[K3] Close c112 source-line and raw 433-1b/O0a workboards

experimental/agents-log.md

@@ -3682,3 +3682,98 @@ Keep entries concise and link to the relevant files.
 - **What to do next:** Run verifiers and audits on the integrated material,
   review mathematical notes before promotion, and close the original PRs as
   manually integrated once the integration commit is pushed.
+
+## 2026-08-09 — [K3] living progress branch opened (k3-433-progress-export)
+
+Four unit certificates: c112 source-line coverage COMPLETE (incl.
+the M01-R11/M02-R11 Singular-replay discharge at PR #1144's pinned
+commit); 433-1b cell 4 CLOSED (105/105 slices); 433-1b cells 12-13
+CLOSED; 433-1b universal structure (105 -> 60 orbit quotient +
+transports). 204 theorem nodes pinned by path + verifier sha256 in
+AllenGrahamHart/rs-mca-prize-dag @ 594aaa985; all verifiers
+coordinator-replayed. Ledger movement 0; K3 and the KoalaBear row
+remain open (cell 9 in flight; [5,8], [11], cell-3 xi4 residual).
+Incremental pushes will land here as cells close.
+
+## 2026-08-09 — [K3] 433-1b coordinate-positive cell 9 closed
+
+Added `kb-mca-v4-433-1b-cell9-close-v1`: 105/105 labeled slices paid
+by 30 endpoint labels and 75 active labels in 24 exact orbits. The packet
+pins 28 PROVED theorem nodes and verifier digests in
+AllenGrahamHart/rs-mca-prize-dag @ 68ac9e383; the executable aggregate
+reconstructs the universal router and checks the 17-owner partition. All 56
+node verifier and audit scripts were coordinator-replayed. Ledger movement 0;
+K3 and the KoalaBear row remain open ([5,8], [11], cell-3 xi4 residual).
+
+## 2026-08-09 — [K3] 433-1b source role cell 3 re-pinned complete
+
+Added `kb-mca-v4-433-1b-cell3-close-v1`. The common rank-drop branch is
+empty in all four source-sign rows, and a disjoint supplier census pays all
+`7 * 15 * 4 * 4 = 1680` principal systems, including all 240 `xi4` systems
+by exact outside-role transport. The packet pins 28 PROVED theorem nodes at
+AllenGrahamHart/rs-mca-prize-dag @ a001708ae. Modal replay
+`ap-jYkVRdvSHQuofSrzIJzAG1` passed all 28 primary verifiers and 28 audits.
+Ledger movement 0; K3 and the KoalaBear row remain open only on role orbits
+`[5,8]` and `[11]` within this exported workboard.
+
+## 2026-08-09 — [K3] 433-1b common-role orbit [5,8] closed
+
+Added `kb-mca-v4-433-1b-cells5-8-close-v1`. Cell 5 is closed at 105/105:
+75 active labels are paid by 16 exact owner packets over 24 quotient orbits,
+and all 30 endpoint labels are excluded because eight degree-16/degree-11
+eliminants have no deployed base-field root. An exact B/C transport closes
+cell 8 over all 1,680 signed principal systems, with the global rank-drop
+theorem paying the complement. The packet pins 23 PROVED theorem nodes at
+AllenGrahamHart/rs-mca-prize-dag @ 3fa298743024. Ledger movement 0; K3 and
+the KoalaBear row remain open only on role orbit `[11]` within this exported
+workboard.
+
+## 2026-08-10 — [K3] 433-1b source-role cell 11 closed
+
+Added `kb-mca-v4-433-1b-cell11-close-v1`. Cell 11 is closed at 105/105:
+75 active labels are paid by 16 exact owner packets over all 24 quotient
+orbits, and the separate endpoint theorem pays the remaining 30 labels. The
+final pairings 7, 8, and 11 have complete direct equation and leading-boundary
+replays; a shared FLINT packet reconstructs 61 profiles and 302 roots through
+degree 5192. The packet pins 22 PROVED theorem nodes at
+AllenGrahamHart/rs-mca-prize-dag @ 7824a826a283. All 44 cell-11 verifier and
+hostile-audit scripts passed. The exported raw-label workboard now has no
+open role orbit. Ledger movement remains 0; K3 and the KoalaBear row remain
+open on labels-to-distinct-affine-slopes conversion, the genuine-pencil
+ledger, and fresh independent proof review.
