Research: WaveLock Curvature-Capacity Core — CC-Core-v0 (A) + CC-Core-v1 (B), formalize/implement/attack/falsify - #19
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Audit and classify the existing P-vs-NP / curvature / inevitability claims into exact definition / proved theorem / observation / conjecture. Establish that no exponential attack-cost or heat lower bound is proved. Define measurable curvature/signature functionals on lifted integers and show curvature magnitude is lifting-convention dependent (diagnostic, not a cryptographic invariant). Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01BqTM7VZ2gMtmTmwLH6vx22
Three explicit resource models (R_comp, R_phys, R_machine) with concrete numbers. Forward cost is polynomial O(blocks*T*N^2). Landauer/Margolus-Levitin/ Bremermann/Bekenstein bounds constrain an implementation, not the problem; the heat argument is interpretive, not a hardness proof. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01BqTM7VZ2gMtmTmwLH6vx22
CC-Core-v0: co-evolve the unmodified Design A wave field with a path-binding accumulator field C (Candidate A) so the digest commits to the ordered trajectory, not only the terminal state. Reference + optimized (byte-parity), hash-free. Design A is reused verbatim and untouched. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01BqTM7VZ2gMtmTmwLH6vx22
Wave round byte-identical to frozen Design A; reference/optimized parity; pinned CC-Core-v0 vectors; Design A digests and the eigenmode-collision theorem pinned so any regression in the frozen primitive fails here too. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01BqTM7VZ2gMtmTmwLH6vx22
Central result: Design A eigenmode states all collapse to terminal wave 0 yet yield 9/9 distinct trajectory digests (min Hamming 116). No accumulator zero-preimage (530k checked), no symmetry preserves the digest, zero-wave digest is non-degenerate. Pebble property holds (100% distinct over 1200 pairs); truncated collisions generic; avalanche 127.7; low bias. All budgeted, no proof. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01BqTM7VZ2gMtmTmwLH6vx22
Curvature saturates in T (no exponential growth) and is ~constant in message length; exponential-fit R^2 ~ 5e-5. The 256-bit description size is fixed. No measured quantity grows exponentially -- 'exponential curvature' is unsupported. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01BqTM7VZ2gMtmTmwLH6vx22
Toy coupled cores (N=2; p=5,7,11). The accumulator reduces wave-round collisions by a large factor but does NOT eliminate them (residual dominated by N=2 neighbour degeneracy, per Design A Phase 8B); coupled-round injectivity at N=16 is unresolved and not extrapolated. z3/Groebner unavailable (limitation). Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01BqTM7VZ2gMtmTmwLH6vx22
Full audit runner + INDEX.json. Results report with the 20-point final report and decision-criteria checklist. Verdict: Experimental -- mechanism partially supported (Design A collisions separated, no bypass within budget) but no lower-bound theorem, curvature is a diagnostic only, heat argument interpretive. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01BqTM7VZ2gMtmTmwLH6vx22
Isolated workflow: forbidden-import guard, parity + pinned vectors + exact trace, Design A preservation, eigenmode regression, full fast tests. No large searches in ordinary CI (heavy suite lives behind run_audit.py). Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01BqTM7VZ2gMtmTmwLH6vx22
…h binding Enumerates all 47 zero-preimage states (r=1: 8, r=2: 36, r=4: 2, zero: 1) from periodic-tile Laplacian eigenvectors up to 4x4 tiles. Every state is verified to map to zero under the Design A wave round. All 47 trajectory digests are distinct (min pairwise Hamming 98), superseding the 9-state representative result from Phase 1. Artifacts: curvature_audit/artifacts/phase8j_full_collision_family.json curvature_audit/artifacts/full_family_path_binding.json
Documents the complete algebraic structure of Phi_t: - j(u,v) degree: 2 in u (ETA*u^2), 1 in v - Proved 2-to-1: j(u,v) = j(u',v) for u+u' = -(1+gamma*v)/ETA mod p - Degree growth upper bound: heuristically exceeds p-1 by round 4 - Candidate A vs B trade-off table (degree vs injectivity in u) - Known structural weaknesses table
Six attack categories: 1. One-round collision search (no collision in 6000 random + structured) 2. Cancellation family: 500/500 u-pairing partners confirmed (provable 2-to-1) 3. Fixed-point search: none found in 5000 candidates 4. Two-cycle search: none found in 3000 candidates 5. Degree-growth trace: heuristic upper bound saturates Fermat cap by round 4 6. ETA pairing attack: 0 digest collisions in 200 trials All negative results carry stated budgets; none is a proof of absence.
