pentagon.lean
new file mode 100644
index 00000000..d260c284
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/Pentagon.lean
@@ -0,0 +1,105 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.Gram
+
+/-! # Erdős 97 convex-octagon formalization: Pentagon -/
+
+namespace Erdos97Octagon
+
+open scoped InnerProductSpace
+
+/-- Five equal chords cannot form an odd cycle on a circle with the same radius. -/
+theorem no_unit_pentagon_centre
+    {o a b c d e : Plane} {R : ℝ} (hR : 0 < R)
+    (oa : dist o a = R) (ob : dist o b = R) (oc : dist o c = R)
+    (od : dist o d = R) (oe : dist o e = R)
+    (ab : dist a b = R) (bc : dist b c = R) (cd : dist c d = R)
+    (de : dist d e = R) (ea : dist e a = R) : False := by
+  set u0 : Plane := a - o with hu0
+  set u1 : Plane := b - o with hu1
+  set u2 : Plane := c - o with hu2
+  set u3 : Plane := d - o with hu3
+  set u4 : Plane := e - o with hu4
+  set s : ℝ := R ^ 2 with hs
+  have hs0 : 0 < s := by positivity
+  have norm_sq : ∀ {x : Plane}, dist o x = R → ⟪x - o, x - o⟫_ℝ = s := by
+    intro x hx
+    rw [real_inner_self_eq_norm_sq, ← dist_eq_norm, dist_comm, hx, hs]
+  have n0 : ⟪u0, u0⟫_ℝ = s := norm_sq oa
+  have n1 : ⟪u1, u1⟫_ℝ = s := norm_sq ob
+  have n2 : ⟪u2, u2⟫_ℝ = s := norm_sq oc
+  have n3 : ⟪u3, u3⟫_ℝ = s := norm_sq od
+  have n4 : ⟪u4, u4⟫_ℝ = s := norm_sq oe
+  have inner_half : ∀ {x y : Plane}, dist o x = R → dist o y = R →
+      dist x y = R → ⟪x - o, y - o⟫_ℝ = s / 2 := by
+    intro x y hox hoy hxy
+    have hsub : (x - o) - (y - o) = x - y := by abel
+    have hxynorm : ‖(x - o) - (y - o)‖ = R := by
+      rw [hsub, ← dist_eq_norm, hxy]
+    have hpolar := norm_sub_sq_real (x - o) (y - o)
+    have hnx : ‖x - o‖ ^ 2 = s := by
+      rw [← real_inner_self_eq_norm_sq]
+      exact norm_sq hox
+    have hny : ‖y - o‖ ^ 2 = s := by
+      rw [← real_inner_self_eq_norm_sq]
+      exact norm_sq hoy
+    rw [hxynorm, hnx, hny] at hpolar
+    have hR2 : R ^ 2 = s := hs.symm
+    nlinarith only [hpolar, hR2]
+  have i01 : ⟪u0, u1⟫_ℝ = s / 2 := inner_half oa ob ab
+  have i12 : ⟪u1, u2⟫_ℝ = s / 2 := inner_half ob oc bc
+  have i23 : ⟪u2, u3⟫_ℝ = s / 2 := inner_half oc od cd
+  have i34 : ⟪u3, u4⟫_ℝ = s / 2 := inner_half od oe de
+  have i40 : ⟪u4, u0⟫_ℝ = s / 2 := inner_half oe oa ea
+  set p : ℝ := ⟪u0, u2⟫_ℝ with hp
+  set q : ℝ := ⟪u0, u3⟫_ℝ with hq
+  have i10 : ⟪u1, u0⟫_ℝ = s / 2 := by rw [real_inner_comm]; exact i01
+  have i21 : ⟪u2, u1⟫_ℝ = s / 2 := by rw [real_inner_comm]; exact i12
+  have i32 : ⟪u3, u2⟫_ℝ = s / 2 := by rw [real_inner_comm]; exact i23
+  have i43 : ⟪u4, u3⟫_ℝ = s / 2 := by rw [real_inner_comm]; exact i34
+  have i04 : ⟪u0, u4⟫_ℝ = s / 2 := by rw [real_inner_comm]; exact i40
+  have p20 : ⟪u2, u0⟫_ℝ = p := by rw [hp, real_inner_comm]
+  have q30 : ⟪u3, u0⟫_ℝ = q := by rw [hq, real_inner_comm]
+  have hE1 := gram_det_eq_zero ![u0, u1, u2]
+  rw [gram3_expand] at hE1
+  simp only [n0, n1, n2, i01, i12, i10, i21, ← hp, p20] at hE1
+  have hE2 := gram_det_eq_zero ![u0, u2, u3]
+  rw [gram3_expand] at hE2
+  simp only [n0, n2, n3, i23, i32, ← hp, p20, ← hq, q30] at hE2
+  have hE3 := gram_det_eq_zero ![u0, u3, u4]
+  rw [gram3_expand] at hE3
+  simp only [n0, n3, n4, i34, i43, ← hq, q30, i04, i40] at hE3
+  ring_nf at hE1 hE2 hE3
+  have hp0 : s * ((p - s) * (2 * p + s)) = 0 := by
+    nlinarith only [hE1]
+  have hp_factor : (p - s) * (2 * p + s) = 0 :=
+    (mul_eq_zero.mp hp0).resolve_left (ne_of_gt hs0)
+  have hq0 : s * ((q - s) * (2 * q + s)) = 0 := by
+    nlinarith only [hE3]
+  have hq_factor : (q - s) * (2 * q + s) = 0 :=
+    (mul_eq_zero.mp hq0).resolve_left (ne_of_gt hs0)
+  have hs3 : 0 < s ^ 3 := by positivity
+  rcases mul_eq_zero.mp hp_factor with hp_branch | hp_branch <;>
+    rcases mul_eq_zero.mp hq_factor with hq_branch | hq_branch
+  · have ep : p = s := by linarith only [hp_branch]
+    have eq : q = s := by linarith only [hq_branch]
+    rw [ep, eq] at hE2
+    nlinarith only [hE2, hs3]
+  · have ep : p = s := by linarith only [hp_branch]
+    have eq : q = -(s / 2) := by linarith only [hq_branch]
+    rw [ep, eq] at hE2
+    nlinarith only [hE2, hs3]
+  · have ep : p = -(s / 2) := by linarith only [hp_branch]
+    have eq : q = s := by linarith only [hq_branch]
+    rw [ep, eq] at hE2
+    nlinarith only [hE2, hs3]
+  · have ep : p = -(s / 2) := by linarith only [hp_branch]
+    have eq : q = -(s / 2) := by linarith only [hq_branch]
+    rw [ep, eq] at hE2
+    nlinarith only [hE2, hs3]
+
+end Erdos97Octagon
diff --git a/LeanPool/Erdos97ConvexOctagon/Radius.lean b/LeanPool/Erdos97ConvexOctagon/Radius.lean
new file mode 100644
index 00000000..4cfe8009
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/Radius.lean
@@ -0,0 +1,84 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.GeometryReduction
+
+/-! # Erdős 97 convex-octagon formalization: Radius -/
+
+namespace Erdos97Octagon
+
+namespace OctagonIncidence
+
+/-- Two centres are mutually selected. -/
+def Mutual (Q : OctagonIncidence) (a b : Vertex) : Prop :=
+  b ∈ Q.targets a ∧ a ∈ Q.targets b
+
+/-- Two centres lie in the same connected component of mutual selections. -/
+def SameComponent (Q : OctagonIncidence) (a b : Vertex) : Prop :=
+  Relation.ReflTransGen Q.Mutual a b
+
+/-- An undirected pair is labelled by the radius of a mutual component when
+one endpoint in that component selects the other. -/
+def LabelledEdge (Q : OctagonIncidence) (root a b : Vertex) : Prop :=
+  (Q.SameComponent root a ∧ b ∈ Q.targets a) ∨
+    (Q.SameComponent root b ∧ a ∈ Q.targets b)
+
+end OctagonIncidence
+
+/-- An injective realisation admits a positive radius at every centre. -/
+theorem exists_positive_radii
+    {p : Vertex → Plane} (hp : Function.Injective p)
+    (Q : OctagonIncidence) (hR : Realises p Q) :
+    ∃ radius : Vertex → ℝ,
+      (∀ v, 0 < radius v) ∧
+        ∀ v w, w ∈ Q.targets v → dist (p v) (p w) = radius v := by
+  classical
+  choose radius hradius using hR
+  refine ⟨radius, ?_, hradius⟩
+  intro v
+  have hne : (Q.targets v).Nonempty := by
+    rw [Finset.nonempty_iff_ne_empty]
+    intro hempty
+    have := Q.card_targets v
+    rw [hempty] at this
+    simp at this
+  obtain ⟨w, hw⟩ := hne
+  have hvw : v ≠ w := fun h => Q.centre_not_mem v (h ▸ hw)
+  have hpvw : p v ≠ p w := hp.ne hvw
+  have hpos : 0 < dist (p v) (p w) := dist_pos.mpr hpvw
+  rwa [hradius v w hw] at hpos
+
+/-- Mutual centres have equal radii in any realisation. -/
+theorem radius_eq_of_mutual
+    {p : Vertex → Plane} {Q : OctagonIncidence} {radius : Vertex → ℝ}
+    (hR : ∀ v w, w ∈ Q.targets v → dist (p v) (p w) = radius v)
+    {a b : Vertex} (hab : Q.Mutual a b) :
+    radius a = radius b := by
+  rw [← hR a b hab.1, ← hR b a hab.2, dist_comm]
+
+/-- Radii are constant along a mutual connected component. -/
+theorem radius_eq_of_sameComponent
+    {p : Vertex → Plane} {Q : OctagonIncidence} {radius : Vertex → ℝ}
+    (hR : ∀ v w, w ∈ Q.targets v → dist (p v) (p w) = radius v)
+    {a b : Vertex} (hab : Q.SameComponent a b) :
+    radius a = radius b := by
+  induction hab with
+  | refl => rfl
+  | tail _ hedge ih =>
+      exact ih.trans (radius_eq_of_mutual hR hedge)
+
+/-- A labelled edge has the radius of its mutual component. -/
+theorem dist_eq_radius_of_labelledEdge
+    {p : Vertex → Plane} {Q : OctagonIncidence} {radius : Vertex → ℝ}
+    (hR : ∀ v w, w ∈ Q.targets v → dist (p v) (p w) = radius v)
+    {root a b : Vertex} (hab : Q.LabelledEdge root a b) :
+    dist (p a) (p b) = radius root := by
+  rcases hab with ⟨hroot, hedge⟩ | ⟨hroot, hedge⟩
+  · exact (hR a b hedge).trans (radius_eq_of_sameComponent hR hroot).symm
+  · rw [dist_comm]
+    exact (hR b a hedge).trans (radius_eq_of_sameComponent hR hroot).symm
+
+end Erdos97Octagon
diff --git a/LeanPool/Erdos97ConvexOctagon/Regenerate.lean b/LeanPool/Erdos97ConvexOctagon/Regenerate.lean
new file mode 100644
index 00000000..3403c19e
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/Regenerate.lean
@@ -0,0 +1,832 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.LRAT.Elab
+
+/-!
+# Deterministic master-certificate regeneration
+
+Run from the repository root, replacing the two executable paths:
+
+```
+lake env lean --stdin <<'EOF'
+import LeanPool.Erdos97ConvexOctagon.Regenerate
+regenerate_erdos97 "check" "." "/path/to/cadical" "/path/to/drat-trim"
+EOF
+```
+
+Use `write` instead of `check` to replace generated Lean modules.  The supplied
+executables must come from the pinned source commits recorded below.  Ordinary
+library builds only check the committed packed certificate and never run
+external tools.
+-/
+
+namespace Erdos97Octagon.Regenerate
+
+open LRAT RawIncidence
+open System
+open Std
+
+private def cadicalCommit :=
+  "c60730422e758ef1cebe7aeddf2dda31c996bf04"
+
+private def dratTrimCommit :=
+  "2e3b2dc0ecf938addbd779d42877b6ed69d9a985"
+
+private def solverInitialClauseCount := 6582
+private def initialClauseCount := 3263
+private def additionsPerStage := 1432
+private def encodedLineWidth := 94
+private def linesPerDataModule := 500
+
+private def stageCount (additionCount : ℕ) : ℕ :=
+  (additionCount + additionsPerStage - 1) / additionsPerStage
+
+private def stageStart (index : ℕ) : ℕ :=
+  index * additionsPerStage
+
+private def stageStop (additionCount index : ℕ) : ℕ :=
+  min additionCount ((index + 1) * additionsPerStage)
+
+private inductive Mode where
+  | check
+  | write
+
+private def Mode.text : Mode → String
+  | .check => "check"
+  | .write => "write"
+
+private structure Configuration where
+  mode : Mode
+  repository : FilePath
+  cadical : FilePath
+  dratTrim : FilePath
+
+private inductive ParsedAction where
+  | deletion
+  | addition (value : Addition)
+
+private structure ParsedCertificate where
+  proofSteps : Array Addition
+  actions : ℕ
+  deletions : ℕ
+
+private structure DerivedCore where
+  identifiers : HashMap ℕ ℕ
+  referenceWords : Array UInt64
+  excludedMaskWords : Array UInt64
+
+private def parseNatural (token : String) : Except String ℕ :=
+  match token.toNat? with
+  | some value => pure value
+  | none => throw s!"expected a natural number, got '{token}'"
+
+private def parseInteger (token : String) : Except String Int :=
+  match token.toInt? with
+  | some value => pure value
+  | none => throw s!"expected an integer, got '{token}'"
+
+private def takeIntegersUntilZero :
+    List String → Except String (Array Int × List String)
+  | [] => throw "unterminated integer sequence"
+  | token :: remaining => do
+      let value ← parseInteger token
+      if value = 0 then
+        pure (#[], remaining)
+      else
+        let (values, remaining) ← takeIntegersUntilZero remaining
+        pure (values.insertIdx 0 value, remaining)
+
+private def takeNaturalsUntilZero :
+    List String → Except String (Array ℕ × List String)
+  | [] => throw "unterminated natural-number sequence"
+  | token :: remaining => do
+      let value ← parseNatural token
+      if value = 0 then
+        pure (#[], remaining)
+      else
+        let (values, remaining) ← takeNaturalsUntilZero remaining
+        pure (values.insertIdx 0 value, remaining)
+
+private def lineTokens (line : String) : List String :=
+  (line.trimAscii.copy.splitOn " ").filter fun token => !token.isEmpty
+
+private def parseActionLine (line : String) : Except String ParsedAction := do
+  let tokens := lineTokens line
+  let identifierToken :: remaining := tokens
+    | throw "empty LRAT action"
+  let identifier ← parseNatural identifierToken
+  match remaining with
+  | "d" :: deletionTokens =>
+      let (_, trailing) ← takeNaturalsUntilZero deletionTokens
+      unless trailing.isEmpty do
+        throw "trailing tokens after LRAT deletion"
+      pure .deletion
+  | _ =>
+      let (literals, remaining) ← takeIntegersUntilZero remaining
+      let (antecedents, trailing) ← takeNaturalsUntilZero remaining
+      unless trailing.isEmpty do
+        throw "trailing tokens after LRAT addition"
+      pure <| .addition { identifier, literals, antecedents }
+
+private def parseCertificate (text : String) : Except String ParsedCertificate := do
+  let mut proofSteps := #[]
+  let mut actions := 0
+  let mut deletions := 0
+  for line in text.splitOn "\n" do
+    unless line.trimAscii.isEmpty do
+      actions := actions + 1
+      match ← parseActionLine line with
+      | .deletion => deletions := deletions + 1
+      | .addition addition => proofSteps := proofSteps.push addition
+  pure { proofSteps, actions, deletions }
+
+private def packedLiteralCode (literal : Int) : Except String ℕ :=
+  if literal = 0 then
+    throw "zero is not a literal"
+  else if literal < 0 then
+    pure (2 * ((-literal).toNat - 1) + 1)
+  else
+    pure (2 * (literal.toNat - 1))
+
+private def varintByteCountWithFuel :
+    ℕ → ℕ → Option ℕ
+  | 0, _ => none
+  | fuel + 1, value =>
+      if value < 128 then
+        some 1
+      else
+        (varintByteCountWithFuel fuel (value / 128)).map Nat.succ
+
+private def packedNaturalValues
+    (initialClauses : ℕ) (steps : Array Addition) :
+    Except String (Array ℕ) := do
+  let mut previous := initialClauses
+  let mut values := #[]
+  for addition in steps do
+    values := values.push (addition.identifier - previous)
+    values := values.push addition.literals.size
+    for literal in addition.literals do
+      values := values.push (← packedLiteralCode literal)
+    values := values.push addition.antecedents.size
+    for antecedent in addition.antecedents do
+      values := values.push (addition.identifier - antecedent)
+    previous := addition.identifier
+  pure values
+
+private def maximumVarintByteCount
+    (initialClauses : ℕ) (steps : Array Addition) :
+    Except String ℕ := do
+  let values ← packedNaturalValues initialClauses steps
+  let mut maximum := 0
+  for value in values do
+    let some count :=
+        varintByteCountWithFuel packedVarintByteBound value
+      | throw "packed natural exceeds the decoder byte bound"
+    maximum := max maximum count
+  pure maximum
+
+private def literalInteger : Literal → Int
+  | .positive index => Int.ofNat (index + 1)
+  | .negative index => -Int.ofNat (index + 1)
+
+private def renderClause (clause : Clause) : String :=
+  let literals := clause.map fun literal => toString (literalInteger literal)
+  String.intercalate " " literals ++ " 0\n"
+
+private def retiredPatternCount : ℕ := 508
+
+private def retiredPatternPackedBytes : ℕ := 5080
+
+private def retiredPatternEncoded : String :=
+  String.join [
+    "HAAAAGFhAAAAAD0AAAAARUUAAABGAAAAAGRkAAAAWgAAAADBwQAAAG0AAAAAAEVFAACYAAAAACUAACUAuAAAAACk",
+    "AACkALkAAAAAAKQApADJAAAAACUAAAAlygAAAAAAJQAAJcsAAAAAAAAAJSXaAAAAAABFAABF6AAAAABkAAAAZOwA",
+    "AAAAAGgAAGgIAQAsKiIAAAAACgEALCImAAAAAAsBACwoJgAAAAAPAQBMSkQAAAAAEAEATEJGAAAAABEBAExIRgAA",
+    "AAASAQBESkYAAAAAGAEAhIqGAAAAADUBAAA4NCQAAAA7AQAAODQoAAAAQAEAADgkLAAAAEEBAAA4MCwAAABKAQBE",
+    "UgBGAAAATQEAAFhUSAAAAFABAEgAUkoAAABSAQAAWERMAAAAUwEAAFhQTAAAAFQBAABIVEwAAABcAQCEkgCGAAAA",
+    "aAEAJSMAAAMAAGsBACUjAAAFAABxAQAAKSUACQAAewESAAAAIxMAAIsBAABoZABIAACrAQCkoAAAhgAAyAEARUMA",
+    "AAADAMwBAEVDAAAABQDRAQYAQwAAAAcA2wEAAFEARQARAOYBAAAAYQBJIQDnAQAAAABhUSEA7QEAAAAAYlIiAAkC",
+    "AAAAYQBBKQAKAgAAACEASSkACwIAAABBAEkpAA4CACgAYgAAKgAZAgAAcABkADAAGgIAAABwaAAwACACAAAAACFR",
+    "MQAhAgAAAABBUTEAKQIAAHAAYAA0AC8CAAAAcGAAOAA9AgDEwAAAAIYAgAIAAKIAAIYAIoUCAACwAKQAACSwAgAA",
+    "oACkAAA0tgIAAACgqAAAOMcCAMTAAAAAAEb/AgAAAOAAAChoAAMAAAAA4FAAcAEDAAAAAOAAMHAOAw4FCgYAAAAA",
+    "NAMcABEFDAAAAFEDFAAwACUFAABSAwAsCiIABgAAVQMALAokAAYAAGUDDAApIQAJAABwAwAsIgYACgAAdQMAJCgm",
+    "AAoAAIgDAAA4FCQMAACJAwAAODAkDAAAjQMAADA0KAwAALIDACQyAAYUAAC9AwAAKDAsFAAAxAMAKAAyChgAAMcD",
+    "AAAwNAwYAADOAwAAMBQsGAAA0AMYAAAhCRkAANQDGAAAESgZAAD/AwBkYAAARAYAEgQYAABBSQAJABQEAExCBgAA",
+    "CgAiBAAoAGIAQgoAKQQKSAADAAALADQEAABYFEQADAA8BAAAKGQARAwAQgQMAEEFAAANAEYEDAAJRAAADQBKBBgA",
+    "AFFBABEAYwQAYAAAYkISAG4EAERSAAYAFAB8BAAAMABkRBQAgQQAAGAAZFAUAIIEFABBAAUAFQCGBBQAEQBEABUA",
+    "iAQASABSCgAYAIoEAABIVAwAGACNBAAASFREABgAkgQAAFAUTAAYAJUEAAAAcGBIGACcBBgAAEEJABkApwQAaABg",
+    "AAoiAK0EAGAAAGISIgCwBAAoAGIAQiIAwgQAKABgAEoiAM0EAGRgAAAGJADPBABgYgAABiQA2wQAYGIAAEIkANwE",
+    "AGQiAABEJADlBABgQgAARiQA6gQAAChEAEwkAO4EAABwAERQJAAFBQAAAHBgGCgADAUAAGgkAEQoABAFAGgAIgBI",
+    "KAASBQBoAEIASCgAFQUAAABQaEgoABcFAGAAIgBKKAAdBQAAYEQATCgAHgUAAABwSFAoACAFAAAAMGhQKAAnBQAo",
+    "AGAAQioALAUAAEgkAEQsADYFAABwAEQUMABCBQAAcAAkRDAARAUAAFAAZEQwAEgFAAAAUGhIMABPBQAAAHBIUDAA",
+    "VwUAAGAARFQwAIcFHgAJBgsAAACeBQAtIyIACQAAugUcADA1AAwAAMcFACUzACQRAADOBRYkAAAnEgAA4AUWACIA",
+    "JxQAAOsFHAAAJSEVAAD+BRopAAAhGQAA/wUcACkAIRkAAAMGHAARACwZAAAFBgAoaGYAQgAACAYAKAByaEIAACwG",
+    "AABYJGRMAABBBgAAMHBMVAAARwYYAABhSVgAAEwGACSqpACCAABtBgAoAJKoigAAdQYAACiUqIwAAIoGFACRAKGU",
+    "AACNBgAAqJQomAAAkwYYAACBqZgAAK4GDkUARgAACgCvBg5EAEcAAAoAvgYOAEpDAAAMANEGAEVTAEQAEQDTBgBh",
+    "AABgUxEA7AYcAFgASQAUAAUHHABJAEEAGQAIBwBlQwAAQiEAEwcAbAAmAEQiACsHACVjAABBJAA5BwAsaAAASiQA",
+    "WAcAbEoAAEIoAHQHACxiQgAAKgCBBwBkKkQAACwAhAcAAEg0aAAsAK0HAGEAAGARMwCxBwAAUHAsADQAsgcAZDIA",
+    "RAA0AN8HAADQUMwAiAD5BwDEkgBEAJQAEwgOAIoFAAAABxsIDoQAhwAAAAogCA4Ag4EAAAALJQgOAIuCAAAADCoI",
+    "HACYkQAAAAwsCBwAkJUAAAAMNAgWhAAAhwAAEjkIFgCDAIEAABM9CBYAkwCCAAAUQAgWAIIAhwAAFEEIHACZAIgA",
+    "ABRECBwAiACNAAAUTAgaAACCiwAAGGMIACyoAACKACRkCAAAoiYAigAkfAgALACkAIYAKIsIAAAA8ACQOCihCAAA",
+    "cADgxAAwsQgAAJiwAIgANL0IAMQAAEYAlELRCAAAwgBGAJJE1AgAZOIAAACgRNYIAADwAGQAoETmCABMAMQAAIZI",
+    "5wgAAADwAFiQSOoIAABY0AAAlEjtCAAAaOQAAKBI7ggAAADwaACgSPwIAMQAhgAAgkwBCQAAUgDCAIZQCQkAAHAA",
+    "5ACgUAoJAAAAcOgAoFAZCQAAmNAAAIhUGgkAAADEjACIVEAJHgwSAwYAAABSCR4MCRIJAAAAUwkeBQoSCQAAAFYJ",
+    "HgwDFAkAAABZCR4FEhQJAAAAXgkeBRERCgAAAGAJHgUSEQoAAABlCRYNERIKAAAAawkWDBESCwAAAHQJHgUKEQwA",
+    "AAB8CR4FChQMAAAAlgkaIQAyCQMAAJcJGigAMgkDAACeCRohADEoAwAAoAkaIQARKgMAAKUJDiEqBQAFAADLCQ4s",
+    "IQUABgAAzgkOLCgFAAYAANIJFiQxAAMGAADcCQ4hCgUABwAA7gkOLAMhAAkAAO8JDiUiIQAJAADwCQ4kIyEACQAA",
+    "8wkGLSEiAAkAABcKDiUJIgAKAAAdCg4hAyYACgAARAoOBSgjAAwAAHIKFiQjACERAABzChYFMgAhEQAAiAoGJTIA",
+    "JBEAAI4KFiERACYRAACmChYhAwAmEgAArwoaKAARKhIAALsKGigAISETAADSChYFIQAmFAAA5goWISIAIRUAAPEK",
+    "FgUSACQVAAABCxwACTAlGAAAEwscABEhDBkAACwLDkxBAwAAAwA/Cw5MQgMAAAUAWQsOQUoDAAAGAGILFkRRAAMA",
+    "BgCWCw5EQ0EAAAkAmgsGTENCAAAJAJwLBkVKRAAACQCrCw5MCUEAAAoArAsORQlCAAAKALALDkwJRAAACgC4CxpB",
+    "AFIDAAoA3QsOREJBAAALAA4MAAA4RGgUDAATDAAASDRkGAwAGQwKQUgHAAANACsMFkVCAEEAEQA6DAZFUQBEABEA",
+    "QQwWRREAQgASAEMMFkQRAEMAEgBQDBpBAANKABIAcAwWBUIAQQATAIcMFgVBAEYAFACIDBYFQgBGABQApQwAAFBk",
+    "LBgUAK0MFkQDAEEAFQCuDBYFEgBBABUAwQwcABFURAAYANQMAABwNEQMGADVDAAAcDRIDBgAIA0GYUMAAEQiADIN",
+    "BmQDAABFIgA0DQZhIgAARSIAbQ0AaAAwKlAiAIkNBiVBAABCIwCKDQYkQwAAQiMAkg0GJWIAAEEkAK4NBmFDAABE",
+    "JAC9DQYlQgAARSQACg4AAEgwLFQkAC0OCikAYQBBKADSDgBkUgAGQjAA3Q4AJGIAZEIwAC0PFABRAEFUMABaDxQA",
+    "IQBFUDQAfw8GxMEAAAADBo4PDoSDgQAAAAmrDw6EgoEAAAALuA8cAJCUCQAADL4PAACINKQYAAz0DxwAiBGMAAAU",
+    "+g8AAJCkLBgAFAAQAACQxEwAGBQGEBwAiISBAAAVDBAcAAmQhQAAGCIQHACIhIEAABlhEAwACaEAhQAodBAAAGjA",
+    "AMgkKHcQAAAA0GCYKCh+EBQAEQChhQAwpxAGxAMAAACFQs4QAGTAAAAGokTuEAAAaKAARKhICxEAAHAAoESwUBcR",
+    "AAAAMGDImGAYEQAAAGAo0JhgLxEAAKjAAAyIZDARAACwAMAUkGQ0EQAAwKQADIRoOREeITgRAAYAAEERHiE4AAkG",
+    "AABGER4hOAAMBgAASREWLAASCQcAAFcRHiEZMAAKAACLEQ4sGQAkEgAAjhEOLQAUKBIAAJERHiEYACwSAACcER4N",
+    "KAAhFAAAphEOACsSKBQAAKgRHgkhACoUAACqER4AIQMqFAAArBEeACESKhQAALQRHg0AJCEYAAC4ER4ACiYhGAAA",
+    "xREWDAAiJxgAAMwRCmVoBQBCAADNEQphagUAQgAA1hESYXIABUIAAOgRCmFqBQBEAAASEgplYiEASAAAExIMZGMh",
+    "AEgAAFUSFGRjACFQAABkEhRkAwBjUAAAqRIKoaoFAIIAAMQSCqGqBQCEAADMEhKhsgAFhAAAGhMKIQCRqIoAAB4T",
+    "CqGiIQCMAAAfEwoFqoEAjAAAOxMSBbIAoZAAAFgTCiEAsYiSAACCEwAMoiKkmAAAhBMeQVgRAAAGAIoTHkFYAAkA",
+    "BgCOEx5BWAAMAAYAnhMOAFIRDAAHALATHkEAVAwACgDDEw4AEVIMAAsA0BMeAFJBAwAMANkTFgBSUAsADAD3Ew5M",
+    "GQBEABIA+hMeQQkATAASABMUFgAJFEoAEwAYFB4NSABBABQAHBQeAEoGQQAUAEUUHgAKRkEAGABPFB4AEkFGABgA",
+    "WhQcAABkQQ0YAHUUCmFqBQAAIgB/FAphABFqACIAgRQOTCkAAEQiAJwUDkEABQBNIgCfFBZFAAAmUCIAthQKYWoF",
+    "AAAkALoUEmFyAAUAJADZFA4pQQAASSQAVhUaAABDKlAoAGkVAGwSACRYKABqFQ4hSQAAQikAgBUAADAyDEYqAJIV",
+    "CmUiQQAALACTFQxkI0EAACwApBUOIQAFAEItALYVFiUAAEZCMAC3FRYkAABHQjAAuRUaKQAASkIwAMcVFiUAAEFF",
+    "MADUFRoAACNKSDAA+hUSJWIAQQAyABcWFGQjAEEANAAkFhYhEQAAQjUAJRYWIQAABUI1AC8WAGQSYkQAOAAzFgBs",
+    "EgBESDgANxYaIQAACUI5AFQWCgXKgQAAjABXFhTEwwBBAJAAcBYeAAuCgQAAGHEWHg0AhIEAABh5FgAkQgAAg6Uh",
+    "mRYAAAAwSMmRQSYXHgUwIQYMAAAsFx4AMTIGDAAAaxcOLBgFJBIAAKUXHgwjACoUAADsFxIlcgBhQgAABRgKYWol",
+    "AEgAAB4YDmEhQwBMAABqGAolqqEAggAAbBgSJbIAoYIAAJwYBqGLJACMAACeGA6hIYMAjAAArxgSobIAJZAAAL0Y",
+    "FCSjAIWSAADDGBahgwAhlAAAyRgGoZMAJJQAABsZEkFIFEoABwAnGR5FElQAAAoARxkGQVJQDAALAEoZEkEYREYA",
+    "CwBbGR4AUVIGAAwAihkOTBgFRAASAI8ZDkwJFEgAEgCSGR5FCgBMABIAnxkGZCMAYBESALIZHgVIBkEAFADDGR4A",
+    "ShJJABQA3BkeDAlCQQAYAN0ZHgUKQkEAGADfGR4MA0RBABgA4xkeBRJBQgAYAAQaHAxSQwAAGQALGg5FKAMARCIA",
+    "GhoWRTAAA0QiAD8aGkEAMgNIIgBFGg5sAwAASSIAUBoWQRMAIlAiAKcaFiFSAAZCJADPGg4haAAASyQAFhsKYWpF",
+    "AAAoABsbDiQjQQBBKAArGw4pA0QAQigAWhsOJANBAEUoAFsbDiQiQQBFKACqGw5hQSMAACwArRsOYSNBAAAsAPUb",
+    "FiQiAEFDMAATHBYkAwBBRTAAUxwWJWEAQQAyAFccBiVxAEQAMgBcHBZkAABBRTIAxRweDIIFgQAAFMYcHgyCBoEA",
+    "ABTNHB4MCoSBAAAYHB0ODYFEAACIRCMdBmGjAAAApEQmHQ4NSIEAAIRIbx0eIRImBQoAAAweCgVyEWhEAAAbHhJl",
+    "YjAJSAAALh4KZWIRKFAAAC8eDGRjEShQAABgHhIFqrAJhAAAaB4GCbESqIQAAN4eHkRSQQUACQDhHh5MGEEFAAoA",
+    "5R4eQRJGBQAKAOseHkERUgYACgA9Hx5BCQZKABIAaR8aAGAjSgwUAMcfHkE4AAlEIgAkIB4hWAAJQiQA/SAOLRgA",
+    "REIwAAkhHgwqAEFEMACDIR6BEZIGAAAKnCEegQkGigAAErAhHoE4AAmEACKyIR6BETQAiAAiviEOgUkAAMApIsYh",
+    "HgCSIQOIACTMIR4AgQMqkAAk2CEeIQCUBYIAKOYhDkQAhwDAIijuIR4hCQCMggAwAiIegVgRAACEQgQiHoFYAAkA",