+
+## 2026-08-10 — [K3] complete raw 433-1b to O0a workboard exclusion
+
+Added `kb-mca-v4-433-1b-raw-workboard-close-v1`. An explicit B/C
+duplicate-role transport closes the previously implicit cell-10 step from
+cell 9 over all 105 labels and 1,680 signed principal systems. Nine disjoint
+owner packets now cover all 15 role cells, 1,575 labels, and 25,200 signed
+principal systems; the global rank-drop theorem excludes the complement.
+The packet pins three aggregate PROVED nodes and hostile audits at
+AllenGrahamHart/rs-mca-prize-dag @ `8df090339e3e`. Ledger movement remains
+0. K3 remains open on eleven other positive routes, orientation/source-cover
+assembly, exact distinct-slope allocation, and independent review.
+
+## 2026-08-10 — [K3] repeated-BC O0b cell-11 off-guard route cut
+
+Added `kb-mca-v4-433-1b-o0b-cell11-offguard-v1`. Across eight source
+towers, three missing representatives, two outside signs, and 15 residual
+matchings, all 720 exact paired-product systems are empty at every deployed
+nonzero-guard source value. Nested norms leave 1,584 exceptional-root
+occurrences over 126 base values; exact all-pair replay excludes all 1,584.
+The packet pins two PROVED nodes and 19 source artifacts at
+AllenGrahamHart/rs-mca-prize-dag @ `81f218e38285`. Ledger movement remains
+0. Missing `BE/CF`, guard and selected-cofactor boundaries, cell 14,
+orientation, allocation, independent review, K3, and the KoalaBear row remain
+open.
+
+## 2026-08-10 — [K3] repeated-BC O0b cell-11 colored off-guard cut
+
+Added `kb-mca-v4-433-1b-o0b-cell11-colored-offguard-v1`.  The missing
+`BE/CF` endpoint product fixes the colored endpoint, and its reconstructed
+squared sum gives one necessary source-algebra consistency identity.  All 16
+exact norms are units on the deployed rational open: their only base-field
+roots are `x=0,1` for `BC-` and `x=0,-1` for `BC+`, all registered guards.
+The packet pins one PROVED node and four evidence files at
+AllenGrahamHart/rs-mca-prize-dag @ `96868562394e`.  Ledger movement is 0;
+finite guard/cofactor fibers and all later K3 obligations remain open.

experimental/data/certificates/kb-mca-v4-433-1b-cell11-close-v1/README.md

@@ -0,0 +1,59 @@
+---
+workboard_item: K3
+row: KoalaBear MCA at 2^-128
+object: MCA
+target_epsilon: 2^-128
+agreement: 1116048
+B_star: 274980728111395087
+direct_statement: Every one of the 105 raw direct labels in positive 433-1b source-role cell 11 is empty on the deployed guarded route.
+architecture: positive-433-1b-coordinate-guarded-route
+partition_digest: sha256:82df776b06b375e9bee6fcc77aead1ebca4594028fa2e51df6318422a9d2f9bb
+atom_or_cell: coordinate-positive 433-1b source-role cell 11
+quantifier: every raw direct label in the declared source-role cell
+projection_and_unit: raw workboard labels, not distinct bad slopes
+claimed_bound: 0 surviving labels out of 105
+status: PROVED
+impact: LOCAL_ONLY
+falsifier: a deployed guarded-route solution in cell 11, an omitted quotient orbit, an invalid endpoint rootlessness certificate, or a verifier digest mismatch
+replay: tools/ramguard local -- python3 <node path>/verify.py && tools/ramguard local -- python3 <node path>/verify_audit.py
+---
+
+# Complete closure of source-role cell 11 of the positive 433-1b workboard
+
+The JSON certificate in this directory summarizes 22 PROVED nodes of the
+public campaign repository https://github.com/AllenGrahamHart/rs-mca-prize-dag
+at commit `7824a826a28360fabcb1e50bf36f1cec14685292`. Each node carries a
+machine verifier whose sha256 is pinned in the certificate. All 44 cell-11
+verifier and hostile-audit scripts passed at that exact commit.