Documents six candidate shortcuts (skip wave, backward inversion, MITM, cycle detection, low-degree solve, 2-to-1 exploit); none demonstrated. Per-cell backward inversion is algebraically solvable but the full coupled 256-variable degree-2 system was not invoked. No cycle in 1000 steps. Shortcut computation artifact records bounded negative results.
Defines four protocol variants (A: plain digest, B: trajectory-state, C: prefix-binding, D: interactive sketch) with explicit soundness and zero-knowledge status (all unproved). Formally separates three distinct claims: - Path binding for eigenmode family: CONFIRMED (47/47 distinct, min HD 98) - Trajectory uniqueness: UNRESOLVED (toy-scale collisions found) - Hardness of inversion: UNPROVED (no lower bound) These must not be conflated in any security assertion.
Extends Phase 1 reduced_models (which fixed C) to enumerate the full joint (psi, C) state space: p=3, N=2 (6561 joint states): 5562 coupled collisions -- NOT injective p=5, N=2 (390625 joint states): 375073 coupled collisions -- NOT injective p=7, N=2: too large (5.76M) for full enumeration This is a stronger negative finding than Phase 1's C-fixed-slice analysis. N=2 degeneracy (up==down, left==right on 2x2 torus) is acknowledged and results are NOT extrapolated to N=16.
Candidate A (CC-Core-v0): j_A = u + GAMMA*u*v + ETA*u^2 + ZETA*v - Separation: 47/47 (min HD 98) - Structural flaw: provable 2-to-1 in u (j_A(u,v) = j_A(u',v)) - Avalanche mean HD: 127.2 Candidate B (ETA=0, linear injection): j_B = u + GAMMA*u*v + ZETA*v - Separation: 47/47 (min HD 105) - Injective in u for all v with (1+GAMMA*v) != 0 (prob ~1/p) - Avalanche mean HD: 128.0 Trade-off documented: Candidate B avoids the 2-to-1 weakness but has lower algebraic degree. Adopting Candidate B requires a spec revision.
test_phase_cc1.py covers: - Complete family: count (47), per-r counts, all verified, all distinct - Known amplitudes presence (r=4, r=2, r=1) - Design A preservation guard - Full-family trajectory binding: all distinct, min HD >= 64 - Accumulator algebra: 2-to-1 proved, rho_t varies, weights distinct - Prover/verifier: determinism, consistency, claim separation - Candidate B: eigenmode separation, ETA=0 documented - Reduced exhaustive: artifact exists, wave non-injective at toy scale CI: added Phase CC-1 step before the full fast-test step.
…ndation run_audit.py: adds five Phase CC-1 modules to the full suite runner. WAVELOCK_CURVATURE_CAPACITY_RESULTS.md extended to 25 points: - Points 19-25 cover Phase CC-1 findings - Full decision-criteria checklist updated - PR #19 merge recommendation added Merge recommendation: DO NOT merge as-is. Retain as draft until at least one: 1. Coupled-round injectivity resolved at N=16 (prove or find explicit collision) 2. ETA 2-to-1 weakness resolved (adopt Candidate B, or prove no bypass) 3. A restricted-model lower bound established Verdict remains: Experimental
docs/CC_CORE_V0_BASELINE.md records the immutable Candidate A reference: exact equations, constants, the proved generic 2-to-1 injection relation, the 47-state separation (min HD 98), reduced-model collisions, shortcut audit, allowed/forbidden claims, and pinned digests. test_candidate_a_frozen.py fails if any Candidate A equation, constant, or pinned output changes. Candidate A stays reproducible for A/B comparison.
docs/CC_CORE_V1_SPEC.md and wavelock/curvature_capacity_v1/spec.py define the linear-injection candidate j_B(u,v) = u + GAMMA*u*v = u*(1+GAMMA*v) (ETA=ZETA=0). All field/lattice/wave/weight/round-constant/IV/squeeze parameters are identical to Candidate A to isolate the single injection change for A/B comparison. Message-level domain separation via distinct D_TAG (WCC2) and VERSION (v1). Records the new singular hyperplane v_star = -GAMMA^-1 mod p = 195225786 where j_B(u, v_star) = 0 for all u, to be audited in Part IV before any claim.