+    "hEIVIh5BmBEAAIJEFyIeQZgACQCCRDIiHgUAgUYAkEg/Ih5BCQCMAIJQUSIWQTEAAJGCYF4iDiFJAACCiWBjIhop",
+    "AABBiZBgcCMKYVASDAsGAFIkDkUJEihQIgBiJB4sWAAFQiQAbyQWDFEiA0gkAMgkHiEJUAxCKAA0Jh5MAMSBAAoY",
+    "QSYehAoDIZAAIosmFiQhkAmDACiVJh4FEoEikAAotCYOJCERiIMAMEwnHgwDRIEAiFBwJwYpgQAAyIpkvigagSgG",
+    "qhQAEjQpFgAywEOEGChAKR4AE4FCwDAoqykWJbAABUGgRLcpHgmBACpQoETYKRYlAJAJRaBI/ioODRhBJJCIYA",
+  ]
+
+private def packedByteAt (bytes : ByteArray) (index : ℕ) : Except String ℕ :=
+  match bytes[index]? with
+  | some byte => pure byte.toNat
+  | none => throw "retired-pattern data ended early"
+
+private def decodeLittleEndianUInt64
+    (bytes : ByteArray) (offset : ℕ) : Except String UInt64 := do
+  let mut value : ℕ := 0
+  for index in [0:8] do
+    value := value + (← packedByteAt bytes (offset + index)) * 256 ^ index
+  pure (UInt64.ofNat value)
+
+private def decodeRetiredPatterns : Except String (Array (ℕ × UInt64)) := do
+  let bytes ← decodeBase64 retiredPatternEncoded
+  unless bytes.size = retiredPatternPackedBytes do
+    throw "retired-pattern packed size mismatch"
+  let mut result := Array.mkEmpty retiredPatternCount
+  let mut previousOrigin : Option ℕ := none
+  for index in [0:retiredPatternCount] do
+    let offset := 10 * index
+    let low ← packedByteAt bytes offset
+    let high ← packedByteAt bytes (offset + 1)
+    let origin := low + 256 * high
+    let mask ← decodeLittleEndianUInt64 bytes (offset + 2)
+    unless origin < 11043 do
+      throw s!"retired pattern origin {origin} is out of range"
+    if let some previous := previousOrigin then
+      unless previous < origin do
+        throw "retired pattern origins are not strictly increasing"
+    result := result.push (origin, mask)
+    previousOrigin := some origin
+  pure result
+
+private def retiredPatternMap : Except String (HashMap ℕ UInt64) := do
+  let entries ← decodeRetiredPatterns
+  let mut result : HashMap ℕ UInt64 := {}
+  for (origin, mask) in entries do
+    unless (patternEntry origin).isNone do
+      throw s!"retired pattern origin {origin} remains in semantic coverage data"
+    result := result.insert origin mask
+  pure result
+
+private def solverExcludedMasks : List ℕ :=
+  (List.range 256).filter fun mask =>
+    decide (packedRow (UInt64.ofNat mask) ∉ canonicalRows)
+
+private def retiredPatternClause (mask : UInt64) : Clause :=
+  ((List.range 64).filter fun index => bitSetB mask index).map .negative
+
+private def isPatternReference (reference : ℕ) : Bool :=
+  decide (3376 ≤ reference ∧ reference < 14419)
+
+private def solverReferenceValidB
+    (retired : HashMap ℕ UInt64) (reference : ℕ) : Bool :=
+  if isPatternReference reference then
+    (tagOfRef 0 0 reference).validB ||
+      retired.contains (reference - 3376)
+  else
+    (tagOfRef 0 0 reference).validB
+
+private def solverReferenceClause
+    (retired : HashMap ℕ UInt64) (reference : ℕ) : Clause :=
+  if isPatternReference reference then
+    match retired[reference - 3376]? with
+    | some mask => retiredPatternClause mask
+    | none => (tagOfRef 0 0 reference).toClause
+  else
+    (tagOfRef 0 0 reference).toClause
+
+private def solverReferences (retired : HashMap ℕ UInt64) : List ℕ :=
+  (List.range 20659).filter (solverReferenceValidB retired)
+
+private def solverFormula (retired : HashMap ℕ UInt64) : Formula :=
+  (solverReferences retired).map (solverReferenceClause retired) ++
+    solverExcludedMasks.map fun mask =>
+      rowExclusionClause (packedRow (UInt64.ofNat mask))
+
+private def renderMasterCnf (retired : HashMap ℕ UInt64) :
+    Except String String := do
+  let formula := solverFormula retired
+  unless formula.length = solverInitialClauseCount do
+    throw s!"expected {solverInitialClauseCount} solver clauses, got {formula.length}"
+  pure <| s!"p cnf 64 {solverInitialClauseCount}\n" ++
+    String.join (formula.map renderClause)
+
+private def bitsetWords
+    (size : ℕ) (values : Array ℕ) : Except String (Array UInt64) := do
+  let mut words := Array.replicate ((size + 63) / 64) 0
+  for value in values do
+    unless value < size do
+      throw s!"bitset value {value} is out of range"
+    let index := value / 64
+    let word := words.getD index 0
+    words := words.set! index (word + 2 ^ (value % 64))
+  pure <| words.map UInt64.ofNat
+
+private def deriveCore
+    (retired : HashMap ℕ UInt64) (steps : Array Addition) :
+    Except String DerivedCore := do
+  let mut usedSourceIdentifiers : HashSet ℕ := {}
+  for addition in steps do
+    for antecedent in addition.antecedents do
+      if antecedent ≤ solverInitialClauseCount then
+        usedSourceIdentifiers := usedSourceIdentifiers.insert antecedent
+  let mut identifiers : HashMap ℕ ℕ := {}
+  let mut references := #[]
+  let mut excludedMasks := #[]
+  let mut oldIdentifier := 1
+  let mut newIdentifier := 1
+  for reference in solverReferences retired do
+    if usedSourceIdentifiers.contains oldIdentifier then
+      identifiers := identifiers.insert oldIdentifier newIdentifier
+      references := references.push reference
+      newIdentifier := newIdentifier + 1
+    oldIdentifier := oldIdentifier + 1
+  for mask in solverExcludedMasks do
+    if usedSourceIdentifiers.contains oldIdentifier then
+      identifiers := identifiers.insert oldIdentifier newIdentifier
+      excludedMasks := excludedMasks.push mask
+      newIdentifier := newIdentifier + 1
+    oldIdentifier := oldIdentifier + 1
+  unless oldIdentifier = solverInitialClauseCount + 1 do
+    throw "solver source metadata has the wrong clause count"
+  unless usedSourceIdentifiers.size = newIdentifier - 1 do
+    throw "certificate contains an invalid source-clause identifier"
+  unless newIdentifier = initialClauseCount + 1 do
+    throw s!"expected {initialClauseCount} core clauses, got {newIdentifier - 1}"
+  pure {
+    identifiers
+    referenceWords := ← bitsetWords 20659 references
+    excludedMaskWords := ← bitsetWords 256 excludedMasks
+  }
+
+private def recodeAdditions
+    (core : DerivedCore) (steps : Array Addition) :
+    Except String (Array Addition) := do
+  let mut identifiers := core.identifiers
+  for index in [0:steps.size] do
+    let some addition := steps[index]?
+      | throw "certificate addition index is out of range"
+    identifiers := identifiers.insert addition.identifier
+      (initialClauseCount + index + 1)
+  let mut result := #[]
+  for addition in steps do
+    let some identifier := identifiers[addition.identifier]?
+      | throw "certificate addition identifier is missing"
+    let mut antecedents := #[]
+    for antecedent in addition.antecedents do
+      let some recoded := identifiers[antecedent]?
+        | throw s!"certificate uses source clause outside the committed core: {antecedent}"
+      antecedents := antecedents.push recoded
+    result := result.push { addition with identifier, antecedents }
+  pure result
+
+private def processOutput
+    (executable : FilePath) (arguments : Array String) : IO IO.Process.Output :=
+  IO.Process.output {
+    cmd := executable.toString
+    args := arguments
+    stdout := .piped
+    stderr := .piped
+  }
+
+private def verifySourceCommit
+    (executable : FilePath) (expected : String) : IO Unit := do
+  let immediateParent := executable.parent.getD "."
+  let sourceDirectory :=
+    if executable.fileName.getD "" = "cadical" then
+      immediateParent.parent.getD "."
+    else
+      immediateParent
+  let output ← processOutput "git"
+    #["-C", sourceDirectory.toString, "rev-parse", "HEAD"]
+  unless output.exitCode = 0 do
+    throw <| IO.userError s!"cannot read tool commit:\n{output.stderr}"
+  let actual := output.stdout.trimAscii.copy
+  unless actual = expected do
+    throw <| IO.userError
+      s!"tool at {sourceDirectory} is {actual}; expected {expected}"
+
+private def runCertificateTools
+    (configuration : Configuration) (directory : FilePath)
+    (retired : HashMap ℕ UInt64) :
+    IO (FilePath × FilePath × FilePath) := do
+  verifySourceCommit configuration.cadical cadicalCommit
+  verifySourceCommit configuration.dratTrim dratTrimCommit
+  let cnfPath := directory / "master.cnf"
+  let dratPath := directory / "master.drat"
+  let optimizedDratPath := directory / "master-optimized.drat"
+  let lratPath := directory / "master.lrat"
+  IO.FS.writeFile cnfPath (← IO.ofExcept <| renderMasterCnf retired)
+  let solver ← processOutput configuration.cadical
+    #["-P2", "--shrink=1", "--chrono=0", "--stabilizeonly=true",
+      cnfPath.toString, dratPath.toString]
+  unless solver.exitCode = 20 do
+    throw <| IO.userError
+      s!"CaDiCaL failed with {solver.exitCode}:\n{solver.stderr}"
+  let optimizer ← processOutput configuration.dratTrim
+    #[cnfPath.toString, dratPath.toString, "-O", "-l", optimizedDratPath.toString]
+  unless optimizer.exitCode = 0 do
+    throw <| IO.userError
+      s!"drat-trim optimization failed with {optimizer.exitCode}:\n{optimizer.stderr}"
+  let converter ← processOutput configuration.dratTrim
+    #[cnfPath.toString, optimizedDratPath.toString, "-L", lratPath.toString]
+  unless converter.exitCode = 0 do
+    throw <| IO.userError
+      s!"drat-trim failed with {converter.exitCode}:\n{converter.stderr}"
+  pure (cnfPath, optimizedDratPath, lratPath)
+
+private def hashOutput (executable : FilePath) (arguments : Array String) :
+    IO (Option String) := do
+  try
+    let output ← processOutput executable arguments
+    if output.exitCode = 0 then
+      pure <| (output.stdout.trimAscii.copy.splitOn " ").head?
+    else
+      pure none
+  catch _ =>
+    pure none
+
+private def sha256 (path : FilePath) : IO String := do
+  if let some digest ← hashOutput "sha256sum" #[path.toString] then
+    pure digest
+  else if let some digest ← hashOutput "shasum" #["-a", "256", path.toString] then
+    pure digest
+  else
+    throw <| IO.userError "neither sha256sum nor shasum is available"
+
+private def chunksOfWithFuel :
+    ℕ → ℕ → List α → List (List α)
+  | 0, _, _ => []
+  | _, _, [] => []
+  | _fuel + 1, 0, _ => []
+  | fuel + 1, size, values =>
+      values.take size :: chunksOfWithFuel fuel size (values.drop size)
+
+private def chunksOf (size : ℕ) (values : List α) : List (List α) :=
+  chunksOfWithFuel (values.length + 1) size values
+
+private def encodedLines (encoded : String) : Except String (List String) := do
+  let bytes := encoded.toUTF8
+  let mut result := #[]
+  for block in [0:(bytes.size + encodedLineWidth - 1) / encodedLineWidth] do
+    let start := block * encodedLineWidth
+    let stop := min bytes.size (start + encodedLineWidth)
+    let mut line := ByteArray.empty
+    for index in [start:stop] do
+      let some byte := bytes[index]?
+        | throw "encoded certificate line index is out of range"
+      line := line.push byte
+    let some text := String.fromUTF8? line
+      | throw "encoded certificate line is not valid UTF-8"
+    result := result.push text
+  pure result.toList
+
+private def header : String :=
+  "/-\n" ++
+  "Copyright (c) 2026 Egor Lyfar. All rights reserved.\n" ++
+  "Released under Apache 2.0 license as described in the file LICENSE.\n" ++
+  "Authors: Egor Lyfar\n" ++
+  "-/\n\n"
+
+private def renderWordArray (words : Array UInt64) : String :=
+  let lines := (chunksOf 4 words.toList).map fun line =>
+    "  " ++ String.intercalate ", " (line.map toString)
+  "#[\n" ++ String.intercalate ",\n" lines ++ "\n]"
+
+private def renderMasterFormulaData (core : DerivedCore) : String :=
+  header ++
+    "import LeanPool.Erdos97ConvexOctagon.RowSymmetry\n\n" ++
+    "/-! # Generated master-formula core data -/\n\n" ++
+    "namespace Erdos97Octagon.RawIncidence\n\n" ++
+    "/-- Bitset of source-clause references retained in the unsatisfiable core. -/\n" ++
+    "def masterReferenceWords : Array UInt64 := " ++
+    renderWordArray core.referenceWords ++ "\n\n" ++
+    "/-- Bitset of first-row masks retained in the unsatisfiable core. -/\n" ++
+    "def masterExcludedMaskWords : Array UInt64 := " ++
+    renderWordArray core.excludedMaskWords ++ "\n\n" ++
+    "/-- Whether a shared clause belongs to the committed unsatisfiable core. -/\n" ++
+    "def masterReferenceUsedB (reference : ℕ) : Bool :=\n" ++
+    "  bitSetB (masterReferenceWords.getD (reference / 64) 0) (reference % 64)\n\n" ++
+    "/-- Whether a noncanonical first-row mask belongs to the committed core. -/\n" ++
+    "def masterExcludedMaskUsedB (mask : ℕ) : Bool :=\n" ++
+    "  bitSetB (masterExcludedMaskWords.getD (mask / 64) 0) (mask % 64)\n\n" ++
+    "end Erdos97Octagon.RawIncidence\n"
+
+private def renderDataModule
+    (moduleIndex : ℕ) (lines : List String) : String :=
+  let name := s!"masterCertificatePart{moduleIndex}"
+  let body := lines.map fun line => s!"  \"{line}\",\n"
+  header ++
+    "import LeanPool.Erdos97ConvexOctagon.LRAT.Format\n\n" ++
+    "/-! # Generated packed master-certificate data -/\n\n" ++
+    "namespace Erdos97Octagon.RawIncidence\n\n" ++
+    s!"/-- Packed certificate data part {moduleIndex}. -/\n" ++
+    s!"def {name} : List String := [\n" ++
+    String.join body ++
+    "]\n\nend Erdos97Octagon.RawIncidence\n"
+
+private def dataModuleName (index : ℕ) : String :=
+  s!"MasterCertificateData{index}"
+
+private def stageModuleName (index : ℕ) : String :=
+  if index < 10 then
+    s!"MasterCertificateStage0{index}"
+  else
+    s!"MasterCertificateStage{index}"
+
+private def renderNaturalList (values : List ℕ) : String :=
+  "[" ++ String.intercalate ", " (values.map toString) ++ "]"
+
+private def renderManifest
+    (additionCount deletionCount actionCount dataModuleCount packedByteCount
+      encodedCharacterCount maximumVarintBytes : ℕ)
+    (cnfHash lratHash packedHash : String) : String :=
+  let count := stageCount additionCount
+  let stageCounts := (List.range count).map fun index =>
+    stageStop additionCount index - stageStart index
+  let stageBoundaries :=
+    (List.range count).map stageStart ++ [additionCount]
+  let stageBoundarySplit := (stageBoundaries.length + 1) / 2
+  header ++
+    "import LeanPool.Erdos97ConvexOctagon.LRAT.Format\n\n" ++
+    "/-! # Generated master-certificate manifest -/\n\n" ++
+    "namespace Erdos97Octagon.RawIncidence\n\n" ++
+    "/-- Packed certificate format version. -/\n" ++
+    "def masterCertificateFormatVersion : ℕ := 1\n\n" ++
+    "/-- Number of initial clauses. -/\n" ++
+    s!"def masterCertificateInitialClauses : ℕ := {initialClauseCount}\n\n" ++
+    "/-- Number of retained LRAT additions. -/\n" ++
+    s!"def masterCertificateAdditions : ℕ := {additionCount}\n\n" ++
+    "/-- Number of omitted LRAT deletion records. -/\n" ++
+    s!"def masterCertificateDeletions : ℕ := {deletionCount}\n\n" ++
+    "/-- Total number of actions in the generated LRAT text. -/\n" ++
+    s!"def masterCertificateActions : ℕ := {actionCount}\n\n" ++
+    "/-- Number of packed bytes. -/\n" ++
+    s!"def masterCertificatePackedBytes : ℕ := {packedByteCount}\n\n" ++
+    "/-- Number of base64 characters. -/\n" ++
+    s!"def masterCertificateEncodedCharacters : ℕ := {encodedCharacterCount}\n\n" ++
+    "/-- Number of generated data modules. -/\n" ++
+    s!"def masterCertificateDataModules : ℕ := {dataModuleCount}\n\n" ++
+    "/-- Number of sequential proof-stage modules. -/\n" ++
+    s!"def masterCertificateStageModules : ℕ := {count}\n\n" ++
+    "/-- Maximum retained additions reconstructed in one proof stage. -/\n" ++
+    s!"def masterCertificateMaximumAdditionsPerStage : ℕ := {additionsPerStage}\n\n" ++
+    "/-- Retained additions reconstructed by each sequential proof stage. -/\n" ++
+    "def masterCertificateStageAdditionCounts : List ℕ :=\n" ++
+    s!"  {renderNaturalList stageCounts}\n\n" ++
+    "/-- Zero-based addition boundaries of the sequential proof stages. -/\n" ++
+    "def masterCertificateStageBoundaries : List ℕ :=\n" ++
+    s!"  {renderNaturalList (stageBoundaries.take stageBoundarySplit)} ++\n" ++
+    s!"    {renderNaturalList (stageBoundaries.drop stageBoundarySplit)}\n\n" ++
+    "/-- Maximum measured bytes used by one packed natural number. -/\n" ++
+    s!"def masterCertificateMaximumVarintBytes : ℕ := {maximumVarintBytes}\n\n" ++
+    "/-- Decoder byte bound for one packed natural number. -/\n" ++
+    s!"def masterCertificateVarintByteBound : ℕ := {packedVarintByteBound}\n\n" ++
+    "/-- Maximum string literals emitted in one generated data part. -/\n" ++
+    s!"def masterCertificateMaximumStringsPerPart : ℕ := {linesPerDataModule}\n\n" ++
+    "/-- Maximum measured compiled-expression steps used by one generated data part. -/\n" ++
+    "def masterCertificateMaximumStringListExpressionSteps : ℕ := " ++
+    s!"{embeddedCertificatePartMaximumExpressionSteps}\n\n" ++
+    "/-- Structural fuel used to decode one generated string-list part. -/\n" ++
+    s!"def masterCertificateStringListFuel : ℕ := {embeddedCertificatePartFuel}\n\n" ++
+    "/-- SHA-256 of the generated DIMACS formula. -/\n" ++
+    "def masterCertificateCnfSha256 : String :=\n" ++
+    s!"  \"{cnfHash}\"\n\n" ++
+    "/-- SHA-256 of the normalized LRAT text. -/\n" ++
+    "def masterCertificateLratSha256 : String :=\n" ++
+    s!"  \"{lratHash}\"\n\n" ++
+    "/-- SHA-256 of the packed certificate bytes. -/\n" ++
+    "def masterCertificatePackedSha256 : String :=\n" ++
+    s!"  \"{packedHash}\"\n\n" ++
+    "/-- Pinned CaDiCaL source commit. -/\n" ++
+    "def masterCertificateCadicalCommit : String :=\n" ++
+    s!"  \"{cadicalCommit}\"\n\n" ++
+    "/-- Pinned drat-trim source commit. -/\n" ++
+    "def masterCertificateDratTrimCommit : String :=\n" ++
+    s!"  \"{dratTrimCommit}\"\n\n" ++
+    "end Erdos97Octagon.RawIncidence\n"
+
+private def renderStageModule
+    (dataModuleCount additionCount stageIndex : ℕ) : String :=
+  let imports := (List.range dataModuleCount).map fun index =>
+    s!"import LeanPool.Erdos97ConvexOctagon.{dataModuleName index}\n"
+  let parts := (List.range dataModuleCount).map fun index =>
+    s!"    masterCertificatePart{index}\n"
+  let dependencyImport :=
+    if stageIndex = 0 then
+      "import LeanPool.Erdos97ConvexOctagon.LRAT.Elab\n" ++
+        String.join imports
+    else
+      s!"import LeanPool.Erdos97ConvexOctagon." ++
+        s!"{stageModuleName (stageIndex - 1)}\n"
+  header ++
+    dependencyImport ++
+    s!"\n/-! # Master-certificate proof stage {stageIndex} -/\n\n" ++
+    "namespace Erdos97Octagon.RawIncidence\n\n" ++
+    "master_lrat_stage\n" ++
+    s!"  initial_clauses {initialClauseCount}\n" ++
+    s!"  additions {additionCount}\n" ++
+    s!"  stage_start {stageStart stageIndex}\n" ++
+    s!"  stage_stop {stageStop additionCount stageIndex}\n" ++
+    "  clause_prefix masterCertificateClause\n" ++
+    "  final_theorem masterFormula_unsatisfiable\n" ++
+    "  data_parts\n" ++
+    String.join parts ++
+    "\n\nend Erdos97Octagon.RawIncidence\n"
+
+private def renderCertificateModule (count : ℕ) : String :=
+  header ++
+    s!"import LeanPool.Erdos97ConvexOctagon." ++
+    s!"{stageModuleName (count - 1)}\n\n" ++
+    "/-! # Kernel-checked master coverage certificate -/\n"
+
+private def generatedDirectory (repository : FilePath) : FilePath :=
+  repository / "LeanPool" / "Erdos97ConvexOctagon"
+
+private def reconcileFile
+    (mode : Mode) (path : FilePath) (expected : String) : IO Unit := do
+  match mode with
+  | .write => IO.FS.writeFile path expected
+  | .check =>
+      let fileExists ← path.pathExists
+      unless fileExists do
+        throw <| IO.userError s!"generated file is missing: {path}"
+      let actual ← IO.FS.readFile path
+      unless actual = expected do
+        throw <| IO.userError s!"generated file differs: {path}"
+
+private def removeOrRejectExtraModules
+    (configuration : Configuration) (stem : String) (expectedCount : ℕ) :
+    IO Unit := do
+  let directory := generatedDirectory configuration.repository
+  for entry in ← directory.readDir do
+    let name := entry.fileName
+    if name.startsWith stem ∧ name.endsWith ".lean" then
+      let suffix := ((name.drop stem.length).dropEnd 5).copy
+      let isExpected : Bool :=
+        match suffix.toNat? with
+        | some index => decide (index < expectedCount)
+        | none => false
+      unless isExpected do
+        match configuration.mode with
+        | .write => IO.FS.removeFile entry.path
+        | .check =>
+            throw <| IO.userError s!"obsolete generated file remains: {entry.path}"
+
+private def removeOrRejectObsoleteFile
+    (configuration : Configuration) (path : FilePath) : IO Unit := do
+  if ← path.pathExists then
+    match configuration.mode with
+    | .write => IO.FS.removeFile path
+    | .check => throw <| IO.userError s!"obsolete generated file remains: {path}"
+
+private def generate
+    (configuration : Configuration) (temporaryDirectory : FilePath) : IO Unit := do
+  let retired ← IO.ofExcept retiredPatternMap
+  let (cnfPath, _, lratPath) ←
+    runCertificateTools configuration temporaryDirectory retired
+  let lratText ← IO.FS.readFile lratPath
+  let certificate ← IO.ofExcept <| parseCertificate lratText
+  let core ← IO.ofExcept <| deriveCore retired certificate.proofSteps
+  let proofAdditions ← IO.ofExcept <|
+    recodeAdditions core certificate.proofSteps
+  let additionCount := proofAdditions.size
+  let count := stageCount additionCount
+  for index in [0:proofAdditions.size] do
+    let some addition := proofAdditions[index]?