+
+Cell 11 has 75 active labels in 24 exact quotient orbits. Sixteen owner
+packets pay one representative of every orbit. The remaining 30 endpoint
+labels are excluded by the independent endpoint rootlessness theorem. The
+aggregate verifiers reconstruct the exact `75+30=105` disjoint cover.
+
+The final outside-role packet closes pairings 7, 8, and 11. Pairings 7 and 8
+each retain 64 compatible lifts and 128 colored lanes; pairing 11 retains 16
+lifts and 32 lanes. Every colored value is nonzero. A shared independent
+FLINT reconstruction covers 61 polynomial profiles, 302 deployed roots, and
+degrees through 5192. Three direct audits replay every candidate union,
+source relation, paired-scalar equation, and cell-11 leading-boundary
+payment.
+
+This closes the last role orbit named as open by the preceding living K3
+packet. Thus the exported positive-433-1b workboard has no remaining raw
+label cell. This packet moves no ledger value and does not close K3 or the
+KoalaBear row: conversion from raw labels to distinct affine slopes, the
+genuine-pencil ledger, and fresh independent proof review remain required.
+
+## Provenance annotation (2026-08-10, coordinator)
+
+The `provenance.commit` hash is the durable pin; the
+`provenance.branch` field names a worker-local branch that is not
+published. As of source-repo master
+`711fcb9775ef6561fde1f6e7eb11d28e0a04d205`
+(https://github.com/AllenGrahamHart/rs-mca-prize-dag), the pinned
+commit and every node listed in this certificate are reachable from
+public master with their verifiers. Worker certificate pushes land
+on this PR ahead of the coordinator's audited merge to master, so a
+pinned commit may be briefly unreachable (typically hours) between
+the two — replay against master at or after the commit above.

experimental/data/certificates/kb-mca-v4-433-1b-cell11-close-v1/kb_mca_v4_433_1b_cell11_close_v1.json

@@ -0,0 +1,184 @@
+{
+  "K3_closed": false,
+  "KoalaBear_row_closed": false,
+  "bankability_contract": {
+    "B_star": 274980728111395087,
+    "agreement": 1116048,
+    "architecture": "positive-433-1b-coordinate-guarded-route",
+    "atom_or_cell": "coordinate-positive 433-1b source-role cell 11",
+    "claimed_bound": "0 surviving labels out of 105",
+    "direct_statement": "Every one of the 105 raw direct labels in positive 433-1b source-role cell 11 is empty on the deployed guarded route.",
+    "falsifier": "a deployed guarded-route solution in cell 11, an omitted quotient orbit, an invalid endpoint rootlessness certificate, or a verifier digest mismatch",
+    "impact": "LOCAL_ONLY",
+    "object": "MCA",
+    "partition_digest": "sha256:82df776b06b375e9bee6fcc77aead1ebca4594028fa2e51df6318422a9d2f9bb",
+    "projection_and_unit": "raw workboard labels, not distinct bad slopes",
+    "quantifier": "every raw direct label in the declared source-role cell",
+    "row": "KoalaBear MCA at 2^-128",
+    "status": "PROVED",
+    "target_epsilon": "2^-128",
+    "workboard_item": "K3"
+  },
+  "nodes": [
+    {
+      "id": "rate_half_kb_m2_r4_coordinate_positive_433_1b_cell11_complete_exclusion",
+      "path": "background/nodes/rate_half_kb_m2_r4_coordinate_positive_433_1b_cell11_complete_exclusion",
+      "status": "PROVED",