wavelock/curvature_capacity_v1/: state, commit (j_B linear injection), evolve (frozen Design A wave round + coupled round), reference (pure Python) and optimized (NumPy) cores, package init. Wave round verified byte-identical to Design A (20 random states). Reference and optimized agree byte-for-byte. Does not touch Candidate A or the frozen primitive.
docs/CC_CORE_V1_ALGEBRA.md answers the eight mandatory structural questions:
j_B is linear in u with slope (1+GAMMA*v); injective in u for every v except the
unique singular value v_star = 195225786 where the slope is 0 and j_B collapses
to 0 for all u. Zero set is exactly {u=0} U {v=v_star} (2p-1 pairs, measure ~2/p).
Replaces Candidate A's generic everywhere-present 2-to-1 fold with a single
measure-1/p singular hyperplane. No algebraic-superiority claim made yet.
curvature_audit/candidate_b_singular_hyperplane.py + artifact. Findings: - j_B(u, v_star)=0 for all u confirmed (collapse). - v_star reachability: 0 hits in 1.28M random coordinates; 0 of 47 family states; 0 transits over T rounds from 400 states (no attractor); v_star not a fixed point. - Constructible: unique constant state c=357959172 maps full lattice to v_star for ONE round (cubic F(c)=v_star has a single GF(p) root). - Path erasure: NONE. Perturbing the full-collapse state changed the digest in 256/256 trials; the singular round zeroes only one round's injection. - Singular set measure ~1/p, same order as Candidate A's injection-zero set. Candidate B does not fail the singular-hyperplane decision criterion.
All 47 zero-collapse states produce distinct Candidate B trajectory digests (47/47, min HD 105, max 157, mean 128.06) -- acceptance condition met. Records clustering by eigenvalue (r) class and amplitude label, plus cross-candidate check (zero state matches A; all nonzero states differ). Min HD 105 > A's 98. Described as separation of the known collision family, NOT collision resistance.
Identical messages/trajectories/seeds/budgets. Findings:
- Structural: A is generic 2-to-1 in u; B is injective in u off the single
v_star hyperplane. B zero set {u=0}U{v=v_star}; A zero set is a parabola.
- Avalanche: A mean 128.6, B mean 127.6 (both ~128). Bias: both max|z|~3.3.
- Truncated 24-bit: neither collides in 4000 (generic). Order sensitivity: 80/80.
- Runtime: A 42.2ms, B 40.3ms per 1-block digest. Memory identical.
- Reduced joint (p=3 full): A img 999 maxmult 33; B img 1054 maxmult 48 (comparable).
p=5 identical; p=7 slice comparable. Neither injective on N=2 toy.
Decision deferred to Part XV (not made on Hamming distance alone).
Coupled map (psi,C)->(psi',C') over p in {3,5,7,11,13} (full joint at p=3,
psi-slice at larger). Findings:
- B image size and max preimage multiplicity comparable to A at every prime;
at p=11 B is injective on the slice (maxmult 1 vs A's 2).
- Singular-coordinate occupancy (v==v_star) tracks the uniform rate 1/p exactly
at every prime; collisions do NOT concentrate on the 1+gamma*v=0 line.
- Neither candidate injective on N=2 toy (degeneracy, not extrapolated).
B does not show substantially worse multiplicity than A.
sympy 1.14.0 and z3 4.16.0 now available. Results: - SymPy: j_B factors as u*(1+GAMMA*v); injection degree 1 in u (vs A's 2). - z3 collision variety j_B(u,v)=j_B(u',v'): SAT (codimension-1, expected). - z3 computer-assisted result: for fixed v != v_star, j_B(.,v)=j_B(.,v) with u != u' is UNSAT -> injective in u off the singular hyperplane. - z3 collapse at v_star: SAT (all u give 0). - z3 one-round coupled 2x2 collision over the REAL prime: UNKNOWN (timeout). - z3 one-round 2x2 preimage over the real prime: UNKNOWN (timeout). Timeouts are explicitly NOT security results; full N=16/T=32 is beyond solvers.