+      | throw <| IO.userError "LRAT addition index is out of range"
+    if addition.literals.isEmpty ∧ index + 1 ≠ proofAdditions.size then
+      throw <| IO.userError "empty clause occurs before the final LRAT addition"
+  let some finalAddition := proofAdditions[proofAdditions.size - 1]?
+    | throw <| IO.userError "LRAT certificate has no additions"
+  unless finalAddition.literals.isEmpty do
+    throw <| IO.userError "final LRAT addition is not the empty clause"
+  let packed ← IO.ofExcept <|
+    encodeAdditions initialClauseCount proofAdditions
+  let encoded ← IO.ofExcept <| encodeBase64 packed
+  let maximumVarintBytes ← IO.ofExcept <|
+    maximumVarintByteCount initialClauseCount proofAdditions
+  let roundTripBytes ← IO.ofExcept <| decodeBase64 encoded
+  let roundTrip ← IO.ofExcept <|
+    decodeAdditions initialClauseCount proofAdditions.size roundTripBytes
+  unless roundTrip == proofAdditions do
+    throw <| IO.userError "packed certificate round trip changed an action"
+  let packedPath := temporaryDirectory / "master.packed"
+  IO.FS.writeBinFile packedPath packed
+  let lines ← IO.ofExcept <| encodedLines encoded
+  let lineModules := chunksOf linesPerDataModule lines
+  let directory := generatedDirectory configuration.repository
+  reconcileFile configuration.mode
+    (directory / "MasterFormulaData.lean")
+    (renderMasterFormulaData core)
+  for index in List.range lineModules.length do
+    let lines := lineModules.getD index []
+    reconcileFile configuration.mode
+      (directory / s!"{dataModuleName index}.lean")
+      (renderDataModule index lines)
+  removeOrRejectExtraModules configuration
+    "MasterCertificateData" lineModules.length
+  removeOrRejectObsoleteFile configuration
+    (directory / "MasterCertificateContext.lean")
+  for index in List.range count do
+    reconcileFile configuration.mode
+      (directory / s!"{stageModuleName index}.lean")
+      (renderStageModule lineModules.length additionCount index)
+  removeOrRejectExtraModules configuration
+    "MasterCertificateStage" count
+  reconcileFile configuration.mode
+    (directory / "MasterCertificateManifest.lean")
+    (renderManifest additionCount certificate.deletions certificate.actions
+      lineModules.length packed.size encoded.length maximumVarintBytes
+      (← sha256 cnfPath) (← sha256 lratPath) (← sha256 packedPath))
+  reconcileFile configuration.mode
+    (directory / "MasterCertificate.lean")
+    (renderCertificateModule count)
+  IO.println <| s!"{configuration.mode.text}: {solverInitialClauseCount} solver clauses, " ++
+    s!"{initialClauseCount} core clauses, " ++
+    s!"{certificate.actions} actions, {proofAdditions.size} additions, " ++
+    s!"{packed.size} packed bytes, {lineModules.length} data modules, " ++
+    s!"{count} proof stages"
+
+private def configuration (mode repository cadical dratTrim : String) :
+    Except String Configuration := do
+  let parsedMode ←
+    match mode with
+    | "check" => pure Mode.check
+    | "write" => pure Mode.write
+    | _ => throw "mode must be check or write"
+  pure {
+    mode := parsedMode
+    repository
+    cadical
+    dratTrim
+  }
+
+/-- Run the deterministic master-certificate generator with explicit tool paths. -/
+syntax (name := regenerateErdos97)
+  "regenerate_erdos97 " str str str str : command
+
+elab_rules : command
+  | `(regenerate_erdos97 $mode:str $repository:str $cadical:str $dratTrim:str) => do
+      let configuration ← IO.ofExcept <|
+        configuration mode.getString repository.getString cadical.getString dratTrim.getString
+      Lean.Elab.Command.liftIO <| IO.FS.withTempDir fun directory =>
+        generate configuration directory
+
+end Erdos97Octagon.Regenerate
diff --git a/LeanPool/Erdos97ConvexOctagon/Relabelling.lean b/LeanPool/Erdos97ConvexOctagon/Relabelling.lean
new file mode 100644
index 00000000..caae8272
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/Relabelling.lean
@@ -0,0 +1,122 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.GeometryReduction
+import Mathlib.Logic.Equiv.Fintype
+
+/-! # Erdős 97 convex-octagon formalization: Relabelling -/
+
+namespace Erdos97Octagon
+
+/-- The canonical first witness row used by the finite classification. -/
+def standardTargets : Finset Vertex := {1, 2, 3, 4}
+
+/-- The canonical witness row has four vertices. -/
+@[simp] theorem card_standardTargets : standardTargets.card = 4 := by
+  decide
+
+/-- The canonical witness row does not contain its centre. -/
+@[simp] theorem zero_notMem_standardTargets : (0 : Vertex) ∉ standardTargets := by
+  decide
+
+namespace OctagonIncidence
+
+/-- Simultaneously relabel the centres and every entry of their witness rows. -/
+def relabel (Q : OctagonIncidence) (e : Vertex ≃ Vertex) : OctagonIncidence where
+  targets v := (Q.targets (e.symm v)).map e.toEmbedding
+  card_targets v := by simp [Q.card_targets]
+  centre_not_mem v := by simpa using Q.centre_not_mem (e.symm v)
+
+/-- A system is normalized when row zero is the canonical four-set. -/
+def Normalized (Q : OctagonIncidence) : Prop :=
+  Q.targets 0 = standardTargets
+
+private theorem exists_perm_fix_zero_map
+    (S : Finset Vertex) (hcard : S.card = 4) (hzero : (0 : Vertex) ∉ S) :
+    ∃ e : Vertex ≃ Vertex,
+      e 0 = 0 ∧ S.map e.toEmbedding = standardTargets := by
+  classical
+  obtain ⟨σ, hσ⟩ := Equiv.Perm.exists_map_finset_eq S standardTargets (by
+    simpa only [card_standardTargets] using hcard)
+  have hσzero : σ 0 ∉ standardTargets := by
+    intro hmem
+    rw [← hσ] at hmem
+    obtain ⟨x, hxS, hx⟩ := Finset.mem_map.mp hmem
+    apply hzero
+    have hxzero : x = 0 := σ.injective (by simpa using hx)
+    simpa [hxzero] using hxS
+  let τ : Vertex ≃ Vertex := Equiv.swap (σ 0) 0
+  have hτ (x : Vertex) (hx : x ∈ standardTargets) : τ x = x := by
+    apply Equiv.swap_apply_of_ne_of_ne
+    · exact fun h => hσzero (h ▸ hx)
+    · exact fun h => zero_notMem_standardTargets (h ▸ hx)
+  let e := σ.trans τ
+  refine ⟨e, ?_, ?_⟩
+  · simp [e, τ]
+  · rw [show e.toEmbedding = σ.toEmbedding.trans τ.toEmbedding by rfl]
+    rw [← Finset.map_map, hσ]
+    ext x
+    constructor
+    · intro hx
+      obtain ⟨y, hy, rfl⟩ := Finset.mem_map.mp hx
+      change τ y ∈ standardTargets
+      rw [hτ y hy]
+      exact hy
+    · intro hx
+      exact Finset.mem_map.mpr ⟨x, hx, hτ x hx⟩
+
+/-- Every octagon incidence system is isomorphic to one with canonical row zero. -/
+theorem exists_normalized_relabel (Q : OctagonIncidence) :
+    ∃ e : Vertex ≃ Vertex, (Q.relabel e).Normalized := by
+  obtain ⟨e, he0, hmap⟩ :=
+    exists_perm_fix_zero_map (Q.targets 0) (Q.card_targets 0) (Q.centre_not_mem 0)
+  have hesymm : e.symm 0 = 0 := by
+    apply e.injective
+    simp [he0]
+  refine ⟨e, ?_⟩
+  simpa [Normalized, relabel, hesymm] using hmap
+
+end OctagonIncidence
+
+/-- Relabel a planar configuration contragrediently with its incidence system. -/
+def relabelPoints (p : Vertex → Plane) (e : Vertex ≃ Vertex) : Vertex → Plane :=
+  p ∘ e.symm
+
+/-- Equal-distance realisability is invariant under simultaneous relabelling. -/
+theorem realises_relabel
+    {p : Vertex → Plane} {Q : OctagonIncidence} (hR : Realises p Q)
+    (e : Vertex ≃ Vertex) :
+    Realises (relabelPoints p e) (Q.relabel e) := by
+  intro v
+  obtain ⟨r, hr⟩ := hR (e.symm v)
+  refine ⟨r, fun w hw => ?_⟩
+  have hw' : e.symm w ∈ Q.targets (e.symm v) := by
+    simpa [OctagonIncidence.relabel] using hw
+  simpa [relabelPoints] using hr (e.symm w) hw'
+
+/-- Convex independence is invariant under relabelling. -/
+theorem convexIndependent_relabel
+    {p : Vertex → Plane} (hC : ConvexIndependent ℝ p) (e : Vertex ≃ Vertex) :
+    ConvexIndependent ℝ (relabelPoints p e) := by
+  simpa [relabelPoints] using hC.comp_embedding e.symm.toEmbedding
+
+/-- A failed convex octagon has a normalized balanced pair-sparse realisation. -/
+theorem normalized_reduction_of_all_hasFour
+    {p : Vertex → Plane} (hC : ConvexIndependent ℝ p)
+    (h : ∀ v, HasFourEquidistant p v) :
+    ∃ p' : Vertex → Plane, ∃ Q : OctagonIncidence,
+      ConvexIndependent ℝ p' ∧ Realises p' Q ∧ Q.Normalized ∧
+        Q.PairSparse ∧ Q.Balanced := by
+  obtain ⟨Q, hR⟩ := incidence_of_all_hasFour h
+  obtain ⟨e, hN⟩ := Q.exists_normalized_relabel
+  let p' := relabelPoints p e
+  let Q' := Q.relabel e
+  have hC' : ConvexIndependent ℝ p' := convexIndependent_relabel hC e
+  have hR' : Realises p' Q' := realises_relabel hR e
+  have hS' : Q'.PairSparse := pairSparse_of_realises hC' Q' hR'
+  exact ⟨p', Q', hC', hR', hN, hS', Q'.balanced_of_pairSparse hS'⟩
+
+end Erdos97Octagon
diff --git a/LeanPool/Erdos97ConvexOctagon/ResidualAlgebra00.lean b/LeanPool/Erdos97ConvexOctagon/ResidualAlgebra00.lean
new file mode 100644
index 00000000..5d3bb112
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/ResidualAlgebra00.lean
@@ -0,0 +1,99 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.CayleyMenger
+import LeanPool.Erdos97ConvexOctagon.ResidualRepresentatives
+
+/-! # Erdős 97 convex-octagon formalization: Residual Algebra00 -/
+
+namespace Erdos97Octagon
+
+/-- Residual class 0 has no injective planar realisation. -/
+theorem residualRepresentative00_not_realises
+    {p : Vertex → Plane} (hp : Function.Injective p) :
+    ¬ Realises p residualRepresentative00 := by
+  intro hRealises
+  obtain ⟨radius, hpos, hdist⟩ :=
+    exists_positive_radii hp residualRepresentative00 hRealises
+  have r01 : radius 0 = radius 1 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative00])
+  have r02 : radius 0 = radius 2 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative00])
+  have r15 : radius 1 = radius 5 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative00])
+  have r34 : radius 3 = radius 4 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative00])
+  have r37 : radius 3 = radius 7 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative00])
+  have r46 : radius 4 = radius 6 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative00])
+  have radius0 : radius 0 = radius 0 := rfl
+  have radius1 : radius 1 = radius 0 := (r01).symm
+  have radius2 : radius 2 = radius 0 := (r02).symm
+  have radius5 : radius 5 = radius 0 := ((r01).trans r15).symm
+  have radius3 : radius 3 = radius 3 := rfl
+  have radius4 : radius 4 = radius 3 := (r34).symm
+  have radius6 : radius 6 = radius 3 := ((r34).trans r46).symm
+  have radius7 : radius 7 = radius 3 := (r37).symm
+  let base : ℝ := radius 0 ^ 2
+  have hbase : base ≠ 0 := by
+    dsimp [base]
+    exact pow_ne_zero 2 (ne_of_gt (hpos 0))
+  let s1 : ℝ := radius 3 ^ 2 / base
+  have d01 : sqDist (p 0) (p 1) / base = 1 := by
+    rw [sqDist, hdist 0 1 (by decide), radius0]
+    exact div_self hbase
+  have d02 : sqDist (p 0) (p 2) / base = 1 := by
+    rw [sqDist, hdist 0 2 (by decide), radius0]
+    exact div_self hbase
+  have d03 : sqDist (p 0) (p 3) / base = 1 := by
+    rw [sqDist, hdist 0 3 (by decide), radius0]
+    exact div_self hbase
+  have d06 : sqDist (p 0) (p 6) / base = s1 := by
+    rw [sqDist, dist_comm, hdist 6 0 (by decide), radius6]
+  have d07 : sqDist (p 0) (p 7) / base = s1 := by
+    rw [sqDist, dist_comm, hdist 7 0 (by decide), radius7]
+  have d12 : sqDist (p 1) (p 2) / base = 1 := by
+    rw [sqDist, hdist 1 2 (by decide), radius1]
+    exact div_self hbase
+  have d13 : sqDist (p 1) (p 3) / base = 1 := by
+    rw [sqDist, hdist 1 3 (by decide), radius1]
+    exact div_self hbase
+  have d16 : sqDist (p 1) (p 6) / base = s1 := by
+    rw [sqDist, dist_comm, hdist 6 1 (by decide), radius6]
+  have d17 : sqDist (p 1) (p 7) / base = s1 := by
+    rw [sqDist, dist_comm, hdist 7 1 (by decide), radius7]
+  have d26 : sqDist (p 2) (p 6) / base = 1 := by
+    rw [sqDist, hdist 2 6 (by decide), radius2]
+    exact div_self hbase
+  have d37 : sqDist (p 3) (p 7) / base = s1 := by
+    rw [sqDist, hdist 3 7 (by decide), radius3]
+  have hcm0 := cm4_normalized_eq_zero
+    (p 0) (p 1) (p 2) (p 6) hbase
+  rw [d01, d02, d06, d12, d16, d26] at hcm0
+  have e0 : -2*s1  ^  2 + 8*s1 - 2 = 0 := by
+    dsimp [cm4] at hcm0
+    nlinarith only [hcm0]
+  have hcm1 := cm4_normalized_eq_zero
+    (p 0) (p 1) (p 3) (p 7) hbase
+  rw [d01, d03, d07, d13, d17, d37] at hcm1
+  have e1 : 6*s1 - 2 = 0 := by
+    dsimp [cm4] at hcm1
+    nlinarith only [hcm1]
+  have certificate :
+      (9/4 : ℝ) * (-2*s1  ^  2 + 8*s1 - 2) +
+        (3/4*s1-11/4 : ℝ) * (6*s1 - 2) = 1 := by
+    ring
+  rw [e0, e1] at certificate
+  norm_num at certificate
+
+end Erdos97Octagon
diff --git a/LeanPool/Erdos97ConvexOctagon/ResidualAlgebra01.lean b/LeanPool/Erdos97ConvexOctagon/ResidualAlgebra01.lean
new file mode 100644
index 00000000..c9a81348
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/ResidualAlgebra01.lean
@@ -0,0 +1,97 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.CayleyMenger
+import LeanPool.Erdos97ConvexOctagon.ResidualRepresentatives
+
+/-! # Erdős 97 convex-octagon formalization: Residual Algebra01 -/
+
+namespace Erdos97Octagon
+
+/-- Residual class 1 has no injective planar realisation. -/
+theorem residualRepresentative01_not_realises
+    {p : Vertex → Plane} (hp : Function.Injective p) :
+    ¬ Realises p residualRepresentative01 := by
+  intro hRealises
+  obtain ⟨radius, hpos, hdist⟩ :=
+    exists_positive_radii hp residualRepresentative01 hRealises
+  have r01 : radius 0 = radius 1 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative01])
+  have r02 : radius 0 = radius 2 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative01])
+  have r34 : radius 3 = radius 4 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative01])
+  have r57 : radius 5 = radius 7 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative01])
+  have r76 : radius 7 = radius 6 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative01])
+  have radius0 : radius 0 = radius 0 := rfl
+  have radius1 : radius 1 = radius 0 := (r01).symm
+  have radius2 : radius 2 = radius 0 := (r02).symm
+  have radius3 : radius 3 = radius 3 := rfl
+  have radius4 : radius 4 = radius 3 := (r34).symm
+  have radius5 : radius 5 = radius 5 := rfl
+  have radius6 : radius 6 = radius 5 := ((r57).trans r76).symm
+  have radius7 : radius 7 = radius 5 := (r57).symm
+  let base : ℝ := radius 0 ^ 2
+  have hbase : base ≠ 0 := by
+    dsimp [base]
+    exact pow_ne_zero 2 (ne_of_gt (hpos 0))
+  let s1 : ℝ := radius 3 ^ 2 / base
+  let s2 : ℝ := radius 5 ^ 2 / base
+  have d01 : sqDist (p 0) (p 1) / base = 1 := by
+    rw [sqDist, hdist 0 1 (by decide), radius0]
+    exact div_self hbase
+  have d02 : sqDist (p 0) (p 2) / base = 1 := by
+    rw [sqDist, hdist 0 2 (by decide), radius0]
+    exact div_self hbase
+  have d06 : sqDist (p 0) (p 6) / base = s2 := by
+    rw [sqDist, dist_comm, hdist 6 0 (by decide), radius6]
+  have d12 : sqDist (p 1) (p 2) / base = 1 := by
+    rw [sqDist, hdist 1 2 (by decide), radius1]
+    exact div_self hbase
+  have d15 : sqDist (p 1) (p 5) / base = 1 := by
+    rw [sqDist, hdist 1 5 (by decide), radius1]
+    exact div_self hbase
+  have d16 : sqDist (p 1) (p 6) / base = s2 := by
+    rw [sqDist, dist_comm, hdist 6 1 (by decide), radius6]
+  have d17 : sqDist (p 1) (p 7) / base = s2 := by
+    rw [sqDist, dist_comm, hdist 7 1 (by decide), radius7]
+  have d25 : sqDist (p 2) (p 5) / base = 1 := by
+    rw [sqDist, hdist 2 5 (by decide), radius2]
+    exact div_self hbase
+  have d26 : sqDist (p 2) (p 6) / base = 1 := by
+    rw [sqDist, hdist 2 6 (by decide), radius2]
+    exact div_self hbase
+  have d27 : sqDist (p 2) (p 7) / base = s2 := by
+    rw [sqDist, dist_comm, hdist 7 2 (by decide), radius7]
+  have d57 : sqDist (p 5) (p 7) / base = s2 := by
+    rw [sqDist, hdist 5 7 (by decide), radius5]
+  have hcm0 := cm4_normalized_eq_zero
+    (p 0) (p 1) (p 2) (p 6) hbase
+  rw [d01, d02, d06, d12, d16, d26] at hcm0
+  have e0 : -2*s2  ^  2 + 8*s2 - 2 = 0 := by
+    dsimp [cm4] at hcm0
+    nlinarith only [hcm0]
+  have hcm1 := cm4_normalized_eq_zero
+    (p 1) (p 2) (p 5) (p 7) hbase
+  rw [d12, d15, d17, d25, d27, d57] at hcm1
+  have e1 : 6*s2 - 2 = 0 := by
+    dsimp [cm4] at hcm1
+    nlinarith only [hcm1]
+  have certificate :
+      (9/4 : ℝ) * (-2*s2  ^  2 + 8*s2 - 2) +
+        (3/4*s2-11/4 : ℝ) * (6*s2 - 2) = 1 := by
+    ring
+  rw [e0, e1] at certificate
+  norm_num at certificate
+
+end Erdos97Octagon
diff --git a/LeanPool/Erdos97ConvexOctagon/ResidualAlgebra02.lean b/LeanPool/Erdos97ConvexOctagon/ResidualAlgebra02.lean
new file mode 100644
index 00000000..79826f8e
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/ResidualAlgebra02.lean
@@ -0,0 +1,93 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.CayleyMenger
+import LeanPool.Erdos97ConvexOctagon.ResidualRepresentatives
+
+/-! # Erdős 97 convex-octagon formalization: Residual Algebra02 -/
+
+namespace Erdos97Octagon
+
+/-- Residual class 2 has no injective planar realisation. -/
+theorem residualRepresentative02_not_realises
+    {p : Vertex → Plane} (hp : Function.Injective p) :
+    ¬ Realises p residualRepresentative02 := by
+  intro hRealises
+  obtain ⟨radius, hpos, hdist⟩ :=
+    exists_positive_radii hp residualRepresentative02 hRealises
+  have r01 : radius 0 = radius 1 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative02])
+  have r02 : radius 0 = radius 2 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative02])
+  have r36 : radius 3 = radius 6 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative02])
+  have r67 : radius 6 = radius 7 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative02])
+  have r45 : radius 4 = radius 5 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative02])
+  have radius0 : radius 0 = radius 0 := rfl
+  have radius1 : radius 1 = radius 0 := (r01).symm
+  have radius2 : radius 2 = radius 0 := (r02).symm
+  have radius3 : radius 3 = radius 3 := rfl
+  have radius6 : radius 6 = radius 3 := (r36).symm
+  have radius7 : radius 7 = radius 3 := ((r36).trans r67).symm
+  have radius4 : radius 4 = radius 4 := rfl
+  have radius5 : radius 5 = radius 4 := (r45).symm
+  let base : ℝ := radius 0 ^ 2
+  have hbase : base ≠ 0 := by
+    dsimp [base]
+    exact pow_ne_zero 2 (ne_of_gt (hpos 0))
+  let s1 : ℝ := radius 3 ^ 2 / base
+  let s2 : ℝ := radius 4 ^ 2 / base
+  have d01 : sqDist (p 0) (p 1) / base = 1 := by
+    rw [sqDist, hdist 0 1 (by decide), radius0]
+    exact div_self hbase
+  have d02 : sqDist (p 0) (p 2) / base = 1 := by
+    rw [sqDist, hdist 0 2 (by decide), radius0]
+    exact div_self hbase
+  have d04 : sqDist (p 0) (p 4) / base = 1 := by
+    rw [sqDist, hdist 0 4 (by decide), radius0]
+    exact div_self hbase
+  have d12 : sqDist (p 1) (p 2) / base = 1 := by
+    rw [sqDist, hdist 1 2 (by decide), radius1]
+    exact div_self hbase
+  have d14 : sqDist (p 1) (p 4) / base = s2 := by
+    rw [sqDist, dist_comm, hdist 4 1 (by decide), radius4]
+  have d15 : sqDist (p 1) (p 5) / base = 1 := by
+    rw [sqDist, hdist 1 5 (by decide), radius1]
+    exact div_self hbase
+  have d24 : sqDist (p 2) (p 4) / base = s2 := by
+    rw [sqDist, dist_comm, hdist 4 2 (by decide), radius4]
+  have d25 : sqDist (p 2) (p 5) / base = 1 := by
+    rw [sqDist, hdist 2 5 (by decide), radius2]
+    exact div_self hbase
+  have d45 : sqDist (p 4) (p 5) / base = s2 := by
+    rw [sqDist, hdist 4 5 (by decide), radius4]
+  have hcm0 := cm4_normalized_eq_zero
+    (p 0) (p 1) (p 2) (p 4) hbase
+  rw [d01, d02, d04, d12, d14, d24] at hcm0
+  have e0 : -2*s2  ^  2 + 8*s2 - 2 = 0 := by
+    dsimp [cm4] at hcm0
+    nlinarith only [hcm0]
+  have hcm1 := cm4_normalized_eq_zero
+    (p 1) (p 2) (p 4) (p 5) hbase
+  rw [d12, d14, d15, d24, d25, d45] at hcm1
+  have e1 : 6*s2 - 2 = 0 := by
+    dsimp [cm4] at hcm1
+    nlinarith only [hcm1]
+  have certificate :
+      (9/4 : ℝ) * (-2*s2  ^  2 + 8*s2 - 2) +
+        (3/4*s2-11/4 : ℝ) * (6*s2 - 2) = 1 := by
+    ring
+  rw [e0, e1] at certificate
+  norm_num at certificate
+
+end Erdos97Octagon
diff --git a/LeanPool/Erdos97ConvexOctagon/ResidualAlgebra03.lean b/LeanPool/Erdos97ConvexOctagon/ResidualAlgebra03.lean
new file mode 100644
index 00000000..0c209d0e
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/ResidualAlgebra03.lean
@@ -0,0 +1,93 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.CayleyMenger
+import LeanPool.Erdos97ConvexOctagon.ResidualRepresentatives
+
+/-! # Erdős 97 convex-octagon formalization: Residual Algebra03 -/
+
+namespace Erdos97Octagon
+