+      "verify_sha256": "b0cdd85e528cf0032307dc8b488201632f24962adda7d053c42a5abef3d938ba"
+    },
+    {
+      "id": "rate_half_kb_m2_r4_coordinate_positive_433_1b_cell11_active_labels_complete_exclusion",
+      "path": "background/nodes/rate_half_kb_m2_r4_coordinate_positive_433_1b_cell11_active_labels_complete_exclusion",
+      "status": "PROVED",
+      "verify_sha256": "7121a13db2a249a27aec9db84c5ed1148238fdda1c81211472858ff356097081"
+    },
+    {
+      "id": "rate_half_kb_m2_r4_coordinate_positive_433_1b_cell11_endpoint_roles_complete_exclusion",
+      "path": "background/nodes/rate_half_kb_m2_r4_coordinate_positive_433_1b_cell11_endpoint_roles_complete_exclusion",
+      "status": "PROVED",
+      "verify_sha256": "66b186aeee95b6c8c59193df5e484f85078de2014324db7ee906bedf1d562c3e"
+    },
+    {
+      "id": "rate_half_kb_m2_r4_coordinate_positive_433_1b_universal_generic_outside_label_orbit_quotient",
+      "path": "background/nodes/rate_half_kb_m2_r4_coordinate_positive_433_1b_universal_generic_outside_label_orbit_quotient",
+      "status": "PROVED",
+      "verify_sha256": "cd49f5cd6b74e733908eac92149fc8e3aafbbd4a846fcf0428d2089f1b84e7c2"
+    },
+    {
+      "id": "rate_half_kb_m2_r4_coordinate_positive_433_1b_cell11_quadratic_four_basis_common_locus",
+      "path": "background/nodes/rate_half_kb_m2_r4_coordinate_positive_433_1b_cell11_quadratic_four_basis_common_locus",
+      "status": "PROVED",
+      "verify_sha256": "b459aec1f4f169566b117d39a3dfdb15caa739a2223be3fc8414038c30db7125"
+    },
+    {
+      "id": "rate_half_kb_m2_r4_coordinate_positive_433_1b_cell11_global_common_kernel",
+      "path": "background/nodes/rate_half_kb_m2_r4_coordinate_positive_433_1b_cell11_global_common_kernel",
+      "status": "PROVED",
+      "verify_sha256": "60106a40dcd9964859297f7a3cffb62d527917c55d5a38539fd409a3f1bcb45a"
+    },
+    {
+      "id": "rate_half_kb_m2_r4_coordinate_positive_433_1b_cell11_parallel_de_first_pair_complete_exclusion",
+      "path": "background/nodes/rate_half_kb_m2_r4_coordinate_positive_433_1b_cell11_parallel_de_first_pair_complete_exclusion",
+      "status": "PROVED",
+      "verify_sha256": "7136b9b76d3f842f57e086b7b44bc6c19d5dea61b8c0761a786144660911de71"
+    },
+    {
+      "id": "rate_half_kb_m2_r4_coordinate_positive_433_1b_cell11_parallel_de_pairing11_14_common_f_resultant_exclusion",
+      "path": "background/nodes/rate_half_kb_m2_r4_coordinate_positive_433_1b_cell11_parallel_de_pairing11_14_common_f_resultant_exclusion",
+      "status": "PROVED",
+      "verify_sha256": "0bebe83f5e0a34440992a2a5cd5695e7bcf608c33a696e30aaed793e08691922"
+    },
+    {
+      "id": "rate_half_kb_m2_r4_coordinate_positive_433_1b_cell11_parallel_de_pairing3_6_nested_quadratic_exclusion",
+      "path": "background/nodes/rate_half_kb_m2_r4_coordinate_positive_433_1b_cell11_parallel_de_pairing3_6_nested_quadratic_exclusion",
+      "status": "PROVED",
+      "verify_sha256": "e8724e835e5e451b9263f5ec555d81a99e8cf7c3c600f68587f94681fb05c85f"
+    },
+    {
+      "id": "rate_half_kb_m2_r4_coordinate_positive_433_1b_cell11_parallel_de_pairing4_7_9_10_nested_quadratic_exclusion",
+      "path": "background/nodes/rate_half_kb_m2_r4_coordinate_positive_433_1b_cell11_parallel_de_pairing4_7_9_10_nested_quadratic_exclusion",