docs/CC_CORE_V1_SHORTCUT_AUDIT.md + module + artifact. Decisive finding: the scalar accumulator degree in u0 is IDENTICAL for A and B ([4,12,36,108,...]), because the shared cross-term gamma*u*v (degree 4 in u0, since v=F(psi) is degree 3) dominates A's removed eta*u^2 (degree 2) and zeta*v (degree 3) terms. The shared self-square A_C*cd^2 then triples the degree each round. So B's lower INJECTION degree does NOT lower the TRAJECTORY degree or the backward-inversion (MITM) degree. Linear predictor ~50% (no shortcut); not affine at 2 rounds; no blockwise factorization. Shortcut resistance no worse than A.
docs/CC_CORE_V1_RESTRICTED_BINDING.md proves, with explicit rigor labels: - [theorem] j_B(.,v) is a bijection in u for every v != v_star (field nonzero multiplier), corroborated by z3 UNSAT. - [theorem] the Design A wave round F is odd; hence for every Phase 8J sign pair (+s*sigma, -s*sigma) the first-round Candidate B injection differs at EVERY cell by exactly 2*s*sigma[x] != 0, INDEPENDENT of the wave output (cannot be cancelled). Candidate A's analogous separation 2s*sigma+2*zeta*F could vanish. - [exhaustive finite verification] all 47 family digests distinct (min HD 105). test_candidate_b.py (32 tests): parity, pinned vectors, j_B equation, v_star, collapse, injectivity off-hyperplane, oddness, sign-pair 2u separation, 47-state separation, order/symmetry, domain separation from A, no path erasure. Forbidden-primitive guard now also scans wavelock/curvature_capacity_v1.
Appends a Phase CC-2 section (CC-1 content preserved). Adds mandatory version identifiers CC-Core-v0-A and CC-Core-v1-B with distinct D_TAGs guaranteeing cc_hash domain separation; verifiers MUST reject mismatched-version transcripts. Candidate B becomes the provisional experimental candidate (survived the singular-hyperplane audit and full-family regression), with no security claim. Specifies normative protocol, prover/verifier roles, verifier complexity (~6.55e5 field ops/block), transcript sizes, and failure conditions. Curvature metrics are diagnostic, never consensus-critical.
CI adds separate steps: Candidate A frozen regression; Candidate B parity + pinned vectors + j_B equation + v_star + collapse + injectivity; singular- hyperplane no-erasure + restricted-binding theorems; full 47-state binding; domain separation + frozen Design A guard. Heavy solver/exhaustive runs stay out of CI (they live in run_audit.py). Path triggers include curvature_capacity_v1. run_audit.py now also runs the six CC-2 modules. Full fast suite: 181 tests pass.
Appends Phase CC-2 section to the results report (CC-1 content preserved). Three-layer separation (path preservation / algebraic binding / hardness) kept strict: no conclusion crosses a layer. 23-point final report answers candidate equation, v_star (195225786), reachability (bounded: unreachable; one constant construction), no path erasure, 47/47 separation (min HD 105), structural and degree comparison (trajectory degree identical [4,12,36,108]), reduced-model and shortcut parity, fixed points/cycles (none), solver results (z3 injectivity UNSAT; coupled timeout), restricted theorems, protocol version, 181 tests, CI. FINAL VERDICT: Candidate B preferred experimentally -- removes Candidate A's generic 2-to-1 weakness; general hardness unresolved (Layer 3 untouched). PR #19 stays draft (research-only); both candidates retained. Residual open item: prove or refute global unreachability of v_star under the message protocol.
rickyjreyes
changed the title
docs/CC_CORE_V1_NORMATIVE_PROTOCOL.md fixes the deterministic map
m -> psi_0(m) -> ... -> psi_T(m): byte domain, length bounds, 192-byte block
padding, byte->element packing (each packed elem in [0, 2^24)), IVs, the exact
absorption rule (only rate cells 0..63 + CAP cells written; cells 67..255 never
injected), per-block T=32 rounds with a non-resetting global round index,
finalization/squeeze, validity (byte strings only; arbitrary lattice states are
NOT valid inputs), and the four-level reachability stratification.
Records the exact structural fact: every coordinate of psi_0(m) lies in
[0, 16777397] U {fixed CAP/IV constants}, all < v_star = 195225786.