+/-- Residual class 3 has no injective planar realisation. -/
+theorem residualRepresentative03_not_realises
+    {p : Vertex → Plane} (hp : Function.Injective p) :
+    ¬ Realises p residualRepresentative03 := by
+  intro hRealises
+  obtain ⟨radius, hpos, hdist⟩ :=
+    exists_positive_radii hp residualRepresentative03 hRealises
+  have r01 : radius 0 = radius 1 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative03])
+  have r02 : radius 0 = radius 2 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative03])
+  have r03 : radius 0 = radius 3 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative03])
+  have r04 : radius 0 = radius 4 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative03])
+  have r56 : radius 5 = radius 6 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative03])
+  have r57 : radius 5 = radius 7 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative03])
+  have radius0 : radius 0 = radius 0 := rfl
+  have radius1 : radius 1 = radius 0 := (r01).symm
+  have radius2 : radius 2 = radius 0 := (r02).symm
+  have radius3 : radius 3 = radius 0 := (r03).symm
+  have radius4 : radius 4 = radius 0 := (r04).symm
+  have radius5 : radius 5 = radius 5 := rfl
+  have radius6 : radius 6 = radius 5 := (r56).symm
+  have radius7 : radius 7 = radius 5 := (r57).symm
+  let base : ℝ := radius 0 ^ 2
+  have hbase : base ≠ 0 := by
+    dsimp [base]
+    exact pow_ne_zero 2 (ne_of_gt (hpos 0))
+  let s1 : ℝ := radius 5 ^ 2 / base
+  have d13 : sqDist (p 1) (p 3) / base = 1 := by
+    rw [sqDist, hdist 1 3 (by decide), radius1]
+    exact div_self hbase
+  have d15 : sqDist (p 1) (p 5) / base = 1 := by
+    rw [sqDist, hdist 1 5 (by decide), radius1]
+    exact div_self hbase
+  have d16 : sqDist (p 1) (p 6) / base = s1 := by
+    rw [sqDist, dist_comm, hdist 6 1 (by decide), radius6]
+  have d17 : sqDist (p 1) (p 7) / base = s1 := by
+    rw [sqDist, dist_comm, hdist 7 1 (by decide), radius7]
+  have d35 : sqDist (p 3) (p 5) / base = 1 := by
+    rw [sqDist, hdist 3 5 (by decide), radius3]
+    exact div_self hbase
+  have d36 : sqDist (p 3) (p 6) / base = s1 := by
+    rw [sqDist, dist_comm, hdist 6 3 (by decide), radius6]
+  have d37 : sqDist (p 3) (p 7) / base = 1 := by
+    rw [sqDist, hdist 3 7 (by decide), radius3]
+    exact div_self hbase
+  have d56 : sqDist (p 5) (p 6) / base = s1 := by
+    rw [sqDist, hdist 5 6 (by decide), radius5]
+  have d57 : sqDist (p 5) (p 7) / base = s1 := by
+    rw [sqDist, hdist 5 7 (by decide), radius5]
+  have hcm0 := cm4_normalized_eq_zero
+    (p 1) (p 3) (p 5) (p 7) hbase
+  rw [d13, d15, d17, d35, d37, d57] at hcm0
+  have e0 : -2*s1  ^  2 + 8*s1 - 2 = 0 := by
+    dsimp [cm4] at hcm0
+    nlinarith only [hcm0]
+  have hcm1 := cm4_normalized_eq_zero
+    (p 1) (p 3) (p 5) (p 6) hbase
+  rw [d13, d15, d16, d35, d36, d56] at hcm1
+  have e1 : 6*s1 - 2 = 0 := by
+    dsimp [cm4] at hcm1
+    nlinarith only [hcm1]
+  have certificate :
+      (9/4 : ℝ) * (-2*s1  ^  2 + 8*s1 - 2) +
+        (3/4*s1-11/4 : ℝ) * (6*s1 - 2) = 1 := by
+    ring
+  rw [e0, e1] at certificate
+  norm_num at certificate
+
+end Erdos97Octagon
diff --git a/LeanPool/Erdos97ConvexOctagon/ResidualAlgebra04.lean b/LeanPool/Erdos97ConvexOctagon/ResidualAlgebra04.lean
new file mode 100644
index 00000000..bf6b49d8
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/ResidualAlgebra04.lean
@@ -0,0 +1,145 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.CayleyMenger
+import LeanPool.Erdos97ConvexOctagon.ResidualRepresentatives
+
+/-! # Erdős 97 convex-octagon formalization: Residual Algebra04 -/
+
+namespace Erdos97Octagon
+
+/-- Residual class 4 has no injective planar realisation. -/
+theorem residualRepresentative04_not_realises
+    {p : Vertex → Plane} (hp : Function.Injective p) :
+    ¬ Realises p residualRepresentative04 := by
+  intro hRealises
+  obtain ⟨radius, hpos, hdist⟩ :=
+    exists_positive_radii hp residualRepresentative04 hRealises
+  have r01 : radius 0 = radius 1 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative04])
+  have r02 : radius 0 = radius 2 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative04])
+  have r34 : radius 3 = radius 4 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative04])
+  have r56 : radius 5 = radius 6 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative04])
+  have r57 : radius 5 = radius 7 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative04])
+  have radius0 : radius 0 = radius 0 := rfl
+  have radius1 : radius 1 = radius 0 := (r01).symm
+  have radius2 : radius 2 = radius 0 := (r02).symm
+  have radius3 : radius 3 = radius 3 := rfl
+  have radius4 : radius 4 = radius 3 := (r34).symm
+  have radius5 : radius 5 = radius 5 := rfl
+  have radius6 : radius 6 = radius 5 := (r56).symm
+  have radius7 : radius 7 = radius 5 := (r57).symm
+  let base : ℝ := radius 0 ^ 2
+  have hbase : base ≠ 0 := by
+    dsimp [base]
+    exact pow_ne_zero 2 (ne_of_gt (hpos 0))
+  let s1 : ℝ := radius 3 ^ 2 / base
+  let s2 : ℝ := radius 5 ^ 2 / base
+  have d01 : sqDist (p 0) (p 1) / base = 1 := by
+    rw [sqDist, hdist 0 1 (by decide), radius0]
+    exact div_self hbase
+  have d02 : sqDist (p 0) (p 2) / base = 1 := by
+    rw [sqDist, hdist 0 2 (by decide), radius0]
+    exact div_self hbase
+  have d03 : sqDist (p 0) (p 3) / base = 1 := by
+    rw [sqDist, hdist 0 3 (by decide), radius0]
+    exact div_self hbase
+  have d04 : sqDist (p 0) (p 4) / base = 1 := by
+    rw [sqDist, hdist 0 4 (by decide), radius0]
+    exact div_self hbase
+  have d05 : sqDist (p 0) (p 5) / base = s2 := by
+    rw [sqDist, dist_comm, hdist 5 0 (by decide), radius5]
+  have d12 : sqDist (p 1) (p 2) / base = 1 := by
+    rw [sqDist, hdist 1 2 (by decide), radius1]
+    exact div_self hbase
+  have d13 : sqDist (p 1) (p 3) / base = 1 := by
+    rw [sqDist, hdist 1 3 (by decide), radius1]
+    exact div_self hbase
+  have d14 : sqDist (p 1) (p 4) / base = s1 := by
+    rw [sqDist, dist_comm, hdist 4 1 (by decide), radius4]
+  have d15 : sqDist (p 1) (p 5) / base = 1 := by
+    rw [sqDist, hdist 1 5 (by decide), radius1]
+    exact div_self hbase
+  have d17 : sqDist (p 1) (p 7) / base = s2 := by
+    rw [sqDist, dist_comm, hdist 7 1 (by decide), radius7]
+  have d23 : sqDist (p 2) (p 3) / base = s1 := by
+    rw [sqDist, dist_comm, hdist 3 2 (by decide), radius3]
+  have d24 : sqDist (p 2) (p 4) / base = 1 := by
+    rw [sqDist, hdist 2 4 (by decide), radius2]
+    exact div_self hbase
+  let w2_5 : ℝ := sqDist (p 2) (p 5) / base
+  have d25 : sqDist (p 2) (p 5) / base = w2_5 := rfl
+  have d34 : sqDist (p 3) (p 4) / base = s1 := by
+    rw [sqDist, hdist 3 4 (by decide), radius3]
+  have d35 : sqDist (p 3) (p 5) / base = s2 := by
+    rw [sqDist, dist_comm, hdist 5 3 (by decide), radius5]
+  have d45 : sqDist (p 4) (p 5) / base = s1 := by
+    rw [sqDist, hdist 4 5 (by decide), radius4]
+  have d47 : sqDist (p 4) (p 7) / base = s1 := by
+    rw [sqDist, hdist 4 7 (by decide), radius4]
+  have d57 : sqDist (p 5) (p 7) / base = s2 := by
+    rw [sqDist, hdist 5 7 (by decide), radius5]
+  have hcm0 := cm4_normalized_eq_zero
+    (p 0) (p 2) (p 4) (p 5) hbase
+  rw [d02, d04, d05, d24, d25, d45] at hcm0
+  have e0 :
+      -2*s1  ^  2 + 2*s1*s2 + 2*s1*w2_5 + 2*s1 - 2*s2  ^  2 +
+          2*s2*w2_5 + 2*s2 - 2*w2_5  ^  2 + 2*w2_5 - 2 = 0 := by
+    dsimp [cm4] at hcm0
+    nlinarith only [hcm0]
+  have hcm1 := cm4_normalized_eq_zero
+    (p 0) (p 1) (p 2) (p 3) hbase
+  rw [d01, d02, d03, d12, d13, d23] at hcm1
+  have e1 : -2*s1  ^  2 + 6*s1 = 0 := by
+    dsimp [cm4] at hcm1
+    nlinarith only [hcm1]
+  have hcm2 := cm4_normalized_eq_zero
+    (p 0) (p 1) (p 3) (p 4) hbase
+  rw [d01, d03, d04, d13, d14, d34] at hcm2
+  have e2 : -2*s1  ^  2 + 8*s1 - 2 = 0 := by
+    dsimp [cm4] at hcm2
+    nlinarith only [hcm2]
+  have hcm3 := cm4_normalized_eq_zero
+    (p 0) (p 1) (p 2) (p 5) hbase
+  rw [d01, d02, d05, d12, d15, d25] at hcm3
+  have e3 : -2*s2  ^  2 + 2*s2*w2_5 + 4*s2 - 2*w2_5  ^  2 + 4*w2_5 - 2 = 0 := by
+    dsimp [cm4] at hcm3
+    nlinarith only [hcm3]
+  have hcm4 := cm4_normalized_eq_zero
+    (p 0) (p 1) (p 3) (p 5) hbase
+  rw [d01, d03, d05, d13, d15, d35] at hcm4
+  have e4 : -2*s2  ^  2 + 8*s2 - 2 = 0 := by
+    dsimp [cm4] at hcm4
+    nlinarith only [hcm4]
+  have hcm5 := cm4_normalized_eq_zero
+    (p 1) (p 4) (p 5) (p 7) hbase
+  rw [d14, d15, d17, d45, d47, d57] at hcm5
+  have e5 : 8*s1*s2 - 2*s1 - 2*s2  ^  2 = 0 := by
+    dsimp [cm4] at hcm5
+    nlinarith only [hcm5]
+  have certificate :
+      (-1/4 : ℝ) *
+          (-2*s1  ^  2 + 2*s1*s2 + 2*s1*w2_5 + 2*s1 - 2*s2  ^  2 +
+            2*s2*w2_5 + 2*s2 - 2*w2_5  ^  2 + 2*w2_5 - 2) +
+        (-1/4*w2_5+11/16 : ℝ) * (-2*s1  ^  2 + 6*s1) +
+        (1/4*w2_5-7/16 : ℝ) * (-2*s1  ^  2 + 8*s1 - 2) +
+        (1/4 : ℝ) * (-2*s2  ^  2 + 2*s2*w2_5 + 4*s2 - 2*w2_5  ^  2 + 4*w2_5 - 2) +
+        (-1/16 : ℝ) * (-2*s2  ^  2 + 8*s2 - 2) +
+        (1/16 : ℝ) * (8*s1*s2 - 2*s1 - 2*s2  ^  2) = 1 := by
+    ring
+  rw [e0, e1, e2, e3, e4, e5] at certificate
+  norm_num at certificate
+
+end Erdos97Octagon
diff --git a/LeanPool/Erdos97ConvexOctagon/ResidualAlgebra05.lean b/LeanPool/Erdos97ConvexOctagon/ResidualAlgebra05.lean
new file mode 100644
index 00000000..2caec51b
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/ResidualAlgebra05.lean
@@ -0,0 +1,173 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.CayleyMenger
+import LeanPool.Erdos97ConvexOctagon.ResidualRepresentatives
+
+/-! # Erdős 97 convex-octagon formalization: Residual Algebra05 -/
+
+namespace Erdos97Octagon
+
+/-- Residual class 5 has no injective planar realisation. -/
+theorem residualRepresentative05_not_realises
+    {p : Vertex → Plane} (hp : Function.Injective p) :
+    ¬ Realises p residualRepresentative05 := by
+  intro hRealises
+  obtain ⟨radius, hpos, hdist⟩ :=
+    exists_positive_radii hp residualRepresentative05 hRealises
+  have r01 : radius 0 = radius 1 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative05])
+  have r23 : radius 2 = radius 3 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative05])
+  have r46 : radius 4 = radius 6 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative05])
+  have r57 : radius 5 = radius 7 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative05])
+  have radius0 : radius 0 = radius 0 := rfl
+  have radius1 : radius 1 = radius 0 := (r01).symm
+  have radius2 : radius 2 = radius 2 := rfl
+  have radius3 : radius 3 = radius 2 := (r23).symm
+  have radius4 : radius 4 = radius 4 := rfl
+  have radius6 : radius 6 = radius 4 := (r46).symm
+  have radius5 : radius 5 = radius 5 := rfl
+  have radius7 : radius 7 = radius 5 := (r57).symm
+  let base : ℝ := radius 0 ^ 2
+  have hbase : base ≠ 0 := by
+    dsimp [base]
+    exact pow_ne_zero 2 (ne_of_gt (hpos 0))
+  let s1 : ℝ := radius 2 ^ 2 / base
+  let s2 : ℝ := radius 4 ^ 2 / base
+  let s3 : ℝ := radius 5 ^ 2 / base
+  have d01 : sqDist (p 0) (p 1) / base = 1 := by
+    rw [sqDist, hdist 0 1 (by decide), radius0]
+    exact div_self hbase
+  have d02 : sqDist (p 0) (p 2) / base = 1 := by
+    rw [sqDist, hdist 0 2 (by decide), radius0]
+    exact div_self hbase
+  have d03 : sqDist (p 0) (p 3) / base = 1 := by
+    rw [sqDist, hdist 0 3 (by decide), radius0]
+    exact div_self hbase
+  have d04 : sqDist (p 0) (p 4) / base = 1 := by
+    rw [sqDist, hdist 0 4 (by decide), radius0]
+    exact div_self hbase
+  have d05 : sqDist (p 0) (p 5) / base = s3 := by
+    rw [sqDist, dist_comm, hdist 5 0 (by decide), radius5]
+  have d06 : sqDist (p 0) (p 6) / base = s2 := by
+    rw [sqDist, dist_comm, hdist 6 0 (by decide), radius6]
+  have d07 : sqDist (p 0) (p 7) / base = s3 := by
+    rw [sqDist, dist_comm, hdist 7 0 (by decide), radius7]
+  have d12 : sqDist (p 1) (p 2) / base = 1 := by
+    rw [sqDist, hdist 1 2 (by decide), radius1]
+    exact div_self hbase
+  have d13 : sqDist (p 1) (p 3) / base = s1 := by
+    rw [sqDist, dist_comm, hdist 3 1 (by decide), radius3]
+  have d14 : sqDist (p 1) (p 4) / base = s2 := by
+    rw [sqDist, dist_comm, hdist 4 1 (by decide), radius4]
+  have d15 : sqDist (p 1) (p 5) / base = 1 := by
+    rw [sqDist, hdist 1 5 (by decide), radius1]
+    exact div_self hbase
+  have d16 : sqDist (p 1) (p 6) / base = 1 := by
+    rw [sqDist, hdist 1 6 (by decide), radius1]
+    exact div_self hbase
+  have d17 : sqDist (p 1) (p 7) / base = s3 := by
+    rw [sqDist, dist_comm, hdist 7 1 (by decide), radius7]
+  have d23 : sqDist (p 2) (p 3) / base = s1 := by
+    rw [sqDist, hdist 2 3 (by decide), radius2]
+  have d24 : sqDist (p 2) (p 4) / base = s1 := by
+    rw [sqDist, hdist 2 4 (by decide), radius2]
+  have d25 : sqDist (p 2) (p 5) / base = s1 := by
+    rw [sqDist, hdist 2 5 (by decide), radius2]
+  have d26 : sqDist (p 2) (p 6) / base = s2 := by
+    rw [sqDist, dist_comm, hdist 6 2 (by decide), radius6]
+  have d27 : sqDist (p 2) (p 7) / base = s1 := by
+    rw [sqDist, hdist 2 7 (by decide), radius2]
+  have d34 : sqDist (p 3) (p 4) / base = s2 := by
+    rw [sqDist, dist_comm, hdist 4 3 (by decide), radius4]
+  have d36 : sqDist (p 3) (p 6) / base = s1 := by
+    rw [sqDist, hdist 3 6 (by decide), radius3]
+  have d45 : sqDist (p 4) (p 5) / base = s2 := by
+    rw [sqDist, hdist 4 5 (by decide), radius4]
+  have d46 : sqDist (p 4) (p 6) / base = s2 := by
+    rw [sqDist, hdist 4 6 (by decide), radius4]
+  have d47 : sqDist (p 4) (p 7) / base = s3 := by
+    rw [sqDist, dist_comm, hdist 7 4 (by decide), radius7]
+  have d57 : sqDist (p 5) (p 7) / base = s3 := by
+    rw [sqDist, hdist 5 7 (by decide), radius5]
+  have d67 : sqDist (p 6) (p 7) / base = s2 := by
+    rw [sqDist, hdist 6 7 (by decide), radius6]
+  have hcm0 := cm4_normalized_eq_zero
+    (p 0) (p 1) (p 2) (p 4) hbase
+  rw [d01, d02, d04, d12, d14, d24] at hcm0
+  have e0 : -2*s1  ^  2 + 2*s1*s2 + 4*s1 - 2*s2  ^  2 + 4*s2 - 2 = 0 := by
+    dsimp [cm4] at hcm0
+    nlinarith only [hcm0]
+  have hcm1 := cm4_normalized_eq_zero
+    (p 0) (p 1) (p 2) (p 5) hbase
+  rw [d01, d02, d05, d12, d15, d25] at hcm1
+  have e1 : -2*s1  ^  2 + 2*s1*s3 + 4*s1 - 2*s3  ^  2 + 4*s3 - 2 = 0 := by
+    dsimp [cm4] at hcm1
+    nlinarith only [hcm1]
+  have hcm2 := cm4_normalized_eq_zero
+    (p 0) (p 1) (p 2) (p 7) hbase
+  rw [d01, d02, d07, d12, d17, d27] at hcm2
+  have e2 : -2*s1  ^  2 + 4*s1*s3 + 2*s1 - 2*s3  ^  2 + 4*s3 - 2 = 0 := by
+    dsimp [cm4] at hcm2
+    nlinarith only [hcm2]
+  have hcm3 := cm4_normalized_eq_zero
+    (p 0) (p 1) (p 2) (p 3) hbase
+  rw [d01, d02, d03, d12, d13, d23] at hcm3
+  have e3 : -2*s1  ^  2 + 8*s1 - 2 = 0 := by
+    dsimp [cm4] at hcm3
+    nlinarith only [hcm3]
+  have hcm4 := cm4_normalized_eq_zero
+    (p 1) (p 3) (p 4) (p 6) hbase
+  rw [d13, d14, d16, d34, d36, d46] at hcm4
+  have e4 : -2*s1  ^  2 + 8*s1*s2 - 2*s2 = 0 := by
+    dsimp [cm4] at hcm4
+    nlinarith only [hcm4]
+  have hcm5 := cm4_normalized_eq_zero
+    (p 0) (p 1) (p 2) (p 6) hbase
+  rw [d01, d02, d06, d12, d16, d26] at hcm5
+  have e5 : -2*s2  ^  2 + 8*s2 - 2 = 0 := by
+    dsimp [cm4] at hcm5
+    nlinarith only [hcm5]
+  have hcm6 := cm4_normalized_eq_zero
+    (p 1) (p 4) (p 5) (p 7) hbase
+  rw [d14, d15, d17, d45, d47, d57] at hcm6
+  have e6 : -2*s2  ^  2 + 8*s2*s3 - 2*s3 = 0 := by
+    dsimp [cm4] at hcm6
+    nlinarith only [hcm6]
+  have hcm7 := cm4_normalized_eq_zero
+    (p 0) (p 1) (p 5) (p 7) hbase
+  rw [d01, d05, d07, d15, d17, d57] at hcm7
+  have e7 : -2*s3  ^  3 + 8*s3  ^  2 - 2*s3 = 0 := by
+    dsimp [cm4] at hcm7
+    nlinarith only [hcm7]
+  have hcm8 := cm4_normalized_eq_zero
+    (p 0) (p 4) (p 6) (p 7) hbase
+  rw [d04, d06, d07, d46, d47, d67] at hcm8
+  have e8 : 8*s2*s3 - 2*s2 - 2*s3  ^  2 = 0 := by
+    dsimp [cm4] at hcm8
+    nlinarith only [hcm8]
+  have certificate :
+      (-47*s3+9 : ℝ) * (-2*s1  ^  2 + 2*s1*s2 + 4*s1 - 2*s2  ^  2 + 4*s2 - 2) +
+        (94*s3-18 : ℝ) * (-2*s1  ^  2 + 2*s1*s3 + 4*s1 - 2*s3  ^  2 + 4*s3 - 2) +
+        (-47*s3+9 : ℝ) * (-2*s1  ^  2 + 4*s1*s3 + 2*s1 - 2*s3  ^  2 + 4*s3 - 2) +
+        (-47/4*s3+9/4 : ℝ) * (-2*s1  ^  2 + 8*s1 - 2) +
+        (47/4*s3-9/4 : ℝ) * (-2*s1  ^  2 + 8*s1*s2 - 2*s2) +
+        (187/12*s3-11/4 : ℝ) * (-2*s2  ^  2 + 8*s2 - 2) +
+        (377/12*s3-25/4 : ℝ) * (-2*s2  ^  2 + 8*s2*s3 - 2*s3) +
+        (-187/12 : ℝ) * (-2*s3  ^  3 + 8*s3  ^  2 - 2*s3) +
+        (-377/12*s3+37/4 : ℝ) * (8*s2*s3 - 2*s2 - 2*s3  ^  2) = 1 := by
+    ring
+  rw [e0, e1, e2, e3, e4, e5, e6, e7, e8] at certificate
+  norm_num at certificate
+
+end Erdos97Octagon
diff --git a/LeanPool/Erdos97ConvexOctagon/ResidualAlgebra06.lean b/LeanPool/Erdos97ConvexOctagon/ResidualAlgebra06.lean
new file mode 100644
index 00000000..0bc2645e
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/ResidualAlgebra06.lean
@@ -0,0 +1,113 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.CayleyMenger
+import LeanPool.Erdos97ConvexOctagon.ResidualRepresentatives
+
+/-! # Erdős 97 convex-octagon formalization: Residual Algebra06 -/
+
+namespace Erdos97Octagon
+
+/-- Residual class 6 has no injective planar realisation. -/
+theorem residualRepresentative06_not_realises
+    {p : Vertex → Plane} (hp : Function.Injective p) :
+    ¬ Realises p residualRepresentative06 := by
+  intro hRealises
+  obtain ⟨radius, hpos, hdist⟩ :=
+    exists_positive_radii hp residualRepresentative06 hRealises
+  have r01 : radius 0 = radius 1 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative06])
+  have r02 : radius 0 = radius 2 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative06])
+  have r03 : radius 0 = radius 3 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative06])
+  have r46 : radius 4 = radius 6 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative06])
+  have r47 : radius 4 = radius 7 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative06])
+  have r65 : radius 6 = radius 5 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative06])
+  have radius0 : radius 0 = radius 0 := rfl
+  have radius1 : radius 1 = radius 0 := (r01).symm
+  have radius2 : radius 2 = radius 0 := (r02).symm
+  have radius3 : radius 3 = radius 0 := (r03).symm
+  have radius4 : radius 4 = radius 4 := rfl
+  have radius5 : radius 5 = radius 4 := ((r46).trans r65).symm
+  have radius6 : radius 6 = radius 4 := (r46).symm
+  have radius7 : radius 7 = radius 4 := (r47).symm
+  let base : ℝ := radius 0 ^ 2
+  have hbase : base ≠ 0 := by
+    dsimp [base]
+    exact pow_ne_zero 2 (ne_of_gt (hpos 0))
+  let s1 : ℝ := radius 4 ^ 2 / base
+  have d01 : sqDist (p 0) (p 1) / base = 1 := by
+    rw [sqDist, hdist 0 1 (by decide), radius0]
+    exact div_self hbase
+  have d02 : sqDist (p 0) (p 2) / base = 1 := by
+    rw [sqDist, hdist 0 2 (by decide), radius0]
+    exact div_self hbase
+  have d04 : sqDist (p 0) (p 4) / base = 1 := by
+    rw [sqDist, hdist 0 4 (by decide), radius0]
+    exact div_self hbase
+  have d05 : sqDist (p 0) (p 5) / base = s1 := by
+    rw [sqDist, dist_comm, hdist 5 0 (by decide), radius5]
+  have d12 : sqDist (p 1) (p 2) / base = 1 := by
+    rw [sqDist, hdist 1 2 (by decide), radius1]
+    exact div_self hbase
+  have d14 : sqDist (p 1) (p 4) / base = s1 := by
+    rw [sqDist, dist_comm, hdist 4 1 (by decide), radius4]
+  have d15 : sqDist (p 1) (p 5) / base = 1 := by
+    rw [sqDist, hdist 1 5 (by decide), radius1]
+    exact div_self hbase
+  have d24 : sqDist (p 2) (p 4) / base = 1 := by
+    rw [sqDist, hdist 2 4 (by decide), radius2]
+    exact div_self hbase
+  have d25 : sqDist (p 2) (p 5) / base = s1 := by
+    rw [sqDist, dist_comm, hdist 5 2 (by decide), radius5]
+  have d26 : sqDist (p 2) (p 6) / base = 1 := by
+    rw [sqDist, hdist 2 6 (by decide), radius2]
+    exact div_self hbase
+  have d27 : sqDist (p 2) (p 7) / base = s1 := by
+    rw [sqDist, dist_comm, hdist 7 2 (by decide), radius7]
+  have d56 : sqDist (p 5) (p 6) / base = s1 := by
+    rw [sqDist, hdist 5 6 (by decide), radius5]
+  have d57 : sqDist (p 5) (p 7) / base = s1 := by
+    rw [sqDist, hdist 5 7 (by decide), radius5]
+  have d67 : sqDist (p 6) (p 7) / base = s1 := by
+    rw [sqDist, hdist 6 7 (by decide), radius6]
+  have hcm0 := cm4_normalized_eq_zero
+    (p 0) (p 1) (p 2) (p 4) hbase
+  rw [d01, d02, d04, d12, d14, d24] at hcm0
+  have e0 : -2*s1  ^  2 + 6*s1 = 0 := by
+    dsimp [cm4] at hcm0
+    nlinarith only [hcm0]
+  have hcm1 := cm4_normalized_eq_zero
+    (p 0) (p 1) (p 2) (p 5) hbase
+  rw [d01, d02, d05, d12, d15, d25] at hcm1