+      "status": "PROVED",
+      "verify_sha256": "9023c3eebf43b07f1d98f893450bfdb3ea88cc47acf4627eaf97eee368206be8"
+    },
+    {
+      "id": "rate_half_kb_m2_r4_coordinate_positive_433_1b_cell11_parallel_de_pairing5_8_12_13_nested_quadratic_exclusion",
+      "path": "background/nodes/rate_half_kb_m2_r4_coordinate_positive_433_1b_cell11_parallel_de_pairing5_8_12_13_nested_quadratic_exclusion",
+      "status": "PROVED",
+      "verify_sha256": "f9a8b0d785a686e8d1fd3d5b0df7f400c4f1707387903759c2134ab550d48c7e"
+    },
+    {
+      "id": "rate_half_kb_m2_r4_coordinate_positive_433_1b_cell11_positive_de_pairing9_10_nested_quadratic_exclusion",
+      "path": "background/nodes/rate_half_kb_m2_r4_coordinate_positive_433_1b_cell11_positive_de_pairing9_10_nested_quadratic_exclusion",
+      "status": "PROVED",
+      "verify_sha256": "f9a430407b8935af4abcf7866a1db454fe85eaa4fbbb95afd04de60e45a3849b"
+    },
+    {
+      "id": "rate_half_kb_m2_r4_coordinate_positive_433_1b_cell11_positive_de_pairing12_13_nested_quadratic_exclusion",
+      "path": "background/nodes/rate_half_kb_m2_r4_coordinate_positive_433_1b_cell11_positive_de_pairing12_13_nested_quadratic_exclusion",
+      "status": "PROVED",
+      "verify_sha256": "ebd0fe95c7416d9569224d82eae81d88d81a0b383bec7e22a133f0a887c67e15"
+    },
+    {
+      "id": "rate_half_kb_m2_r4_coordinate_positive_433_1b_cell11_positive_de_pairing14_common_f_resultant_exclusion",
+      "path": "background/nodes/rate_half_kb_m2_r4_coordinate_positive_433_1b_cell11_positive_de_pairing14_common_f_resultant_exclusion",
+      "status": "PROVED",
+      "verify_sha256": "c9f93bd82f5bcb1f16a6909f320064c31f360202bdd2eb7357a367f593c35e95"
+    },
+    {
+      "id": "rate_half_kb_m2_r4_coordinate_positive_433_1b_cell11_xi3_pairing0_reciprocal_square_exclusion",
+      "path": "background/nodes/rate_half_kb_m2_r4_coordinate_positive_433_1b_cell11_xi3_pairing0_reciprocal_square_exclusion",
+      "status": "PROVED",
+      "verify_sha256": "eafb762c9dfcab464ba768bf4d58b481a4b52b6a44802478c5befd7443862847"
+    },
+    {
+      "id": "rate_half_kb_m2_r4_coordinate_positive_433_1b_cell11_xi3_pairings1_2_reciprocal_linear_exclusion",
+      "path": "background/nodes/rate_half_kb_m2_r4_coordinate_positive_433_1b_cell11_xi3_pairings1_2_reciprocal_linear_exclusion",
+      "status": "PROVED",
+      "verify_sha256": "405dd58de350fada69033cff8e7ca4b0cf84303f1b2b4fe32ae1eaadc5f511bf"
+    },
+    {
+      "id": "rate_half_kb_m2_r4_coordinate_positive_433_1b_cell11_xi3_xi4_pairing3_6_reciprocal_square_exclusion",
+      "path": "background/nodes/rate_half_kb_m2_r4_coordinate_positive_433_1b_cell11_xi3_xi4_pairing3_6_reciprocal_square_exclusion",
+      "status": "PROVED",
+      "verify_sha256": "bdd47750e12df36599e07bab6365b85468f5e72e45aeda0ce114492ab8eff6b3"
+    },
+    {
+      "id": "rate_half_kb_m2_r4_coordinate_positive_433_1b_cell11_xi3_xi4_pairing4_9_nested_signfree_exclusion",
+      "path": "background/nodes/rate_half_kb_m2_r4_coordinate_positive_433_1b_cell11_xi3_xi4_pairing4_9_nested_signfree_exclusion",
+      "status": "PROVED",
+      "verify_sha256": "0a4825d084652b97837cd0314915a3ea1cb6fa657ad1b56cc5432efb85cf7270"