+  have e1 : -2*s1  ^  2 + 8*s1 - 2 = 0 := by
+    dsimp [cm4] at hcm1
+    nlinarith only [hcm1]
+  have hcm2 := cm4_normalized_eq_zero
+    (p 2) (p 5) (p 6) (p 7) hbase
+  rw [d25, d26, d27, d56, d57, d67] at hcm2
+  have e2 : 6*s1  ^  2 - 2*s1 = 0 := by
+    dsimp [cm4] at hcm2
+    nlinarith only [hcm2]
+  have certificate :
+      (11/16 : ℝ) * (-2*s1  ^  2 + 6*s1) +
+        (-1/2 : ℝ) * (-2*s1  ^  2 + 8*s1 - 2) +
+        (1/16 : ℝ) * (6*s1  ^  2 - 2*s1) = 1 := by
+    ring
+  rw [e0, e1, e2] at certificate
+  norm_num at certificate
+
+end Erdos97Octagon
diff --git a/LeanPool/Erdos97ConvexOctagon/ResidualAlgebra07.lean b/LeanPool/Erdos97ConvexOctagon/ResidualAlgebra07.lean
new file mode 100644
index 00000000..3a15e839
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/ResidualAlgebra07.lean
@@ -0,0 +1,129 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.CayleyMenger
+import LeanPool.Erdos97ConvexOctagon.ResidualRepresentatives
+
+/-! # Erdős 97 convex-octagon formalization: Residual Algebra07 -/
+
+namespace Erdos97Octagon
+
+/-- Residual class 7 has no injective planar realisation. -/
+theorem residualRepresentative07_not_realises
+    {p : Vertex → Plane} (hp : Function.Injective p) :
+    ¬ Realises p residualRepresentative07 := by
+  intro hRealises
+  obtain ⟨radius, hpos, hdist⟩ :=
+    exists_positive_radii hp residualRepresentative07 hRealises
+  have r01 : radius 0 = radius 1 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative07])
+  have r23 : radius 2 = radius 3 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative07])
+  have r45 : radius 4 = radius 5 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative07])
+  have r67 : radius 6 = radius 7 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative07])
+  have radius0 : radius 0 = radius 0 := rfl
+  have radius1 : radius 1 = radius 0 := (r01).symm
+  have radius2 : radius 2 = radius 2 := rfl
+  have radius3 : radius 3 = radius 2 := (r23).symm
+  have radius4 : radius 4 = radius 4 := rfl
+  have radius5 : radius 5 = radius 4 := (r45).symm
+  have radius6 : radius 6 = radius 6 := rfl
+  have radius7 : radius 7 = radius 6 := (r67).symm
+  let base : ℝ := radius 0 ^ 2
+  have hbase : base ≠ 0 := by
+    dsimp [base]
+    exact pow_ne_zero 2 (ne_of_gt (hpos 0))
+  let s1 : ℝ := radius 2 ^ 2 / base
+  let s2 : ℝ := radius 4 ^ 2 / base
+  let s3 : ℝ := radius 6 ^ 2 / base
+  have d01 : sqDist (p 0) (p 1) / base = 1 := by
+    rw [sqDist, hdist 0 1 (by decide), radius0]
+    exact div_self hbase
+  have d02 : sqDist (p 0) (p 2) / base = 1 := by
+    rw [sqDist, hdist 0 2 (by decide), radius0]
+    exact div_self hbase
+  have d04 : sqDist (p 0) (p 4) / base = 1 := by
+    rw [sqDist, hdist 0 4 (by decide), radius0]
+    exact div_self hbase
+  have d05 : sqDist (p 0) (p 5) / base = s2 := by
+    rw [sqDist, dist_comm, hdist 5 0 (by decide), radius5]
+  have d06 : sqDist (p 0) (p 6) / base = s3 := by
+    rw [sqDist, dist_comm, hdist 6 0 (by decide), radius6]
+  have d07 : sqDist (p 0) (p 7) / base = s3 := by
+    rw [sqDist, dist_comm, hdist 7 0 (by decide), radius7]
+  have d12 : sqDist (p 1) (p 2) / base = 1 := by
+    rw [sqDist, hdist 1 2 (by decide), radius1]
+    exact div_self hbase
+  have d15 : sqDist (p 1) (p 5) / base = 1 := by
+    rw [sqDist, hdist 1 5 (by decide), radius1]
+    exact div_self hbase
+  have d16 : sqDist (p 1) (p 6) / base = s3 := by
+    rw [sqDist, dist_comm, hdist 6 1 (by decide), radius6]
+  have d17 : sqDist (p 1) (p 7) / base = s3 := by
+    rw [sqDist, dist_comm, hdist 7 1 (by decide), radius7]
+  have d25 : sqDist (p 2) (p 5) / base = s2 := by
+    rw [sqDist, dist_comm, hdist 5 2 (by decide), radius5]
+  have d45 : sqDist (p 4) (p 5) / base = s2 := by
+    rw [sqDist, hdist 4 5 (by decide), radius4]
+  have d46 : sqDist (p 4) (p 6) / base = s2 := by
+    rw [sqDist, hdist 4 6 (by decide), radius4]
+  have d47 : sqDist (p 4) (p 7) / base = s3 := by
+    rw [sqDist, dist_comm, hdist 7 4 (by decide), radius7]
+  have d56 : sqDist (p 5) (p 6) / base = s3 := by
+    rw [sqDist, dist_comm, hdist 6 5 (by decide), radius6]
+  have d57 : sqDist (p 5) (p 7) / base = s2 := by
+    rw [sqDist, hdist 5 7 (by decide), radius5]
+  have d67 : sqDist (p 6) (p 7) / base = s3 := by
+    rw [sqDist, hdist 6 7 (by decide), radius6]
+  have hcm0 := cm4_normalized_eq_zero
+    (p 0) (p 1) (p 2) (p 5) hbase
+  rw [d01, d02, d05, d12, d15, d25] at hcm0
+  have e0 : -2*s2  ^  2 + 8*s2 - 2 = 0 := by
+    dsimp [cm4] at hcm0
+    nlinarith only [hcm0]
+  have hcm1 := cm4_normalized_eq_zero
+    (p 0) (p 4) (p 6) (p 7) hbase
+  rw [d04, d06, d07, d46, d47, d67] at hcm1
+  have e1 : -2*s2  ^  2*s3 + 4*s2*s3  ^  2 + 2*s2*s3 - 2*s3  ^  3 + 4*s3  ^  2 - 2*s3 = 0 := by
+    dsimp [cm4] at hcm1
+    nlinarith only [hcm1]
+  have hcm2 := cm4_normalized_eq_zero
+    (p 0) (p 5) (p 6) (p 7) hbase
+  rw [d05, d06, d07, d56, d57, d67] at hcm2
+  have e2 : -2*s2  ^  2*s3 + 8*s2*s3  ^  2 - 2*s3  ^  3 = 0 := by
+    dsimp [cm4] at hcm2
+    nlinarith only [hcm2]
+  have hcm3 := cm4_normalized_eq_zero
+    (p 0) (p 1) (p 6) (p 7) hbase
+  rw [d01, d06, d07, d16, d17, d67] at hcm3
+  have e3 : 6*s3  ^  2 - 2*s3 = 0 := by
+    dsimp [cm4] at hcm3
+    nlinarith only [hcm3]
+  have hcm4 := cm4_normalized_eq_zero
+    (p 0) (p 4) (p 5) (p 7) hbase
+  rw [d04, d05, d07, d45, d47, d57] at hcm4
+  have e4 : 8*s2*s3 - 2*s2 - 2*s3  ^  2 = 0 := by
+    dsimp [cm4] at hcm4
+    nlinarith only [hcm4]
+  have certificate :
+      (-1/2 : ℝ) * (-2*s2  ^  2 + 8*s2 - 2) +
+        (-25/4 : ℝ) *
+          (-2*s2  ^  2*s3 + 4*s2*s3  ^  2 + 2*s2*s3 - 2*s3  ^  3 +
+            4*s3  ^  2 - 2*s3) +
+        (33/4 : ℝ) * (-2*s2  ^  2*s3 + 8*s2*s3  ^  2 - 2*s3  ^  3) +
+        (-37*s2+33/4*s3+25/4 : ℝ) * (6*s3  ^  2 - 2*s3) +
+        (1/2*s2+91/4*s3-2 : ℝ) * (8*s2*s3 - 2*s2 - 2*s3  ^  2) = 1 := by
+    ring
+  rw [e0, e1, e2, e3, e4] at certificate
+  norm_num at certificate
+
+end Erdos97Octagon
diff --git a/LeanPool/Erdos97ConvexOctagon/ResidualAlgebra08.lean b/LeanPool/Erdos97ConvexOctagon/ResidualAlgebra08.lean
new file mode 100644
index 00000000..df48db21
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/ResidualAlgebra08.lean
@@ -0,0 +1,101 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.CayleyMenger
+import LeanPool.Erdos97ConvexOctagon.ResidualRepresentatives
+
+/-! # Erdős 97 convex-octagon formalization: Residual Algebra08 -/
+
+namespace Erdos97Octagon
+
+/-- Residual class 8 has no injective planar realisation. -/
+theorem residualRepresentative08_not_realises
+    {p : Vertex → Plane} (hp : Function.Injective p) :
+    ¬ Realises p residualRepresentative08 := by
+  intro hRealises
+  obtain ⟨radius, hpos, hdist⟩ :=
+    exists_positive_radii hp residualRepresentative08 hRealises
+  have r01 : radius 0 = radius 1 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative08])
+  have r04 : radius 0 = radius 4 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative08])
+  have r15 : radius 1 = radius 5 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative08])
+  have r23 : radius 2 = radius 3 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative08])
+  have r67 : radius 6 = radius 7 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative08])
+  have radius0 : radius 0 = radius 0 := rfl
+  have radius1 : radius 1 = radius 0 := (r01).symm
+  have radius4 : radius 4 = radius 0 := (r04).symm
+  have radius5 : radius 5 = radius 0 := ((r01).trans r15).symm
+  have radius2 : radius 2 = radius 2 := rfl
+  have radius3 : radius 3 = radius 2 := (r23).symm
+  have radius6 : radius 6 = radius 6 := rfl
+  have radius7 : radius 7 = radius 6 := (r67).symm
+  let base : ℝ := radius 0 ^ 2
+  have hbase : base ≠ 0 := by
+    dsimp [base]
+    exact pow_ne_zero 2 (ne_of_gt (hpos 0))
+  let s1 : ℝ := radius 2 ^ 2 / base
+  let s2 : ℝ := radius 6 ^ 2 / base
+  have d01 : sqDist (p 0) (p 1) / base = 1 := by
+    rw [sqDist, hdist 0 1 (by decide), radius0]
+    exact div_self hbase
+  have d02 : sqDist (p 0) (p 2) / base = 1 := by
+    rw [sqDist, hdist 0 2 (by decide), radius0]
+    exact div_self hbase
+  have d07 : sqDist (p 0) (p 7) / base = s2 := by
+    rw [sqDist, dist_comm, hdist 7 0 (by decide), radius7]
+  have d12 : sqDist (p 1) (p 2) / base = 1 := by
+    rw [sqDist, hdist 1 2 (by decide), radius1]
+    exact div_self hbase
+  have d17 : sqDist (p 1) (p 7) / base = s2 := by
+    rw [sqDist, dist_comm, hdist 7 1 (by decide), radius7]
+  have d27 : sqDist (p 2) (p 7) / base = s2 := by
+    rw [sqDist, dist_comm, hdist 7 2 (by decide), radius7]
+  have d45 : sqDist (p 4) (p 5) / base = 1 := by
+    rw [sqDist, hdist 4 5 (by decide), radius4]
+    exact div_self hbase
+  have d46 : sqDist (p 4) (p 6) / base = 1 := by
+    rw [sqDist, hdist 4 6 (by decide), radius4]
+    exact div_self hbase
+  have d47 : sqDist (p 4) (p 7) / base = 1 := by
+    rw [sqDist, hdist 4 7 (by decide), radius4]
+    exact div_self hbase
+  have d56 : sqDist (p 5) (p 6) / base = 1 := by
+    rw [sqDist, hdist 5 6 (by decide), radius5]
+    exact div_self hbase
+  have d57 : sqDist (p 5) (p 7) / base = 1 := by
+    rw [sqDist, hdist 5 7 (by decide), radius5]
+    exact div_self hbase
+  have d67 : sqDist (p 6) (p 7) / base = s2 := by
+    rw [sqDist, hdist 6 7 (by decide), radius6]
+  have hcm0 := cm4_normalized_eq_zero
+    (p 4) (p 5) (p 6) (p 7) hbase
+  rw [d45, d46, d47, d56, d57, d67] at hcm0
+  have e0 : -2*s2  ^  2 + 6*s2 = 0 := by
+    dsimp [cm4] at hcm0
+    nlinarith only [hcm0]
+  have hcm1 := cm4_normalized_eq_zero
+    (p 0) (p 1) (p 2) (p 7) hbase
+  rw [d01, d02, d07, d12, d17, d27] at hcm1
+  have e1 : 6*s2 - 2 = 0 := by
+    dsimp [cm4] at hcm1
+    nlinarith only [hcm1]
+  have certificate :
+      (9/16 : ℝ) * (-2*s2  ^  2 + 6*s2) +
+        (3/16*s2-1/2 : ℝ) * (6*s2 - 2) = 1 := by
+    ring
+  rw [e0, e1] at certificate
+  norm_num at certificate
+
+end Erdos97Octagon
diff --git a/LeanPool/Erdos97ConvexOctagon/ResidualAlgebra09.lean b/LeanPool/Erdos97ConvexOctagon/ResidualAlgebra09.lean
new file mode 100644
index 00000000..067a9050
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/ResidualAlgebra09.lean
@@ -0,0 +1,94 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.CayleyMenger
+import LeanPool.Erdos97ConvexOctagon.ResidualRepresentatives
+
+/-! # Erdős 97 convex-octagon formalization: Residual Algebra09 -/
+
+namespace Erdos97Octagon
+
+/-- Residual class 9 has no injective planar realisation. -/
+theorem residualRepresentative09_not_realises
+    {p : Vertex → Plane} (hp : Function.Injective p) :
+    ¬ Realises p residualRepresentative09 := by
+  intro hRealises
+  obtain ⟨radius, hpos, hdist⟩ :=
+    exists_positive_radii hp residualRepresentative09 hRealises
+  have r01 : radius 0 = radius 1 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative09])
+  have r04 : radius 0 = radius 4 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative09])
+  have r15 : radius 1 = radius 5 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative09])
+  have r23 : radius 2 = radius 3 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative09])
+  have r26 : radius 2 = radius 6 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative09])
+  have r37 : radius 3 = radius 7 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative09])
+  have radius0 : radius 0 = radius 0 := rfl
+  have radius1 : radius 1 = radius 0 := (r01).symm
+  have radius4 : radius 4 = radius 0 := (r04).symm
+  have radius5 : radius 5 = radius 0 := ((r01).trans r15).symm
+  have radius2 : radius 2 = radius 2 := rfl
+  have radius3 : radius 3 = radius 2 := (r23).symm
+  have radius6 : radius 6 = radius 2 := (r26).symm
+  have radius7 : radius 7 = radius 2 := ((r23).trans r37).symm
+  let base : ℝ := radius 0 ^ 2
+  have hbase : base ≠ 0 := by
+    dsimp [base]
+    exact pow_ne_zero 2 (ne_of_gt (hpos 0))
+  let s1 : ℝ := radius 2 ^ 2 / base
+  have d01 : sqDist (p 0) (p 1) / base = 1 := by
+    rw [sqDist, hdist 0 1 (by decide), radius0]
+    exact div_self hbase
+  have d02 : sqDist (p 0) (p 2) / base = 1 := by
+    rw [sqDist, hdist 0 2 (by decide), radius0]
+    exact div_self hbase
+  have d03 : sqDist (p 0) (p 3) / base = 1 := by
+    rw [sqDist, hdist 0 3 (by decide), radius0]
+    exact div_self hbase
+  have d06 : sqDist (p 0) (p 6) / base = s1 := by
+    rw [sqDist, dist_comm, hdist 6 0 (by decide), radius6]
+  have d12 : sqDist (p 1) (p 2) / base = 1 := by
+    rw [sqDist, hdist 1 2 (by decide), radius1]
+    exact div_self hbase
+  have d13 : sqDist (p 1) (p 3) / base = 1 := by
+    rw [sqDist, hdist 1 3 (by decide), radius1]
+    exact div_self hbase
+  have d16 : sqDist (p 1) (p 6) / base = s1 := by
+    rw [sqDist, dist_comm, hdist 6 1 (by decide), radius6]
+  have d23 : sqDist (p 2) (p 3) / base = s1 := by
+    rw [sqDist, hdist 2 3 (by decide), radius2]
+  have d26 : sqDist (p 2) (p 6) / base = s1 := by
+    rw [sqDist, hdist 2 6 (by decide), radius2]
+  have hcm0 := cm4_normalized_eq_zero
+    (p 0) (p 1) (p 2) (p 3) hbase
+  rw [d01, d02, d03, d12, d13, d23] at hcm0
+  have e0 : -2*s1  ^  2 + 6*s1 = 0 := by
+    dsimp [cm4] at hcm0
+    nlinarith only [hcm0]
+  have hcm1 := cm4_normalized_eq_zero
+    (p 0) (p 1) (p 2) (p 6) hbase
+  rw [d01, d02, d06, d12, d16, d26] at hcm1
+  have e1 : 6*s1 - 2 = 0 := by
+    dsimp [cm4] at hcm1
+    nlinarith only [hcm1]
+  have certificate :
+      (9/16 : ℝ) * (-2*s1  ^  2 + 6*s1) +
+        (3/16*s1-1/2 : ℝ) * (6*s1 - 2) = 1 := by
+    ring
+  rw [e0, e1] at certificate
+  norm_num at certificate
+
+end Erdos97Octagon
diff --git a/LeanPool/Erdos97ConvexOctagon/ResidualAlgebra10.lean b/LeanPool/Erdos97ConvexOctagon/ResidualAlgebra10.lean
new file mode 100644
index 00000000..a3c1d356
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/ResidualAlgebra10.lean
@@ -0,0 +1,147 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.CayleyMenger
+import LeanPool.Erdos97ConvexOctagon.ResidualRepresentatives
+
+/-! # Erdős 97 convex-octagon formalization: Residual Algebra10 -/
+
+namespace Erdos97Octagon
+
+/-- Residual class 10 has no injective planar realisation. -/
+theorem residualRepresentative10_not_realises
+    {p : Vertex → Plane} (hp : Function.Injective p) :
+    ¬ Realises p residualRepresentative10 := by
+  intro hRealises
+  obtain ⟨radius, hpos, hdist⟩ :=
+    exists_positive_radii hp residualRepresentative10 hRealises
+  have r01 : radius 0 = radius 1 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative10])
+  have r23 : radius 2 = radius 3 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative10])
+  have r45 : radius 4 = radius 5 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative10])
+  have r67 : radius 6 = radius 7 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative10])
+  have radius0 : radius 0 = radius 0 := rfl
+  have radius1 : radius 1 = radius 0 := (r01).symm
+  have radius2 : radius 2 = radius 2 := rfl
+  have radius3 : radius 3 = radius 2 := (r23).symm
+  have radius4 : radius 4 = radius 4 := rfl
+  have radius5 : radius 5 = radius 4 := (r45).symm
+  have radius6 : radius 6 = radius 6 := rfl
+  have radius7 : radius 7 = radius 6 := (r67).symm
+  let base : ℝ := radius 0 ^ 2
+  have hbase : base ≠ 0 := by
+    dsimp [base]
+    exact pow_ne_zero 2 (ne_of_gt (hpos 0))
+  let s1 : ℝ := radius 2 ^ 2 / base
+  let s2 : ℝ := radius 4 ^ 2 / base
+  let s3 : ℝ := radius 6 ^ 2 / base
+  have d01 : sqDist (p 0) (p 1) / base = 1 := by
+    rw [sqDist, hdist 0 1 (by decide), radius0]
+    exact div_self hbase
+  have d02 : sqDist (p 0) (p 2) / base = 1 := by
+    rw [sqDist, hdist 0 2 (by decide), radius0]
+    exact div_self hbase
+  have d03 : sqDist (p 0) (p 3) / base = 1 := by
+    rw [sqDist, hdist 0 3 (by decide), radius0]
+    exact div_self hbase
+  have d04 : sqDist (p 0) (p 4) / base = 1 := by
+    rw [sqDist, hdist 0 4 (by decide), radius0]
+    exact div_self hbase
+  have d05 : sqDist (p 0) (p 5) / base = s2 := by
+    rw [sqDist, dist_comm, hdist 5 0 (by decide), radius5]
+  have d06 : sqDist (p 0) (p 6) / base = s3 := by
+    rw [sqDist, dist_comm, hdist 6 0 (by decide), radius6]
+  have d07 : sqDist (p 0) (p 7) / base = s3 := by
+    rw [sqDist, dist_comm, hdist 7 0 (by decide), radius7]
+  have d12 : sqDist (p 1) (p 2) / base = 1 := by
+    rw [sqDist, hdist 1 2 (by decide), radius1]
+    exact div_self hbase
+  have d13 : sqDist (p 1) (p 3) / base = 1 := by
+    rw [sqDist, hdist 1 3 (by decide), radius1]
+    exact div_self hbase
+  have d14 : sqDist (p 1) (p 4) / base = s2 := by
+    rw [sqDist, dist_comm, hdist 4 1 (by decide), radius4]
+  have d16 : sqDist (p 1) (p 6) / base = s3 := by
+    rw [sqDist, dist_comm, hdist 6 1 (by decide), radius6]
+  have d17 : sqDist (p 1) (p 7) / base = s3 := by
+    rw [sqDist, dist_comm, hdist 7 1 (by decide), radius7]
+  have d23 : sqDist (p 2) (p 3) / base = s1 := by
+    rw [sqDist, hdist 2 3 (by decide), radius2]
+  have d24 : sqDist (p 2) (p 4) / base = s1 := by
+    rw [sqDist, hdist 2 4 (by decide), radius2]
+  have d26 : sqDist (p 2) (p 6) / base = s1 := by
+    rw [sqDist, hdist 2 6 (by decide), radius2]
+  have d27 : sqDist (p 2) (p 7) / base = s3 := by
+    rw [sqDist, dist_comm, hdist 7 2 (by decide), radius7]
+  have d45 : sqDist (p 4) (p 5) / base = s2 := by
+    rw [sqDist, hdist 4 5 (by decide), radius4]
+  have d46 : sqDist (p 4) (p 6) / base = s2 := by
+    rw [sqDist, hdist 4 6 (by decide), radius4]
+  have d47 : sqDist (p 4) (p 7) / base = s2 := by
+    rw [sqDist, hdist 4 7 (by decide), radius4]
+  have d56 : sqDist (p 5) (p 6) / base = s2 := by
+    rw [sqDist, hdist 5 6 (by decide), radius5]
+  have d57 : sqDist (p 5) (p 7) / base = s2 := by
+    rw [sqDist, hdist 5 7 (by decide), radius5]
+  have d67 : sqDist (p 6) (p 7) / base = s3 := by
+    rw [sqDist, hdist 6 7 (by decide), radius6]
+  have hcm0 := cm4_normalized_eq_zero
+    (p 0) (p 1) (p 2) (p 4) hbase
+  rw [d01, d02, d04, d12, d14, d24] at hcm0
+  have e0 : -2*s1  ^  2 + 2*s1*s2 + 4*s1 - 2*s2  ^  2 + 4*s2 - 2 = 0 := by
+    dsimp [cm4] at hcm0
+    nlinarith only [hcm0]
+  have hcm1 := cm4_normalized_eq_zero
+    (p 0) (p 1) (p 2) (p 6) hbase
+  rw [d01, d02, d06, d12, d16, d26] at hcm1
+  have e1 : -2*s1  ^  2 + 4*s1*s3 + 2*s1 - 2*s3  ^  2 + 4*s3 - 2 = 0 := by
+    dsimp [cm4] at hcm1
+    nlinarith only [hcm1]
+  have hcm2 := cm4_normalized_eq_zero
+    (p 0) (p 1) (p 2) (p 3) hbase
+  rw [d01, d02, d03, d12, d13, d23] at hcm2
+  have e2 : -2*s1  ^  2 + 6*s1 = 0 := by
+    dsimp [cm4] at hcm2
+    nlinarith only [hcm2]
+  have hcm3 := cm4_normalized_eq_zero
+    (p 4) (p 5) (p 6) (p 7) hbase
+  rw [d45, d46, d47, d56, d57, d67] at hcm3
+  have e3 : 6*s2  ^  2*s3 - 2*s2*s3  ^  2 = 0 := by
+    dsimp [cm4] at hcm3
+    nlinarith only [hcm3]
+  have hcm4 := cm4_normalized_eq_zero
+    (p 0) (p 5) (p 6) (p 7) hbase
+  rw [d05, d06, d07, d56, d57, d67] at hcm4
+  have e4 : 6*s2*s3  ^  2 - 2*s3  ^  3 = 0 := by
+    dsimp [cm4] at hcm4
+    nlinarith only [hcm4]
+  have hcm5 := cm4_normalized_eq_zero
+    (p 0) (p 1) (p 2) (p 7) hbase
+  rw [d01, d02, d07, d12, d17, d27] at hcm5
+  have e5 : 6*s3 - 2 = 0 := by
+    dsimp [cm4] at hcm5
+    nlinarith only [hcm5]
+  have certificate :
+      (-81/80 : ℝ) * (-2*s1  ^  2 + 2*s1*s2 + 4*s1 - 2*s2  ^  2 + 4*s2 - 2) +
+        (-243/320*s2+243/320 : ℝ) * (-2*s1  ^  2 + 4*s1*s3 + 2*s1 - 2*s3  ^  2 + 4*s3 - 2) +
+        (243/320*s2+81/320 : ℝ) * (-2*s1  ^  2 + 6*s1) +
+        (-81/80 : ℝ) * (6*s2  ^  2*s3 - 2*s2*s3  ^  2) +
+        (189/40 : ℝ) * (6*s2*s3  ^  2 - 2*s3  ^  3) +
+        (81/160*s1*s2-81/160*s1+81/80*s2 ^ 2-1701/320*s2*s3-81/64*s2+
+            63/40*s3 ^ 2+249/320*s3-79/320 : ℝ) *
+          (6*s3 - 2) = 1 := by
+    ring
+  rw [e0, e1, e2, e3, e4, e5] at certificate
+  norm_num at certificate
+
+end Erdos97Octagon
diff --git a/LeanPool/Erdos97ConvexOctagon/ResidualAlgebra11.lean b/LeanPool/Erdos97ConvexOctagon/ResidualAlgebra11.lean
new file mode 100644
index 00000000..f49ac0fe
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/ResidualAlgebra11.lean
@@ -0,0 +1,555 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.CayleyMenger
+import LeanPool.Erdos97ConvexOctagon.ResidualRepresentatives
+import Mathlib.Analysis.Convex.Combination
+
+/-! # The final residual incidence class
+
+The metric constraints of residual class 11 determine a normalized quadratic
+parameter. Each of its two possible ranges puts a labelled vertex in the
+convex hull of four other vertices.