+    },
+    {
+      "id": "rate_half_kb_m2_r4_coordinate_positive_433_1b_cell11_xi3_xi4_pairing5_12_nested_signfree_exclusion",
+      "path": "background/nodes/rate_half_kb_m2_r4_coordinate_positive_433_1b_cell11_xi3_xi4_pairing5_12_nested_signfree_exclusion",
+      "status": "PROVED",
+      "verify_sha256": "51a69e888deb73c24fde6c258866b6b30ec6def207c9f7ae9bc8fa4216ebace2"
+    },
+    {
+      "id": "rate_half_kb_m2_r4_coordinate_positive_433_1b_cell11_xi3_xi4_pairing7_10_quadratic_resultant_exclusion",
+      "path": "background/nodes/rate_half_kb_m2_r4_coordinate_positive_433_1b_cell11_xi3_xi4_pairing7_10_quadratic_resultant_exclusion",
+      "status": "PROVED",
+      "verify_sha256": "77ee09015f3d3bc148b5aa9cbef5ffca2fbfffbbd67a9ad6d3e4f557c5f40314"
+    },
+    {
+      "id": "rate_half_kb_m2_r4_coordinate_positive_433_1b_cell11_xi3_xi4_pairing8_13_quadratic_resultant_exclusion",
+      "path": "background/nodes/rate_half_kb_m2_r4_coordinate_positive_433_1b_cell11_xi3_xi4_pairing8_13_quadratic_resultant_exclusion",
+      "status": "PROVED",
+      "verify_sha256": "e6b03df3133ac45aa645badfe5df5412e3e85d3a70f2801220823a4b6c143d93"
+    },
+    {
+      "id": "rate_half_kb_m2_r4_coordinate_positive_433_1b_cell11_xi3_xi4_pairing11_14_quadratic_resultant_exclusion",
+      "path": "background/nodes/rate_half_kb_m2_r4_coordinate_positive_433_1b_cell11_xi3_xi4_pairing11_14_quadratic_resultant_exclusion",
+      "status": "PROVED",
+      "verify_sha256": "924d55a68ef68296e1cc657dd1724dfcaa985d437d898995df3b0de3b14fc98d"
+    }
+  ],
+  "nonclaims": [
+    "Does not close K3 or the KoalaBear row.",
+    "Raw-label workboard coverage is not yet converted to distinct bad slopes.",
+    "The genuine-pencil ledger and fresh independent proof review remain required before promotion to a GREEN banked result."
+  ],
+  "provenance": {
+    "branch": "codex/full-prize-resolution-v12-20260807",
+    "commit": "7824a826a28360fabcb1e50bf36f1cec14685292",
+    "node_count": 22,
+    "replay": "from the campaign repo root: tools/ramguard local -- python3 <node path>/verify.py && tools/ramguard local -- python3 <node path>/verify_audit.py",
+    "repo": "https://github.com/AllenGrahamHart/rs-mca-prize-dag"
+  },
+  "schema": "kb-mca-v4-433-1b-cell11-close-v1",
+  "statement": {
+    "claims": {
+      "active_orbits": "75 nonendpoint cell-11 labels partition into 24 exact orbits with size profile 1:1, 2:9, 4:14 and are paid by 16 owner packets",
+      "common_geometry": "24 four-basis chart/sign rows and 40 global-kernel row reductions are exact over the deployed field",
+      "endpoint_labels": "30 cell-11 endpoint labels are excluded by the independent endpoint rootlessness theorem",
+      "final_outside_packet": "pairings 7, 8, and 11 close the final 12 labels with 24 complete rows and no witness",
+      "slices": "cell 11 is closed at 105/105 raw direct labels"
+    },
+    "deployed_characteristic": 2130706433,
+    "ledger_movement": 0,
+    "row": "KoalaBear MCA at 2^-128",
+    "status": "PROVED_UNIT_LABEL_WORKBOARD_COMPLETE_CONVERSION_OPEN",
+    "title": "Complete closure of source-role cell 11 of the positive 433-1b workboard",
+    "workboard_item": "K3"
+  }
+}