+-/
+
+namespace Erdos97Octagon
+
+open scoped InnerProductSpace
+
+private structure Residual11Distances (p : Vertex → Plane) where
+  base : ℝ
+  s : ℝ
+  w05 : ℝ
+  w13 : ℝ
+  w27 : ℝ
+  w46 : ℝ
+  hbase : base ≠ 0
+  hbase_pos : 0 < base
+  hs : 0 < s
+  d01 : sqDist (p 0) (p 1) / base = 1
+  d02 : sqDist (p 0) (p 2) / base = 1
+  d03 : sqDist (p 0) (p 3) / base = 1
+  d04 : sqDist (p 0) (p 4) / base = 1
+  d05 : sqDist (p 0) (p 5) / base = w05
+  d06 : sqDist (p 0) (p 6) / base = s
+  d07 : sqDist (p 0) (p 7) / base = s
+  d12 : sqDist (p 1) (p 2) / base = 1
+  d13 : sqDist (p 1) (p 3) / base = w13
+  d14 : sqDist (p 1) (p 4) / base = s
+  d15 : sqDist (p 1) (p 5) / base = 1
+  d16 : sqDist (p 1) (p 6) / base = 1
+  d17 : sqDist (p 1) (p 7) / base = s
+  d23 : sqDist (p 2) (p 3) / base = s
+  d24 : sqDist (p 2) (p 4) / base = s
+  d25 : sqDist (p 2) (p 5) / base = s
+  d26 : sqDist (p 2) (p 6) / base = s
+  d27 : sqDist (p 2) (p 7) / base = w27
+  d34 : sqDist (p 3) (p 4) / base = 1
+  d35 : sqDist (p 3) (p 5) / base = 1
+  d36 : sqDist (p 3) (p 6) / base = s
+  d37 : sqDist (p 3) (p 7) / base = 1
+  d45 : sqDist (p 4) (p 5) / base = s
+  d46 : sqDist (p 4) (p 6) / base = w46
+  d47 : sqDist (p 4) (p 7) / base = s
+  d56 : sqDist (p 5) (p 6) / base = 1
+  d57 : sqDist (p 5) (p 7) / base = 1
+  d67 : sqDist (p 6) (p 7) / base = s
+
+private noncomputable def residual11_distances
+    {p : Vertex → Plane} (hC : ConvexIndependent ℝ p)
+    (hRealises : Realises p residualRepresentative11) :
+    Residual11Distances p := by
+  classical
+  let radius := Classical.choose
+    (exists_positive_radii hC.injective residualRepresentative11 hRealises)
+  have hradius := Classical.choose_spec
+    (exists_positive_radii hC.injective residualRepresentative11 hRealises)
+  have hpos : ∀ v : Vertex, 0 < radius v := by
+    simpa [radius] using hradius.1
+  have hdist :
+      ∀ v w : Vertex, w ∈ residualRepresentative11.targets v →
+        dist (p v) (p w) = radius v := by
+    simpa [radius] using hradius.2
+  have r01 : radius 0 = radius 1 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative11])
+  have r03 : radius 0 = radius 3 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative11])
+  have r15 : radius 1 = radius 5 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative11])
+  have r24 : radius 2 = radius 4 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative11])
+  have r26 : radius 2 = radius 6 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative11])
+  have r47 : radius 4 = radius 7 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative11])
+  have radius0 : radius 0 = radius 0 := rfl
+  have radius1 : radius 1 = radius 0 := r01.symm
+  have radius2 : radius 2 = radius 2 := rfl
+  have radius3 : radius 3 = radius 0 := r03.symm
+  have radius4 : radius 4 = radius 2 := r24.symm
+  have radius5 : radius 5 = radius 0 := (r01.trans r15).symm
+  have radius6 : radius 6 = radius 2 := r26.symm
+  have radius7 : radius 7 = radius 2 := (r24.trans r47).symm
+  let base : ℝ := radius 0 ^ 2
+  have hbase : base ≠ 0 := by
+    dsimp [base]
+    exact pow_ne_zero 2 (ne_of_gt (hpos 0))
+  have hbase_pos : 0 < base := by
+    dsimp [base]
+    positivity
+  let s : ℝ := radius 2 ^ 2 / base
+  have hs : 0 < s := by
+    dsimp [s]
+    exact div_pos (pow_pos (hpos 2) 2) hbase_pos
+  let w05 : ℝ := sqDist (p 0) (p 5) / base
+  let w13 : ℝ := sqDist (p 1) (p 3) / base
+  let w27 : ℝ := sqDist (p 2) (p 7) / base
+  let w46 : ℝ := sqDist (p 4) (p 6) / base
+  have d01 : sqDist (p 0) (p 1) / base = 1 := by
+    rw [sqDist, hdist 0 1 (by decide), radius0]
+    exact div_self hbase
+  have d02 : sqDist (p 0) (p 2) / base = 1 := by
+    rw [sqDist, hdist 0 2 (by decide), radius0]
+    exact div_self hbase
+  have d03 : sqDist (p 0) (p 3) / base = 1 := by
+    rw [sqDist, hdist 0 3 (by decide), radius0]
+    exact div_self hbase
+  have d04 : sqDist (p 0) (p 4) / base = 1 := by
+    rw [sqDist, hdist 0 4 (by decide), radius0]
+    exact div_self hbase
+  have d05 : sqDist (p 0) (p 5) / base = w05 := rfl
+  have d06 : sqDist (p 0) (p 6) / base = s := by
+    rw [sqDist, dist_comm, hdist 6 0 (by decide), radius6]
+  have d07 : sqDist (p 0) (p 7) / base = s := by
+    rw [sqDist, dist_comm, hdist 7 0 (by decide), radius7]
+  have d12 : sqDist (p 1) (p 2) / base = 1 := by
+    rw [sqDist, hdist 1 2 (by decide), radius1]
+    exact div_self hbase
+  have d13 : sqDist (p 1) (p 3) / base = w13 := rfl
+  have d14 : sqDist (p 1) (p 4) / base = s := by
+    rw [sqDist, dist_comm, hdist 4 1 (by decide), radius4]
+  have d15 : sqDist (p 1) (p 5) / base = 1 := by
+    rw [sqDist, hdist 1 5 (by decide), radius1]
+    exact div_self hbase
+  have d16 : sqDist (p 1) (p 6) / base = 1 := by
+    rw [sqDist, hdist 1 6 (by decide), radius1]
+    exact div_self hbase
+  have d17 : sqDist (p 1) (p 7) / base = s := by
+    rw [sqDist, dist_comm, hdist 7 1 (by decide), radius7]
+  have d23 : sqDist (p 2) (p 3) / base = s := by
+    rw [sqDist, hdist 2 3 (by decide), radius2]
+  have d24 : sqDist (p 2) (p 4) / base = s := by
+    rw [sqDist, hdist 2 4 (by decide), radius2]
+  have d25 : sqDist (p 2) (p 5) / base = s := by
+    rw [sqDist, hdist 2 5 (by decide), radius2]
+  have d26 : sqDist (p 2) (p 6) / base = s := by
+    rw [sqDist, hdist 2 6 (by decide), radius2]
+  have d27 : sqDist (p 2) (p 7) / base = w27 := rfl
+  have d34 : sqDist (p 3) (p 4) / base = 1 := by
+    rw [sqDist, hdist 3 4 (by decide), radius3]
+    exact div_self hbase
+  have d35 : sqDist (p 3) (p 5) / base = 1 := by
+    rw [sqDist, hdist 3 5 (by decide), radius3]
+    exact div_self hbase
+  have d36 : sqDist (p 3) (p 6) / base = s := by
+    rw [sqDist, dist_comm, hdist 6 3 (by decide), radius6]
+  have d37 : sqDist (p 3) (p 7) / base = 1 := by
+    rw [sqDist, hdist 3 7 (by decide), radius3]
+    exact div_self hbase
+  have d45 : sqDist (p 4) (p 5) / base = s := by
+    rw [sqDist, hdist 4 5 (by decide), radius4]
+  have d46 : sqDist (p 4) (p 6) / base = w46 := rfl
+  have d47 : sqDist (p 4) (p 7) / base = s := by
+    rw [sqDist, hdist 4 7 (by decide), radius4]
+  have d56 : sqDist (p 5) (p 6) / base = 1 := by
+    rw [sqDist, hdist 5 6 (by decide), radius5]
+    exact div_self hbase
+  have d57 : sqDist (p 5) (p 7) / base = 1 := by
+    rw [sqDist, hdist 5 7 (by decide), radius5]
+    exact div_self hbase
+  have d67 : sqDist (p 6) (p 7) / base = s := by
+    rw [sqDist, hdist 6 7 (by decide), radius6]
+  exact {
+    base, s, w05, w13, w27, w46, hbase, hbase_pos, hs,
+    d01, d02, d03, d04, d05, d06, d07, d12, d13, d14, d15,
+    d16, d17, d23, d24, d25, d26, d27, d34, d35, d36, d37,
+    d45, d46, d47, d56, d57, d67
+  }
+
+private structure Residual11Normalized (p : Vertex → Plane) where
+  base : ℝ
+  s : ℝ
+  hbase : base ≠ 0
+  hbase_pos : 0 < base
+  hs : 0 < s
+  hs_ne_two : s ≠ 2
+  eS : s ^ 2 - 4 * s + 1 = 0
+  d01 : sqDist (p 0) (p 1) / base = 1
+  d02 : sqDist (p 0) (p 2) / base = 1
+  d03 : sqDist (p 0) (p 3) / base = 1
+  d04 : sqDist (p 0) (p 4) / base = 1
+  d05 : sqDist (p 0) (p 5) / base = 2
+  d06 : sqDist (p 0) (p 6) / base = s
+  d07 : sqDist (p 0) (p 7) / base = s
+  d12 : sqDist (p 1) (p 2) / base = 1
+  d13 : sqDist (p 1) (p 3) / base = 2
+  d15 : sqDist (p 1) (p 5) / base = 1
+  d23 : sqDist (p 2) (p 3) / base = s
+  d24 : sqDist (p 2) (p 4) / base = s
+  d25 : sqDist (p 2) (p 5) / base = s
+  d26 : sqDist (p 2) (p 6) / base = s
+  d27 : sqDist (p 2) (p 7) / base = 2 * s
+  d35 : sqDist (p 3) (p 5) / base = 1
+  d46 : sqDist (p 4) (p 6) / base = 2 * s
+  d47 : sqDist (p 4) (p 7) / base = s
+  d67 : sqDist (p 6) (p 7) / base = s
+
+private def Residual11Distances.normalize
+    {p : Vertex → Plane} (D : Residual11Distances p) :
+    Residual11Normalized p := by
+  have hcmS := cm4_normalized_eq_zero (p 0) (p 1) (p 2) (p 4) D.hbase
+  rw [D.d01, D.d02, D.d04, D.d12, D.d14, D.d24] at hcmS
+  have eS : D.s ^ 2 - 4 * D.s + 1 = 0 := by
+    dsimp [cm4] at hcmS
+    nlinarith only [hcmS]
+  have hcm05a := cm4_normalized_eq_zero (p 0) (p 1) (p 2) (p 5) D.hbase
+  rw [D.d01, D.d02, D.d05, D.d12, D.d15, D.d25] at hcm05a
+  have e05a :
+      D.s ^ 2 - D.s * D.w05 - 2 * D.s + D.w05 ^ 2 - 2 * D.w05 + 1 = 0 := by
+    dsimp [cm4] at hcm05a
+    nlinarith only [hcm05a]
+  have hcm05b := cm4_normalized_eq_zero (p 0) (p 1) (p 4) (p 5) D.hbase
+  rw [D.d01, D.d04, D.d05, D.d14, D.d15, D.d45] at hcm05b
+  have e05b : D.s ^ 2 + D.s * D.w05 ^ 2 - 3 * D.s * D.w05 - 2 * D.s + 1 = 0 := by
+    dsimp [cm4] at hcm05b
+    nlinarith only [hcm05b]
+  have hcm13a := cm4_normalized_eq_zero (p 0) (p 1) (p 2) (p 3) D.hbase
+  rw [D.d01, D.d02, D.d03, D.d12, D.d13, D.d23] at hcm13a
+  have e13a :
+      D.s ^ 2 - D.s * D.w13 - 2 * D.s + D.w13 ^ 2 - 2 * D.w13 + 1 = 0 := by
+    dsimp [cm4] at hcm13a
+    nlinarith only [hcm13a]
+  have hcm13b := cm4_normalized_eq_zero (p 0) (p 1) (p 3) (p 6) D.hbase
+  rw [D.d01, D.d03, D.d06, D.d13, D.d16, D.d36] at hcm13b
+  have e13b : D.s ^ 2 + D.s * D.w13 ^ 2 - 3 * D.s * D.w13 - 2 * D.s + 1 = 0 := by
+    dsimp [cm4] at hcm13b
+    nlinarith only [hcm13b]
+  have hcm27a := cm4_normalized_eq_zero (p 0) (p 1) (p 2) (p 7) D.hbase
+  rw [D.d01, D.d02, D.d07, D.d12, D.d17, D.d27] at hcm27a
+  have e27a :
+      D.s ^ 2 - 2 * D.s * D.w27 - 2 * D.s + D.w27 ^ 2 - D.w27 + 1 = 0 := by
+    dsimp [cm4] at hcm27a
+    nlinarith only [hcm27a]
+  have hcm27b := cm4_normalized_eq_zero (p 0) (p 2) (p 4) (p 7) D.hbase
+  rw [D.d02, D.d04, D.d07, D.d24, D.d27, D.d47] at hcm27b
+  have e27b : D.s ^ 3 - 2 * D.s ^ 2 - 3 * D.s * D.w27 + D.s + D.w27 ^ 2 = 0 := by
+    dsimp [cm4] at hcm27b
+    nlinarith only [hcm27b]
+  have hcm46a := cm4_normalized_eq_zero (p 0) (p 3) (p 4) (p 6) D.hbase
+  rw [D.d03, D.d04, D.d06, D.d34, D.d36, D.d46] at hcm46a
+  have e46a :
+      D.s ^ 2 - 2 * D.s * D.w46 - 2 * D.s + D.w46 ^ 2 - D.w46 + 1 = 0 := by
+    dsimp [cm4] at hcm46a
+    nlinarith only [hcm46a]
+  have hcm46b := cm4_normalized_eq_zero (p 0) (p 2) (p 4) (p 6) D.hbase
+  rw [D.d02, D.d04, D.d06, D.d24, D.d26, D.d46] at hcm46b
+  have e46b : D.s ^ 3 - 2 * D.s ^ 2 - 3 * D.s * D.w46 + D.s + D.w46 ^ 2 = 0 := by
+    dsimp [cm4] at hcm46b
+    nlinarith only [hcm46b]
+  have w05_eq : D.w05 = 2 := by
+    have factor : (D.w05 - 1) * (D.w05 - 2) = 0 := by
+      nlinarith only [eS, e05b]
+    rcases mul_eq_zero.mp factor with h | h
+    · have hw : D.w05 = 1 := by linarith only [h]
+      rw [hw] at e05a
+      nlinarith only [eS, e05a]
+    · linarith only [h]
+  have w13_eq : D.w13 = 2 := by
+    have factor : (D.w13 - 1) * (D.w13 - 2) = 0 := by
+      nlinarith only [eS, e13b]
+    rcases mul_eq_zero.mp factor with h | h
+    · have hw : D.w13 = 1 := by linarith only [h]
+      rw [hw] at e13a
+      nlinarith only [eS, e13a]
+    · linarith only [h]
+  have es3 : D.s ^ 3 = 15 * D.s - 4 := by
+    nlinarith only [eS]
+  have w27_eq : D.w27 = 2 * D.s := by
+    have factor : (D.w27 - 1) * (D.w27 - 2 * D.s) = 0 := by
+      nlinarith only [eS, e27a]
+    rcases mul_eq_zero.mp factor with h | h
+    · have hw : D.w27 = 1 := by linarith only [h]
+      rw [hw] at e27b
+      nlinarith only [eS, e27b, es3]
+    · linarith only [h]
+  have w46_eq : D.w46 = 2 * D.s := by
+    have factor : (D.w46 - 1) * (D.w46 - 2 * D.s) = 0 := by
+      nlinarith only [eS, e46a]
+    rcases mul_eq_zero.mp factor with h | h
+    · have hw : D.w46 = 1 := by linarith only [h]
+      rw [hw] at e46b
+      nlinarith only [eS, e46b, es3]
+    · linarith only [h]
+  have hs_ne_two : D.s ≠ 2 := by
+    intro hs2
+    rw [hs2] at eS
+    norm_num at eS
+  exact {
+    base := D.base, s := D.s, hbase := D.hbase, hbase_pos := D.hbase_pos,
+    hs := D.hs, hs_ne_two, eS, d01 := D.d01, d02 := D.d02, d03 := D.d03,
+    d04 := D.d04, d05 := D.d05.trans w05_eq, d06 := D.d06, d07 := D.d07,
+    d12 := D.d12, d13 := D.d13.trans w13_eq, d15 := D.d15, d23 := D.d23,
+    d24 := D.d24, d25 := D.d25, d26 := D.d26, d27 := D.d27.trans w27_eq,
+    d35 := D.d35, d46 := D.d46.trans w46_eq, d47 := D.d47, d67 := D.d67
+  }
+
+private lemma scaled_of_div_eq
+    {p : Vertex → Plane} {base x : ℝ} {i j : Vertex}
+    (hbase : base ≠ 0) (h : sqDist (p i) (p j) / base = x) :
+    sqDist (p i) (p j) = x * base :=
+  (div_eq_iff hbase).mp h
+
+private lemma inner_scaled
+    {p : Vertex → Plane} {base : ℝ} (o x y : Vertex) (A B C : ℝ)
+    (hox : sqDist (p o) (p x) = A * base)
+    (hoy : sqDist (p o) (p y) = B * base)
+    (hxy : sqDist (p x) (p y) = C * base) :
+    ⟪p x - p o, p y - p o⟫_ℝ = (A + B - C) * base / 2 := by
+  rw [inner_sub_sub_eq, hox, hoy, hxy]
+  ring
+
+private lemma self_scaled
+    {p : Vertex → Plane} {base : ℝ} (o x : Vertex) (A : ℝ)
+    (hox : sqDist (p o) (p x) = A * base) :
+    ⟪p x - p o, p x - p o⟫_ℝ = A * base := by
+  have hxx : sqDist (p x) (p x) = 0 := by simp [sqDist]
+  have hinner := inner_scaled o x x A A 0 hox hox (by simpa using hxx)
+  nlinarith only [hinner]
+
+private lemma residual11_lt_contradiction
+    {p : Vertex → Plane} (hC : ConvexIndependent ℝ p)
+    (D : Residual11Normalized p) (hslt : D.s < 2) : False := by
+  let alpha : ℝ := (2 - D.s) / 4
+  let beta : ℝ := D.s / 4
+  have halpha : 0 ≤ alpha := by dsimp [alpha]; linarith
+  have hbeta : 0 ≤ beta := by
+    dsimp [beta]
+    exact div_nonneg (le_of_lt D.hs) (by norm_num)
+  have hab : 2 * alpha + 2 * beta = 1 := by
+    dsimp [alpha, beta]
+    ring
+  have q01 := scaled_of_div_eq D.hbase D.d01
+  have q02 := scaled_of_div_eq D.hbase D.d02
+  have q03 := scaled_of_div_eq D.hbase D.d03
+  have q05 := scaled_of_div_eq D.hbase D.d05
+  have q12 := scaled_of_div_eq D.hbase D.d12
+  have q13 := scaled_of_div_eq D.hbase D.d13
+  have q15 := scaled_of_div_eq D.hbase D.d15
+  have q23 := scaled_of_div_eq D.hbase D.d23
+  have q25 := scaled_of_div_eq D.hbase D.d25
+  have q35 := scaled_of_div_eq D.hbase D.d35
+  let u1 := p 1 - p 0
+  let u2 := p 2 - p 0
+  let u3 := p 3 - p 0
+  let u5 := p 5 - p 0
+  have i11 : ⟪u1, u1⟫_ℝ = D.base := by
+    simpa [u1] using self_scaled 0 1 1 q01
+  have i22 : ⟪u2, u2⟫_ℝ = D.base := by
+    simpa [u2] using self_scaled 0 2 1 q02
+  have i33 : ⟪u3, u3⟫_ℝ = D.base := by
+    simpa [u3] using self_scaled 0 3 1 q03
+  have i55 : ⟪u5, u5⟫_ℝ = 2 * D.base := by
+    simpa [u5] using self_scaled 0 5 2 q05
+  have i12 : ⟪u1, u2⟫_ℝ = D.base / 2 := by
+    simpa [u1, u2] using inner_scaled 0 1 2 1 1 1 q01 q02 q12
+  have i13 : ⟪u1, u3⟫_ℝ = 0 := by
+    have h := inner_scaled 0 1 3 1 1 2 q01 q03 q13
+    dsimp [u1, u3] at h ⊢
+    ring_nf at h ⊢
+    exact h
+  have i15 : ⟪u1, u5⟫_ℝ = D.base := by
+    simpa [u1, u5] using inner_scaled 0 1 5 1 2 1 q01 q05 q15
+  have i23 : ⟪u2, u3⟫_ℝ = (2 - D.s) * D.base / 2 := by
+    have h := inner_scaled 0 2 3 1 1 D.s q02 q03 q23
+    dsimp [u2, u3] at h ⊢
+    ring_nf at h ⊢
+    exact h
+  have i25 : ⟪u2, u5⟫_ℝ = (3 - D.s) * D.base / 2 := by
+    have h := inner_scaled 0 2 5 1 2 D.s q02 q05 q25
+    dsimp [u2, u5] at h ⊢
+    ring_nf at h ⊢
+    exact h
+  have i35 : ⟪u3, u5⟫_ℝ = D.base := by
+    simpa [u3, u5] using inner_scaled 0 3 5 1 2 1 q03 q05 q35
+  have i21 : ⟪u2, u1⟫_ℝ = D.base / 2 := by rw [real_inner_comm]; exact i12
+  have i31 : ⟪u3, u1⟫_ℝ = 0 := by rw [real_inner_comm]; exact i13
+  have i51 : ⟪u5, u1⟫_ℝ = D.base := by rw [real_inner_comm]; exact i15
+  have i32 : ⟪u3, u2⟫_ℝ = (2 - D.s) * D.base / 2 := by
+    rw [real_inner_comm]
+    exact i23
+  have i52 : ⟪u5, u2⟫_ℝ = (3 - D.s) * D.base / 2 := by
+    rw [real_inner_comm]
+    exact i25
+  have i53 : ⟪u5, u3⟫_ℝ = D.base := by rw [real_inner_comm]; exact i35
+  let z := u2 - (alpha • u5 + alpha • u3 + beta • u1)
+  have hzinner : ⟪z, z⟫_ℝ = 0 := by
+    dsimp [z]
+    simp only [inner_sub_left, inner_sub_right, inner_add_left, inner_add_right,
+      real_inner_smul_left, real_inner_smul_right]
+    rw [i11, i22, i33, i55, i12, i13, i15, i23, i25, i35,
+      i21, i31, i51, i32, i52, i53]
+    dsimp [alpha, beta]
+    linear_combination (norm := ring) (-D.base / 4) * D.eS
+  have hz : z = 0 := inner_self_eq_zero.mp hzinner
+  have hu : u2 = alpha • u5 + alpha • u3 + beta • u1 := sub_eq_zero.mp hz
+  have affine : p 2 =
+      alpha • p 5 + alpha • p 3 + beta • p 0 + beta • p 1 := by
+    dsimp [u1, u2, u3, u5] at hu
+    linear_combination (norm := module) hu - hab • p 0
+  have hmem : p 2 ∈ convexHull ℝ (p '' ({0, 1, 3, 5} : Set Vertex)) := by
+    refine mem_convexHull_of_exists_fintype
+      ![alpha, alpha, beta, beta] ![p 5, p 3, p 0, p 1] ?_ ?_ ?_ ?_
+    · intro i
+      fin_cases i <;> assumption
+    · simp only [Fin.sum_univ_four, Matrix.cons_val_zero, Matrix.cons_val_one,
+        Matrix.cons_val_two, Matrix.cons_val_three, Matrix.tail_cons, Matrix.head_cons]
+      nlinarith only [hab]
+    · intro i
+      fin_cases i <;> simp
+    · simp [Fin.sum_univ_four, affine, add_assoc]
+  have htwo := hC ({0, 1, 3, 5} : Set Vertex) 2 hmem
+  simp at htwo
+
+private lemma residual11_gt_contradiction
+    {p : Vertex → Plane} (hC : ConvexIndependent ℝ p)
+    (D : Residual11Normalized p) (hsgt : D.s > 2) : False := by
+  have hproduct : D.s * (4 - D.s) = 1 := by nlinarith only [D.eS]
+  have hproduct_pos : 0 < D.s * (4 - D.s) := by rw [hproduct]; norm_num
+  have hslt4 : D.s < 4 := by
+    rcases (mul_pos_iff.mp hproduct_pos) with h | h
+    · linarith only [h.2]
+    · linarith only [D.hs, h.1]
+  let alpha : ℝ := (D.s - 2) / 4
+  let beta : ℝ := (4 - D.s) / 4
+  have halpha : 0 ≤ alpha := by dsimp [alpha]; linarith
+  have hbeta : 0 ≤ beta := by dsimp [beta]; linarith
+  have hab : 2 * alpha + 2 * beta = 1 := by
+    dsimp [alpha, beta]
+    ring
+  have q20 : sqDist (p 2) (p 0) = D.base := by
+    have h := scaled_of_div_eq D.hbase D.d02
+    simpa [sqDist, dist_comm] using h
+  have q24 := scaled_of_div_eq D.hbase D.d24
+  have q26 := scaled_of_div_eq D.hbase D.d26
+  have q27 := scaled_of_div_eq D.hbase D.d27
+  have q04 := scaled_of_div_eq D.hbase D.d04
+  have q06 := scaled_of_div_eq D.hbase D.d06
+  have q07 := scaled_of_div_eq D.hbase D.d07
+  have q46 := scaled_of_div_eq D.hbase D.d46
+  have q47 := scaled_of_div_eq D.hbase D.d47
+  have q67 := scaled_of_div_eq D.hbase D.d67
+  let v0 := p 0 - p 2
+  let v4 := p 4 - p 2
+  let v6 := p 6 - p 2
+  let v7 := p 7 - p 2
+  have i00 : ⟪v0, v0⟫_ℝ = D.base := by
+    simpa [v0] using self_scaled 2 0 1 (by simpa using q20)
+  have i44 : ⟪v4, v4⟫_ℝ = D.s * D.base := by
+    simpa [v4] using self_scaled 2 4 D.s q24
+  have i66 : ⟪v6, v6⟫_ℝ = D.s * D.base := by
+    simpa [v6] using self_scaled 2 6 D.s q26
+  have i77 : ⟪v7, v7⟫_ℝ = 2 * D.s * D.base := by
+    have h := self_scaled 2 7 (2 * D.s) q27
+    dsimp [v7] at h ⊢
+    ring_nf at h ⊢
+    exact h
+  have i04 : ⟪v0, v4⟫_ℝ = D.s * D.base / 2 := by
+    have h := inner_scaled 2 0 4 1 D.s 1 (by simpa using q20) q24 (by
+      simpa [sqDist, dist_comm] using q04)
+    dsimp [v0, v4] at h ⊢
+    ring_nf at h ⊢
+    exact h
+  have i06 : ⟪v0, v6⟫_ℝ = D.base / 2 := by
+    have h := inner_scaled 2 0 6 1 D.s D.s (by simpa using q20) q26 (by
+      simpa [sqDist, dist_comm] using q06)
+    dsimp [v0, v6] at h ⊢
+    ring_nf at h ⊢
+    exact h
+  have i07 : ⟪v0, v7⟫_ℝ = (1 + D.s) * D.base / 2 := by
+    have h := inner_scaled 2 0 7 1 (2 * D.s) D.s (by simpa using q20) q27 (by
+      simpa [sqDist, dist_comm] using q07)
+    dsimp [v0, v7] at h ⊢
+    ring_nf at h ⊢
+    exact h
+  have i46 : ⟪v4, v6⟫_ℝ = 0 := by
+    have h := inner_scaled 2 4 6 D.s D.s (2 * D.s) q24 q26 q46
+    dsimp [v4, v6] at h ⊢
+    ring_nf at h ⊢
+    exact h
+  have i47 : ⟪v4, v7⟫_ℝ = D.s * D.base := by
+    have h := inner_scaled 2 4 7 D.s (2 * D.s) D.s q24 q27 q47
+    dsimp [v4, v7] at h ⊢
+    ring_nf at h ⊢
+    exact h
+  have i67 : ⟪v6, v7⟫_ℝ = D.s * D.base := by
+    have h := inner_scaled 2 6 7 D.s (2 * D.s) D.s q26 q27 q67
+    dsimp [v6, v7] at h ⊢
+    ring_nf at h ⊢
+    exact h
+  have i40 : ⟪v4, v0⟫_ℝ = D.s * D.base / 2 := by rw [real_inner_comm]; exact i04
+  have i60 : ⟪v6, v0⟫_ℝ = D.base / 2 := by rw [real_inner_comm]; exact i06
+  have i70 : ⟪v7, v0⟫_ℝ = (1 + D.s) * D.base / 2 := by
+    rw [real_inner_comm]
+    exact i07
+  have i64 : ⟪v6, v4⟫_ℝ = 0 := by rw [real_inner_comm]; exact i46
+  have i74 : ⟪v7, v4⟫_ℝ = D.s * D.base := by rw [real_inner_comm]; exact i47
+  have i76 : ⟪v7, v6⟫_ℝ = D.s * D.base := by rw [real_inner_comm]; exact i67
+  let z := v0 - (beta • v6 + beta • v7 + alpha • v4)
+  have hzinner : ⟪z, z⟫_ℝ = 0 := by
+    dsimp [z]
+    simp only [inner_sub_left, inner_sub_right, inner_add_left, inner_add_right,
+      real_inner_smul_left, real_inner_smul_right]
+    rw [i00, i44, i66, i77, i04, i06, i07, i46, i47, i67,
+      i40, i60, i70, i64, i74, i76]
+    dsimp [alpha, beta]
+    linear_combination (norm := ring) (D.base * (D.s - 4) / 4) * D.eS
+  have hz : z = 0 := inner_self_eq_zero.mp hzinner
+  have hu : v0 = beta • v6 + beta • v7 + alpha • v4 := sub_eq_zero.mp hz
+  have affine : p 0 =
+      alpha • p 2 + beta • p 6 + beta • p 7 + alpha • p 4 := by
+    dsimp [v0, v4, v6, v7] at hu
+    linear_combination (norm := module) hu - hab • p 2
+  have hmem : p 0 ∈ convexHull ℝ (p '' ({2, 4, 6, 7} : Set Vertex)) := by
+    refine mem_convexHull_of_exists_fintype
+      ![alpha, beta, beta, alpha] ![p 2, p 6, p 7, p 4] ?_ ?_ ?_ ?_
+    · intro i
+      fin_cases i <;> assumption
+    · simp only [Fin.sum_univ_four, Matrix.cons_val_zero, Matrix.cons_val_one,
+        Matrix.cons_val_two, Matrix.cons_val_three, Matrix.tail_cons, Matrix.head_cons]
+      nlinarith only [hab]
+    · intro i
+      fin_cases i <;> simp
+    · simp [Fin.sum_univ_four, affine, add_assoc]
+  have hzero := hC ({2, 4, 6, 7} : Set Vertex) 0 hmem
+  simp at hzero
+
+/-- The unique realizable residual class cannot occur in convex position. -/
+theorem residualRepresentative11_not_convex_realises
+    {p : Vertex → Plane} (hC : ConvexIndependent ℝ p) :
+    ¬ Realises p residualRepresentative11 := by
+  intro hRealises
+  let D := (residual11_distances hC hRealises).normalize
+  rcases lt_or_gt_of_ne D.hs_ne_two with hslt | hsgt
+  · exact residual11_lt_contradiction hC D hslt
+  · exact residual11_gt_contradiction hC D hsgt
+
+end Erdos97Octagon
diff --git a/LeanPool/Erdos97ConvexOctagon/ResidualAlgebra12.lean b/LeanPool/Erdos97ConvexOctagon/ResidualAlgebra12.lean
new file mode 100644
index 00000000..7bc31896
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/ResidualAlgebra12.lean
@@ -0,0 +1,141 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.CayleyMenger
+import LeanPool.Erdos97ConvexOctagon.ResidualRepresentatives
+
+/-! # Erdős 97 convex-octagon formalization: Residual Algebra12 -/
+
+namespace Erdos97Octagon
+
+/-- Residual class 12 has no injective planar realisation. -/
+theorem residualRepresentative12_not_realises
+    {p : Vertex → Plane} (hp : Function.Injective p) :
+    ¬ Realises p residualRepresentative12 := by
+  intro hRealises
+  obtain ⟨radius, hpos, hdist⟩ :=
+    exists_positive_radii hp residualRepresentative12 hRealises
+  have r01 : radius 0 = radius 1 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative12])
+  have r25 : radius 2 = radius 5 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative12])
+  have r37 : radius 3 = radius 7 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative12])
+  have r46 : radius 4 = radius 6 :=
+    radius_eq_of_mutual hdist (by
+      simp [OctagonIncidence.Mutual, residualRepresentative12])
+  have radius0 : radius 0 = radius 0 := rfl
+  have radius1 : radius 1 = radius 0 := (r01).symm
+  have radius2 : radius 2 = radius 2 := rfl
+  have radius5 : radius 5 = radius 2 := (r25).symm
+  have radius3 : radius 3 = radius 3 := rfl
+  have radius7 : radius 7 = radius 3 := (r37).symm
+  have radius4 : radius 4 = radius 4 := rfl
+  have radius6 : radius 6 = radius 4 := (r46).symm
+  let base : ℝ := radius 0 ^ 2
+  have hbase : base ≠ 0 := by
+    dsimp [base]
+    exact pow_ne_zero 2 (ne_of_gt (hpos 0))
+  let s1 : ℝ := radius 2 ^ 2 / base
+  let s2 : ℝ := radius 3 ^ 2 / base
+  let s3 : ℝ := radius 4 ^ 2 / base
+  have d01 : sqDist (p 0) (p 1) / base = 1 := by
+    rw [sqDist, hdist 0 1 (by decide), radius0]
+    exact div_self hbase
+  have d02 : sqDist (p 0) (p 2) / base = 1 := by
+    rw [sqDist, hdist 0 2 (by decide), radius0]
+    exact div_self hbase
+  have d03 : sqDist (p 0) (p 3) / base = 1 := by
+    rw [sqDist, hdist 0 3 (by decide), radius0]
+    exact div_self hbase
+  have d04 : sqDist (p 0) (p 4) / base = 1 := by
+    rw [sqDist, hdist 0 4 (by decide), radius0]
+    exact div_self hbase
+  have d06 : sqDist (p 0) (p 6) / base = s3 := by
+    rw [sqDist, dist_comm, hdist 6 0 (by decide), radius6]
+  have d07 : sqDist (p 0) (p 7) / base = s2 := by
+    rw [sqDist, dist_comm, hdist 7 0 (by decide), radius7]
+  have d13 : sqDist (p 1) (p 3) / base = s2 := by
+    rw [sqDist, dist_comm, hdist 3 1 (by decide), radius3]
+  have d14 : sqDist (p 1) (p 4) / base = s3 := by
+    rw [sqDist, dist_comm, hdist 4 1 (by decide), radius4]
+  have d16 : sqDist (p 1) (p 6) / base = 1 := by
+    rw [sqDist, hdist 1 6 (by decide), radius1]
+    exact div_self hbase
+  have d24 : sqDist (p 2) (p 4) / base = s3 := by
+    rw [sqDist, dist_comm, hdist 4 2 (by decide), radius4]
+  have d27 : sqDist (p 2) (p 7) / base = s2 := by
+    rw [sqDist, dist_comm, hdist 7 2 (by decide), radius7]
+  have d34 : sqDist (p 3) (p 4) / base = s2 := by
+    rw [sqDist, hdist 3 4 (by decide), radius3]
+  have d36 : sqDist (p 3) (p 6) / base = s3 := by
+    rw [sqDist, dist_comm, hdist 6 3 (by decide), radius6]
+  have d37 : sqDist (p 3) (p 7) / base = s2 := by
+    rw [sqDist, hdist 3 7 (by decide), radius3]
+  have d46 : sqDist (p 4) (p 6) / base = s3 := by
+    rw [sqDist, hdist 4 6 (by decide), radius4]
+  have d47 : sqDist (p 4) (p 7) / base = s3 := by
+    rw [sqDist, hdist 4 7 (by decide), radius4]
+  have d67 : sqDist (p 6) (p 7) / base = s2 := by
+    rw [sqDist, dist_comm, hdist 7 6 (by decide), radius7]
+  have hcm0 := cm4_normalized_eq_zero
+    (p 0) (p 2) (p 4) (p 7) hbase
+  rw [d02, d04, d07, d24, d27, d47] at hcm0
+  have e0 : -2*s2  ^  2 - 2*s2*s3  ^  2 + 10*s2*s3 - 2*s3 = 0 := by
+    dsimp [cm4] at hcm0
+    nlinarith only [hcm0]
+  have hcm1 := cm4_normalized_eq_zero
+    (p 0) (p 4) (p 6) (p 7) hbase
+  rw [d04, d06, d07, d46, d47, d67] at hcm1
+  have e1 : -2*s2  ^  2*s3 + 4*s2*s3  ^  2 + 6*s2*s3 - 2*s2 - 2*s3  ^  3 = 0 := by
+    dsimp [cm4] at hcm1
+    nlinarith only [hcm1]
+  have hcm2 := cm4_normalized_eq_zero
+    (p 0) (p 1) (p 3) (p 6) hbase
+  rw [d01, d03, d06, d13, d16, d36] at hcm2
+  have e2 : -2*s2  ^  2*s3 + 6*s2*s3 - 2*s3  ^  2 + 4*s3 - 2 = 0 := by
+    dsimp [cm4] at hcm2
+    nlinarith only [hcm2]
+  have hcm3 := cm4_normalized_eq_zero
+    (p 0) (p 3) (p 4) (p 6) hbase
+  rw [d03, d04, d06, d34, d36, d46] at hcm3
+  have e3 : -2*s2  ^  2*s3 + 8*s2*s3 - 2*s2 = 0 := by
+    dsimp [cm4] at hcm3
+    nlinarith only [hcm3]
+  have hcm4 := cm4_normalized_eq_zero
+    (p 0) (p 1) (p 3) (p 4) hbase
+  rw [d01, d03, d04, d13, d14, d34] at hcm4
+  have e4 : -2*s2  ^  2*s3 + 8*s2*s3 - 2*s3  ^  2 = 0 := by
+    dsimp [cm4] at hcm4
+    nlinarith only [hcm4]
+  have hcm5 := cm4_normalized_eq_zero
+    (p 0) (p 1) (p 4) (p 6) hbase
+  rw [d01, d04, d06, d14, d16, d46] at hcm5
+  have e5 : -2*s3  ^  3 + 4*s3  ^  2 + 4*s3 - 2 = 0 := by
+    dsimp [cm4] at hcm5
+    nlinarith only [hcm5]
+  have hcm6 := cm4_normalized_eq_zero
+    (p 0) (p 3) (p 6) (p 7) hbase
+  rw [d03, d06, d07, d36, d37, d67] at hcm6
+  have e6 : 8*s2*s3 - 2*s2 - 2*s3  ^  2 = 0 := by
+    dsimp [cm4] at hcm6
+    nlinarith only [hcm6]
+  have certificate :
+      (-1 : ℝ) * (-2*s2  ^  2 - 2*s2*s3  ^  2 + 10*s2*s3 - 2*s3) +
+        (7/6 : ℝ) * (-2*s2  ^  2*s3 + 4*s2*s3  ^  2 + 6*s2*s3 - 2*s2 - 2*s3  ^  3) +
+        (1/12 : ℝ) * (-2*s2  ^  2*s3 + 6*s2*s3 - 2*s3  ^  2 + 4*s3 - 2) +
+        (17/12 : ℝ) * (-2*s2  ^  2*s3 + 8*s2*s3 - 2*s2) +
+        (4/3 : ℝ) * (-2*s2  ^  2*s3 + 8*s2*s3 - 2*s3  ^  2) +
+        (-7/12 : ℝ) * (-2*s3  ^  3 + 4*s3  ^  2 + 4*s3 - 2) +
+        (s2-7/12*s3-31/12 : ℝ) * (8*s2*s3 - 2*s2 - 2*s3  ^  2) = 1 := by
+    ring
+  rw [e0, e1, e2, e3, e4, e5, e6] at certificate
+  norm_num at certificate
+
+end Erdos97Octagon
diff --git a/LeanPool/Erdos97ConvexOctagon/ResidualObstructions.lean b/LeanPool/Erdos97ConvexOctagon/ResidualObstructions.lean
new file mode 100644
index 00000000..8f2ec5df
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/ResidualObstructions.lean
@@ -0,0 +1,46 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.ResidualAlgebra00
+import LeanPool.Erdos97ConvexOctagon.ResidualAlgebra01
+import LeanPool.Erdos97ConvexOctagon.ResidualAlgebra02
+import LeanPool.Erdos97ConvexOctagon.ResidualAlgebra03
+import LeanPool.Erdos97ConvexOctagon.ResidualAlgebra04
+import LeanPool.Erdos97ConvexOctagon.ResidualAlgebra05
+import LeanPool.Erdos97ConvexOctagon.ResidualAlgebra06
+import LeanPool.Erdos97ConvexOctagon.ResidualAlgebra07
+import LeanPool.Erdos97ConvexOctagon.ResidualAlgebra08
+import LeanPool.Erdos97ConvexOctagon.ResidualAlgebra09
+import LeanPool.Erdos97ConvexOctagon.ResidualAlgebra10
+import LeanPool.Erdos97ConvexOctagon.ResidualAlgebra11
+import LeanPool.Erdos97ConvexOctagon.ResidualAlgebra12
+
+/-! # Erdős 97 convex-octagon formalization: Residual Obstructions -/
+
+namespace Erdos97Octagon
+
+/-- None of the thirteen explicit candidate systems has a convex-independent
+realisation. This statement does not assert that the family is exhaustive. -/
+theorem residualRepresentative_not_convex_realises
+    (classIndex : Fin 13) {p : Vertex → Plane}
+    (hC : ConvexIndependent ℝ p) :
+    ¬ Realises p (residualRepresentative classIndex) := by
+  fin_cases classIndex
+  · exact residualRepresentative00_not_realises hC.injective
+  · exact residualRepresentative01_not_realises hC.injective
+  · exact residualRepresentative02_not_realises hC.injective
+  · exact residualRepresentative03_not_realises hC.injective
+  · exact residualRepresentative04_not_realises hC.injective
+  · exact residualRepresentative05_not_realises hC.injective
+  · exact residualRepresentative06_not_realises hC.injective
+  · exact residualRepresentative07_not_realises hC.injective
+  · exact residualRepresentative08_not_realises hC.injective
+  · exact residualRepresentative09_not_realises hC.injective
+  · exact residualRepresentative10_not_realises hC.injective
+  · exact residualRepresentative11_not_convex_realises hC
+  · exact residualRepresentative12_not_realises hC.injective
+
+end Erdos97Octagon
diff --git a/LeanPool/Erdos97ConvexOctagon/ResidualRepresentatives.lean b/LeanPool/Erdos97ConvexOctagon/ResidualRepresentatives.lean
new file mode 100644
index 00000000..39f9a367
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/ResidualRepresentatives.lean
@@ -0,0 +1,144 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.Radius
+
+/-! # Thirteen explicit candidate incidence representatives
+
+The word “residual” is a historical label from exploratory computation. This
+module defines the systems exactly but makes no claim that they exhaust all
+normalized, balanced, pair-sparse incidence systems.
+-/
+
+namespace Erdos97Octagon
+
+/-- The exact residual incidence representative of class 0. -/
+def residualRepresentative00 : OctagonIncidence where
+  targets := ![
+    {1, 2, 3, 4}, {0, 2, 3, 5}, {0, 4, 5, 6}, {2, 4, 5, 7},
+    {3, 5, 6, 7}, {1, 2, 6, 7}, {0, 1, 4, 7}, {0, 1, 3, 6}
+  ]
+  card_targets v := by fin_cases v <;> decide
+  centre_not_mem v := by fin_cases v <;> decide
+
+/-- The exact residual incidence representative of class 1. -/
+def residualRepresentative01 : OctagonIncidence where
+  targets := ![
+    {1, 2, 3, 4}, {0, 2, 3, 5}, {0, 4, 5, 6}, {2, 4, 6, 7},
+    {1, 3, 5, 7}, {0, 3, 6, 7}, {0, 1, 4, 7}, {1, 2, 5, 6}
+  ]
+  card_targets v := by fin_cases v <;> decide
+  centre_not_mem v := by fin_cases v <;> decide
+
+/-- The exact residual incidence representative of class 2. -/
+def residualRepresentative02 : OctagonIncidence where
+  targets := ![
+    {1, 2, 3, 4}, {0, 2, 3, 5}, {0, 5, 6, 7}, {2, 4, 6, 7},
+    {1, 2, 5, 6}, {0, 3, 4, 7}, {1, 3, 5, 7}, {0, 1, 4, 6}
+  ]
+  card_targets v := by fin_cases v <;> decide
+  centre_not_mem v := by fin_cases v <;> decide
+
+/-- The exact residual incidence representative of class 3. -/
+def residualRepresentative03 : OctagonIncidence where
+  targets := ![
+    {1, 2, 3, 4}, {0, 2, 3, 5}, {0, 1, 4, 6}, {0, 4, 5, 7},
+    {0, 3, 6, 7}, {2, 4, 6, 7}, {1, 3, 5, 7}, {1, 2, 5, 6}
+  ]
+  card_targets v := by fin_cases v <;> decide
+  centre_not_mem v := by fin_cases v <;> decide
+
+/-- The exact residual incidence representative of class 4. -/
+def residualRepresentative04 : OctagonIncidence where
+  targets := ![
+    {1, 2, 3, 4}, {0, 2, 3, 5}, {0, 1, 4, 6}, {2, 4, 6, 7},
+    {1, 3, 5, 7}, {0, 3, 6, 7}, {0, 4, 5, 7}, {1, 2, 5, 6}
+  ]
+  card_targets v := by fin_cases v <;> decide
+  centre_not_mem v := by fin_cases v <;> decide
+
+/-- The exact residual incidence representative of class 5. -/
+def residualRepresentative05 : OctagonIncidence where
+  targets := ![
+    {1, 2, 3, 4}, {0, 2, 5, 6}, {3, 4, 5, 7}, {1, 2, 6, 7},
+    {1, 3, 5, 6}, {0, 3, 6, 7}, {0, 2, 4, 7}, {0, 1, 4, 5}
+  ]
+  card_targets v := by fin_cases v <;> decide
+  centre_not_mem v := by fin_cases v <;> decide
+
+/-- The exact residual incidence representative of class 6. -/
+def residualRepresentative06 : OctagonIncidence where
+  targets := ![
+    {1, 2, 3, 4}, {0, 2, 3, 5}, {0, 1, 4, 6}, {0, 1, 5, 7},
+    {1, 3, 6, 7}, {0, 2, 6, 7}, {3, 4, 5, 7}, {2, 4, 5, 6}
+  ]
+  card_targets v := by fin_cases v <;> decide
+  centre_not_mem v := by fin_cases v <;> decide
+
+/-- The exact residual incidence representative of class 7. -/
+def residualRepresentative07 : OctagonIncidence where
+  targets := ![
+    {1, 2, 3, 4}, {0, 2, 3, 5}, {3, 4, 6, 7}, {2, 5, 6, 7},
+    {1, 3, 5, 6}, {0, 2, 4, 7}, {0, 1, 5, 7}, {0, 1, 4, 6}
+  ]
+  card_targets v := by fin_cases v <;> decide
+  centre_not_mem v := by fin_cases v <;> decide
+
+/-- The exact residual incidence representative of class 8. -/
+def residualRepresentative08 : OctagonIncidence where
+  targets := ![
+    {1, 2, 3, 4}, {0, 2, 3, 5}, {3, 4, 5, 6}, {2, 4, 5, 7},
+    {0, 5, 6, 7}, {1, 4, 6, 7}, {0, 1, 3, 7}, {0, 1, 2, 6}
+  ]
+  card_targets v := by fin_cases v <;> decide
+  centre_not_mem v := by fin_cases v <;> decide
+
+/-- The exact residual incidence representative of class 9. -/
+def residualRepresentative09 : OctagonIncidence where
+  targets := ![
+    {1, 2, 3, 4}, {0, 2, 3, 5}, {3, 4, 5, 6}, {2, 4, 5, 7},
+    {0, 5, 6, 7}, {1, 4, 6, 7}, {0, 1, 2, 7}, {0, 1, 3, 6}
+  ]
+  card_targets v := by fin_cases v <;> decide
+  centre_not_mem v := by fin_cases v <;> decide
+
+/-- The exact residual incidence representative of class 10. -/
+def residualRepresentative10 : OctagonIncidence where
+  targets := ![
+    {1, 2, 3, 4}, {0, 2, 3, 5}, {3, 4, 5, 6}, {2, 4, 5, 7},
+    {1, 5, 6, 7}, {0, 4, 6, 7}, {0, 1, 3, 7}, {0, 1, 2, 6}
+  ]
+  card_targets v := by fin_cases v <;> decide
+  centre_not_mem v := by fin_cases v <;> decide
+
+/-- The exact residual incidence representative of class 11. -/
+def residualRepresentative11 : OctagonIncidence where
+  targets := ![
+    {1, 2, 3, 4}, {0, 2, 5, 6}, {3, 4, 5, 6}, {0, 4, 5, 7},
+    {1, 2, 5, 7}, {1, 3, 6, 7}, {0, 2, 3, 7}, {0, 1, 4, 6}
+  ]
+  card_targets v := by fin_cases v <;> decide
+  centre_not_mem v := by fin_cases v <;> decide
+
+/-- The exact residual incidence representative of class 12. -/
+def residualRepresentative12 : OctagonIncidence where
+  targets := ![
+    {1, 2, 3, 4}, {0, 5, 6, 7}, {1, 3, 5, 6}, {1, 4, 5, 7},
+    {1, 2, 6, 7}, {0, 2, 4, 7}, {0, 3, 4, 5}, {0, 2, 3, 6}
+  ]
+  card_targets v := by fin_cases v <;> decide
+  centre_not_mem v := by fin_cases v <;> decide
+
+/-- The thirteen residual representatives as one finite family. -/
+def residualRepresentative : Fin 13 → OctagonIncidence := ![
+  residualRepresentative00, residualRepresentative01, residualRepresentative02,
+  residualRepresentative03, residualRepresentative04, residualRepresentative05,
+  residualRepresentative06, residualRepresentative07, residualRepresentative08,
+  residualRepresentative09, residualRepresentative10, residualRepresentative11,
+  residualRepresentative12
+]
+
+end Erdos97Octagon
diff --git a/LeanPool/Erdos97ConvexOctagon/RhombusFan.lean b/LeanPool/Erdos97ConvexOctagon/RhombusFan.lean
new file mode 100644
index 00000000..b6b8de5a
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/RhombusFan.lean
@@ -0,0 +1,120 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.Gram
+
+/-! # Erdős 97 convex-octagon formalization: Rhombus Fan -/
+
+namespace Erdos97Octagon
+
+open scoped InnerProductSpace
+
+/-- A same-length rhombus fan cannot have a common point on the two listed bisectors. -/
+theorem no_rhombus_fan
+    {a b c d x : Plane} {R : ℝ} (hR : 0 < R) (hcd : c ≠ d)
+    (hab : dist a b = R) (hac : dist a c = R) (had : dist a d = R)
+    (hbc : dist b c = R) (hbd : dist b d = R)
+    (hx_ac : dist x a = dist x c) (hx_db : dist x d = dist x b) :
+    False := by
+  set u : Plane := b - a with hu
+  set v : Plane := c - a with hv
+  set w : Plane := d - a with hw
+  set y : Plane := x - a with hy
+  set s : ℝ := R ^ 2 with hs
+  have hs0 : 0 < s := by positivity
+  have norm_sq : ∀ {z : Plane}, dist a z = R → ⟪z - a, z - a⟫_ℝ = s := by
+    intro z hz
+    rw [real_inner_self_eq_norm_sq, ← dist_eq_norm, dist_comm, hz, hs]
+  have nu : ⟪u, u⟫_ℝ = s := by simpa [u] using norm_sq hab
+  have nv : ⟪v, v⟫_ℝ = s := by simpa [v] using norm_sq hac
+  have nw : ⟪w, w⟫_ℝ = s := by simpa [w] using norm_sq had
+  have inner_half : ∀ {z t : Plane}, dist a z = R → dist a t = R →
+      dist z t = R → ⟪z - a, t - a⟫_ℝ = s / 2 := by
+    intro z t haz hat hzt
+    have hsub : (z - a) - (t - a) = z - t := by abel
+    have hzt_norm : ‖(z - a) - (t - a)‖ = R := by
+      rw [hsub, ← dist_eq_norm, hzt]
+    have hpolar := norm_sub_sq_real (z - a) (t - a)
+    have hnz : ‖z - a‖ ^ 2 = s := by
+      rw [← real_inner_self_eq_norm_sq]
+      exact norm_sq haz
+    have hnt : ‖t - a‖ ^ 2 = s := by
+      rw [← real_inner_self_eq_norm_sq]
+      exact norm_sq hat
+    rw [hzt_norm, hnz, hnt] at hpolar
+    have hR2 : R ^ 2 = s := hs.symm
+    nlinarith only [hpolar, hR2]
+  have iuv : ⟪u, v⟫_ℝ = s / 2 := by simpa [u, v] using inner_half hab hac hbc
+  have iuw : ⟪u, w⟫_ℝ = s / 2 := by simpa [u, w] using inner_half hab had hbd
+  have ivu : ⟪v, u⟫_ℝ = s / 2 := by rw [real_inner_comm]; exact iuv
+  have iwu : ⟪w, u⟫_ℝ = s / 2 := by rw [real_inner_comm]; exact iuw
+  set t : ℝ := ⟪v, w⟫_ℝ with ht
+  have iwv : ⟪w, v⟫_ℝ = t := by rw [ht, real_inner_comm]
+  have hG := gram_det_eq_zero ![u, v, w]
+  rw [gram3_expand] at hG
+  simp only [nu, nv, nw, iuv, ivu, iuw, iwu, ← ht, iwv] at hG
+  have hfactor_mul : s * ((t - s) * (2 * t + s)) = 0 := by
+    nlinarith only [hG]
+  have hfactor : (t - s) * (2 * t + s) = 0 :=
+    (mul_eq_zero.mp hfactor_mul).resolve_left (ne_of_gt hs0)
+  have ht_ne_s : t ≠ s := by
+    intro hts
+    have hvn : ‖v‖ ^ 2 = s := by simpa only [real_inner_self_eq_norm_sq] using nv
+    have hwn : ‖w‖ ^ 2 = s := by simpa only [real_inner_self_eq_norm_sq] using nw
+    have hpolar := norm_sub_sq_real v w
+    have hvw_norm : ‖v - w‖ = dist c d := by
+      rw [hv, hw]
+      convert (dist_eq_norm c d).symm using 1
+      abel_nf
+    rw [hvw_norm, hvn, hwn, ← ht, hts] at hpolar
+    have hdist_pos : 0 < dist c d := dist_pos.mpr hcd
+    have hdist_sq_pos : 0 < (dist c d) ^ 2 := by positivity
+    nlinarith only [hpolar, hdist_sq_pos]
+  have ht_opp : t = -(s / 2) := by
+    have hsecond :=
+      (mul_eq_zero.mp hfactor).resolve_left (sub_ne_zero.mpr ht_ne_s)
+    linarith only [hsecond]
+  have hz_inner : ⟪w - u + v, w - u + v⟫_ℝ = 0 := by
+    simp only [inner_add_left, inner_add_right, inner_sub_left, inner_sub_right]
+    rw [nu, nv, nw, iuv, ivu, iuw, iwu, ← ht, iwv, ht_opp]
+    ring
+  have hz : w - u + v = 0 := inner_self_eq_zero.mp hz_inner
+  have hx_ac_norm : ‖y‖ = ‖y - v‖ := by
+    rw [hy, hv]
+    rw [dist_eq_norm, dist_eq_norm] at hx_ac
+    convert hx_ac using 1
+    abel_nf
+  have hfan_ac := norm_sub_sq_real y v
+  have hynv : ‖v‖ ^ 2 = s := by simpa only [real_inner_self_eq_norm_sq] using nv
+  rw [← hx_ac_norm, hynv] at hfan_ac
+  have iyv : ⟪y, v⟫_ℝ = s / 2 := by nlinarith only [hfan_ac]
+  have hx_db_norm : ‖y - w‖ = ‖y - u‖ := by
+    rw [hy, hw, hu]
+    rw [dist_eq_norm, dist_eq_norm] at hx_db
+    convert hx_db using 1 <;> abel_nf
+  have hfan_d := norm_sub_sq_real y w
+  have hfan_b := norm_sub_sq_real y u
+  have hwn : ‖w‖ ^ 2 = s := by simpa only [real_inner_self_eq_norm_sq] using nw
+  have hun : ‖u‖ ^ 2 = s := by simpa only [real_inner_self_eq_norm_sq] using nu
+  rw [hx_db_norm, hwn] at hfan_d
+  rw [hun] at hfan_b
+  have iywu : ⟪y, w⟫_ℝ = ⟪y, u⟫_ℝ := by
+    nlinarith only [hfan_d, hfan_b]
+  have hinner_zero : ⟪y, w - u + v⟫_ℝ = 0 := by rw [hz, inner_zero_right]
+  simp only [inner_add_right, inner_sub_right] at hinner_zero
+  nlinarith only [hinner_zero, iywu, iyv, hs0]
+
+/-- The endpoint-swapped form of `no_rhombus_fan`. -/
+theorem no_rhombus_fan_swapped
+    {a b c d x : Plane} {R : ℝ} (hR : 0 < R) (hcd : c ≠ d)
+    (hab : dist a b = R) (hac : dist a c = R) (had : dist a d = R)
+    (hbc : dist b c = R) (hbd : dist b d = R)
+    (hx_bc : dist x b = dist x c) (hx_da : dist x d = dist x a) :
+    False := by
+  exact no_rhombus_fan hR hcd (by simpa [dist_comm] using hab)
+    hbc hbd hac had hx_bc hx_da
+
+end Erdos97Octagon
diff --git a/LeanPool/Erdos97ConvexOctagon/RowSymmetry.lean b/LeanPool/Erdos97ConvexOctagon/RowSymmetry.lean
new file mode 100644
index 00000000..3ccb1064
--- /dev/null
+++ b/LeanPool/Erdos97ConvexOctagon/RowSymmetry.lean
@@ -0,0 +1,208 @@
+/-
+Copyright (c) 2026 Egor Lyfar. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Egor Lyfar
+-/
+
+import LeanPool.Erdos97ConvexOctagon.CoverageFormula
+
+/-!
+# First-row symmetry reduction
+
+The normalized zeroth row splits the remaining labels into `{2,3,4}` and
+`{5,6,7}`.  Permuting within those blocks reduces the 35 possible first rows
+to seven canonical orbits.  The small table below records an explicit forward
+and inverse permutation for every row.
+-/
+
+namespace Erdos97Octagon.RawIncidence
+
+/-- The seven canonical first-row masks, in certificate order. -/
+def canonicalRowMask : Fin 7 → UInt64 :=
+  ![29, 45, 101, 225, 60, 108, 228]
+
+/-- All first-row masks in the lexicographic search order. -/
+def rowOneMask : Fin 35 → UInt64 := ![
+  29, 45, 77, 141, 53, 85, 149, 101, 165, 197, 57, 89, 153, 105, 169, 201,
+  113, 177, 209, 225, 60, 92, 156, 108, 172, 204, 116, 180, 212, 228, 120,
+  184, 216, 232, 240
+]
+
+/-- All second-row masks in the lexicographic search order. -/
+def rowTwoMask : Fin 35 → UInt64 := ![
+  27, 43, 75, 139, 51, 83, 147, 99, 163, 195, 57, 89, 153, 105, 169, 201,
+  113, 177, 209, 225, 58, 90, 154, 106, 170, 202, 114, 178, 210, 226, 120,
+  184, 216, 232, 240
+]
+
+private theorem rowOneOptions_eq :
+    (rowOptions 1).reverse = List.ofFn (fun index => packedRow (rowOneMask index)) := by
+  decide
+
+private theorem rowTwoOptions_eq :
+    (rowOptions 2).reverse = List.ofFn (fun index => packedRow (rowTwoMask index)) := by
+  decide
+
+/-- Every legal first row has one of the 35 explicit masks. -/
+theorem exists_rowOneIndex (Q : OctagonIncidence) :
+    ∃ index : Fin 35, Q.targets 1 = packedRow (rowOneMask index) := by
+  have hmem : Q.targets 1 ∈ (rowOptions 1).reverse := by
+    simpa using target_row_mem_rowOptions Q 1
+  rw [rowOneOptions_eq, List.mem_ofFn] at hmem
+  obtain ⟨index, hindex⟩ := hmem
+  exact ⟨index, hindex.symm⟩
+
+/-- Every legal second row has one of the 35 explicit masks. -/
+theorem exists_rowTwoIndex (Q : OctagonIncidence) :
+    ∃ index : Fin 35, Q.targets 2 = packedRow (rowTwoMask index) := by
+  have hmem : Q.targets 2 ∈ (rowOptions 2).reverse := by
+    simpa using target_row_mem_rowOptions Q 2
+  rw [rowTwoOptions_eq, List.mem_ofFn] at hmem
+  obtain ⟨index, hindex⟩ := hmem
+  exact ⟨index, hindex.symm⟩
+
+/-- One explicit permutation taking a first row to a canonical orbit. -/
+structure RowSymmetryCertificate where
+  /-- Index of the canonical first-row orbit. -/
+  orbit : Fin 7
+  /-- Packed code for the forward vertex permutation. -/
+  forwardCode : UInt64
+  /-- Packed code for the inverse vertex permutation. -/
+  inverseCode : UInt64
+
+/-- Mathematical validity of a row-symmetry certificate. -/
+def RowSymmetryCertificate.Valid
+    (certificate : RowSymmetryCertificate) (sourceMask : UInt64) : Prop :=
+  let forward := decodeMap certificate.forwardCode
+  let inverse := decodeMap certificate.inverseCode
+  (∀ vertex, inverse (forward vertex) = vertex) ∧
+    (∀ vertex, forward (inverse vertex) = vertex) ∧
+    forward 0 = 0 ∧ forward 1 = 1 ∧
+    (∀ vertex, vertex ∈ standardTargets ↔ forward vertex ∈ standardTargets) ∧
+    ∀ vertex, vertex ∈ packedRow sourceMask ↔
+      forward vertex ∈ packedRow (canonicalRowMask certificate.orbit)
+
+instance instDecidableRowSymmetryCertificateValid
+    (certificate : RowSymmetryCertificate) (sourceMask : UInt64) :
+    Decidable (certificate.Valid sourceMask) := by
+  unfold RowSymmetryCertificate.Valid
+  infer_instance
+
+/-- The 35 explicit orbit certificates, aligned with `rowOneMask`. -/
+def rowSymmetryCertificate : Fin 35 → RowSymmetryCertificate := ![
+  { orbit := 0, forwardCode := 16434824, inverseCode := 16434824 },
+  { orbit := 1, forwardCode := 16434824, inverseCode := 16434824 },
+  { orbit := 1, forwardCode := 16205448, inverseCode := 16205448 },
+  { orbit := 1, forwardCode := 12535432, inverseCode := 14141064 },
+  { orbit := 1, forwardCode := 16431240, inverseCode := 16431240 },
+  { orbit := 1, forwardCode := 16201864, inverseCode := 16201864 },
+  { orbit := 1, forwardCode := 12531848, inverseCode := 14137480 },
+  { orbit := 2, forwardCode := 16434824, inverseCode := 16434824 },
+  { orbit := 2, forwardCode := 14599816, inverseCode := 14599816 },
+  { orbit := 2, forwardCode := 14141064, inverseCode := 12535432 },
+  { orbit := 1, forwardCode := 16430344, inverseCode := 16427208 },
+  { orbit := 1, forwardCode := 16200968, inverseCode := 16197832 },
+  { orbit := 1, forwardCode := 12530952, inverseCode := 14133448 },
+  { orbit := 2, forwardCode := 16434376, inverseCode := 16434376 },
+  { orbit := 2, forwardCode := 14599368, inverseCode := 14599368 },
+  { orbit := 2, forwardCode := 14140616, inverseCode := 12534984 },
+  { orbit := 2, forwardCode := 16427208, inverseCode := 16430344 },
+  { orbit := 2, forwardCode := 14592200, inverseCode := 14595336 },
+  { orbit := 2, forwardCode := 14133448, inverseCode := 12530952 },
+  { orbit := 3, forwardCode := 16434824, inverseCode := 16434824 },
+  { orbit := 4, forwardCode := 16434824, inverseCode := 16434824 },
+  { orbit := 4, forwardCode := 16205448, inverseCode := 16205448 },
+  { orbit := 4, forwardCode := 12535432, inverseCode := 14141064 },
+  { orbit := 5, forwardCode := 16434824, inverseCode := 16434824 },
+  { orbit := 5, forwardCode := 14599816, inverseCode := 14599816 },
+  { orbit := 5, forwardCode := 14141064, inverseCode := 12535432 },
+  { orbit := 5, forwardCode := 16431240, inverseCode := 16431240 },
+  { orbit := 5, forwardCode := 14596232, inverseCode := 14596232 },
+  { orbit := 5, forwardCode := 14137480, inverseCode := 12531848 },
+  { orbit := 6, forwardCode := 16434824, inverseCode := 16434824 },
+  { orbit := 5, forwardCode := 16430344, inverseCode := 16427208 },
+  { orbit := 5, forwardCode := 14595336, inverseCode := 14592200 },
+  { orbit := 5, forwardCode := 14136584, inverseCode := 12527816 },
+  { orbit := 6, forwardCode := 16434376, inverseCode := 16434376 },
+  { orbit := 6, forwardCode := 16427208, inverseCode := 16430344 }
+]
+
+/-- Kernel audit of all 35 explicit symmetry certificates. -/
+theorem rowSymmetryCertificate_valid (index : Fin 35) :
+    (rowSymmetryCertificate index).Valid (rowOneMask index) := by
+  fin_cases index <;> decide
+
+/-- Decode a valid row-symmetry certificate as a vertex equivalence. -/
+def RowSymmetryCertificate.toEquiv
+    (certificate : RowSymmetryCertificate) {sourceMask : UInt64}
+    (hvalid : certificate.Valid sourceMask) : Vertex ≃ Vertex where
+  toFun := decodeMap certificate.forwardCode
+  invFun := decodeMap certificate.inverseCode
+  left_inv := hvalid.1
+  right_inv := hvalid.2.1
+
+private theorem map_eq_of_membership
+    (equivalence : Vertex ≃ Vertex) (source target : Finset Vertex)
+    (hmembership : ∀ vertex, vertex ∈ source ↔ equivalence vertex ∈ target) :
+    source.map equivalence.toEmbedding = target := by
+  ext vertex
+  rw [Finset.mem_map]
+  constructor
+  · rintro ⟨preimage, hsource, rfl⟩
+    exact (hmembership preimage).mp hsource
+  · intro htarget
+    refine ⟨equivalence.symm vertex, ?_, by simp⟩
+    exact (hmembership (equivalence.symm vertex)).mpr (by simpa using htarget)
+
+/-- Relabel a normalized system so that row one is one of seven canonical rows. -/
+theorem canonicalize_rowOne
+    {p : Vertex → Plane} {Q : OctagonIncidence}
+    (hC : ConvexIndependent ℝ p) (hR : Realises p Q) (hN : Q.Normalized)
+    (index : Fin 35) (hrow : Q.targets 1 = packedRow (rowOneMask index)) :
+    ∃ orbit : Fin 7, ∃ p' : Vertex → Plane, ∃ Q' : OctagonIncidence,
+      ConvexIndependent ℝ p' ∧ Realises p' Q' ∧ Q'.Normalized ∧
+        Q'.PairSparse ∧ Q'.Balanced ∧
+        Q'.targets 1 = packedRow (canonicalRowMask orbit) := by
+  let certificate := rowSymmetryCertificate index
+  have hvalid : certificate.Valid (rowOneMask index) :=
+    rowSymmetryCertificate_valid index
+  let equivalence := certificate.toEquiv hvalid
+  have hzero : equivalence 0 = 0 := by
+    simpa [equivalence, RowSymmetryCertificate.toEquiv] using hvalid.2.2.1
+  have hone : equivalence 1 = 1 := by
+    simpa [equivalence, RowSymmetryCertificate.toEquiv] using hvalid.2.2.2.1
+  have hzeroSymm : equivalence.symm 0 = 0 := by
+    apply equivalence.injective
+    simp [hzero]
+  have honeSymm : equivalence.symm 1 = 1 := by
+    apply equivalence.injective
+    simp [hone]
+  have hmapStandard :
+      standardTargets.map equivalence.toEmbedding = standardTargets :=
+    map_eq_of_membership equivalence standardTargets standardTargets (by
+      intro vertex
+      simpa [equivalence, RowSymmetryCertificate.toEquiv] using
+        hvalid.2.2.2.2.1 vertex)
+  have hmapRow :
+      (packedRow (rowOneMask index)).map equivalence.toEmbedding =
+        packedRow (canonicalRowMask certificate.orbit) :=
+    map_eq_of_membership equivalence (packedRow (rowOneMask index))
+      (packedRow (canonicalRowMask certificate.orbit)) (by
+        intro vertex
+        simpa [equivalence, RowSymmetryCertificate.toEquiv] using
+          hvalid.2.2.2.2.2 vertex)
+  let p' := relabelPoints p equivalence
+  let Q' := Q.relabel equivalence
+  have hC' : ConvexIndependent ℝ p' := convexIndependent_relabel hC equivalence
+  have hR' : Realises p' Q' := realises_relabel hR equivalence
+  have hN' : Q'.Normalized := by
+    change (Q.targets (equivalence.symm 0)).map equivalence.toEmbedding = standardTargets
+    rw [hzeroSymm, hN, hmapStandard]
+  have hrow' : Q'.targets 1 = packedRow (canonicalRowMask certificate.orbit) := by
+    change (Q.targets (equivalence.symm 1)).map equivalence.toEmbedding = _
+    rw [honeSymm, hrow, hmapRow]
+  have hSparse' : Q'.PairSparse := pairSparse_of_realises hC' Q' hR'
+  refine ⟨certificate.orbit, p', Q', hC', hR', hN', hSparse',
+    Q'.balanced_of_pairSparse hSparse', hrow'⟩
+
+end Erdos97Octagon.RawIncidence
diff --git a/LeanPool/projects.yml b/LeanPool/projects.yml
index 0cfdd676..292b9f3c 100644
--- a/LeanPool/projects.yml
+++ b/LeanPool/projects.yml
@@ -5070,6 +5070,44 @@ projects:
     msc:
       - "11A63"
       - "11B65"
+  - slug: erdos-97-convex-octagon
+    title: The Convex-Octagon Case of Erdős Problem 97
+    summary: >-
+      Proves that among eight labelled points in the Euclidean plane in convex position, at least
+      one point has no four other points at a common distance. The development reduces a geometric
+      counterexample to a finite incidence model, classifies normalized row patterns up to symmetry,
+      proves geometric and algebraic obstructions, and excludes seven canonical first-row masks with
+      one regenerable LRAT certificate checked by a project-owned kernel-safe checker. This is the
+      convex-octagon case only; the general Erdős Problem 97 remains open.
+    branch: discrete geometry
+    entry_module: LeanPool.Erdos97ConvexOctagon
+    authors:
+      - Egor Lyfar
+    source:
+      title: On Sets of Distances of n Points
+      authors:
+        - Paul Erdős
+      doi: "10.1080/00029890.1946.11991674"
+      url: "https://www.erdosproblems.com/97"
+      github_repo: lyfar/erdos-97-octagon-lean
+    license: Apache-2.0
+    status: verified
+    provenance: AI
+    main_declarations:
+      - Erdos97Octagon.erdos97_convex_octagon
+    main_results:
+      - declaration: Erdos97Octagon.erdos97_convex_octagon
+        informal: >-
+          Among eight labelled points in the Euclidean plane in convex position, some point has no
+          four other points at a common distance.
+    tags:
+      - discrete-geometry
+      - distance-geometry
+      - erdos-problems
+      - convexity
+    msc:
+      - "51K05"
+      - "52A10"
   - slug: erdos132-n14
     title: A Conditional Fourteen-Point Case of Erdős Problem 132
     summary: >-