…e model docs/CC_CORE_V1_REACHABILITY_MODEL.md defines four separate reachability questions (coordinate / structured-subset / full-lattice / persistent) and characterizes the post-absorption image R_0: - exact: psi_0(m) is an affine byte-bounded image; rate cells 0..63 each range over 2^24 residues; cells 67..255 fixed at IV; CAP1=1464026030 fixed; not surjective; multi-block additively enlarges R. - exact corollary: no coordinate of psi_0(m) equals v_star at round 0. - approximate: F mixes R_0 toward per-coordinate uniform within a few rounds; per-coordinate v_star incidence ~1/p at rounds >=1; no attractor (empirical). Every claim labeled exact / approximate / conjecture.
…ilies Solves F(psi)[x]=v_star via GF(p) cubics (SymPy). For each sign-eigenvector family F(s*sigma)[x]=sigma[x]*g(s), g(s)=s(1+D*lambda+A*B)-A*s^3; solving g(s)=+/-v_star yields amplitudes placing v_star on a structured half-lattice subset (e.g. checkerboard s=1200021354 -> v_star on exactly 128 cells, verified). The constant family root is the unique c=357959172 (full-lattice F(c)=v_star). Crucially SEPARATES algebraically-constructible math states from valid-message reachable states: NONE of these structured/constant states is reachable as psi_0(m), since absorption fixes cells 67..255 at IV (in [123,374]) and bounds rate cells below 2^24 << v_star. Forward t>=1 reachability deferred to Parts V-VII.
Encodes actual message bytes as variables under the normative absorption map. Results: - Round-0 rate cell == v_star: UNSAT (confirms the exact theorem). - Round-0 rate cell == c=357959172: UNSAT (above the 2^24 byte window). - Round-0 fixed cell == v_star: UNSAT (cell holds the IV constant). - Round-1 single rate coordinate == v_star: SAT. z3 found a 191-byte message; REPLAY through the real protocol confirms psi_1[20] == v_star exactly (1 cell). => v_star IS coordinate-reachable at round 1 by a valid message (witness pinned). - Round-1 full constant c*1: UNSAT in one round (rate-controlled slab probe). Coordinate reachability (question A) is therefore YES at round 1; structured/ full-lattice/persistent reachability remain open (Parts VI-VIII). Timeouts (none here) would be UNKNOWN, not unreachability.
Batched wave trajectories over: all 1-byte messages; 1024 two-byte (reduced
alphabet); all binary-alphabet {0,255} messages of length 3-8 (504); and
structured families (all-zero, all-0xFF, alternating, repeated, counters,
periodic, mirrored, low-Hamming). Across the full multi-block wave trajectory:
0 incidental v_star hits; closest centered distance 46. Confirms incidental hits
occur at the ~1/p rate (essentially never for typical messages), consistent with
the Part V witness being solver-constructed. Bounded absence != global proof.
Simulated annealing over the 64 rate-cell injections (maximize round-1 v_star count) reached count=0 (exact modular target is needle-in-haystack for continuous search; best min centered distance ~4539). Direct z3 multi-cell attempts for 2, 3, 4 simultaneous round-1 v_star coordinates returned UNKNOWN (timeout) -- neither SAT nor UNSAT, hence unresolved (NOT a reachability/unreachability result). Only the single-coordinate Part V witness is confirmed. No multi-coordinate or full-lattice singular state found. Full-lattice requires controlling the 192 never-injected cells (impossible at round 0).
For the confirmed witness (psi_1[20]=v_star): the round-0 wave-injection at the hit cell is exactly 0 (erased), but the SAME rate bytes injected G*elem into C at absorption -- so message information is NOT erased from the commitment. Next-round injection at the hit cell is nonzero (sensitivity restored). Collision attempts: 0/64 single-cell perturbations collide; the cell-20 cubic F(u)[20]=v_star has only ONE message-reachable in-window root, so no same-neighbour singular pair exists -> no collision constructible this way. Classification: REACHABLE BUT HARMLESS IN TESTED CASES. No structural collision.
docs/CC_CORE_V1_VSTAR_REACHABILITY.md: - [theorem] round-0 coordinate unreachability for EVERY valid message (every psi_0 coordinate <= 16777589 or a fixed constant, all != v_star=195225786); corollary: constant c*1 not reachable as psi_0. z3 UNSAT corroboration. - [computer-assisted theorem] round-1 single-coordinate reachability: explicit replay-verified 191-byte witness with psi_1[20]=v_star. - [theorem + bounded evidence] the singular hit is harmless: erases only the round-0 wave-injection while the bytes already entered C at absorption; sensitivity restored next round; no collision found. - [exhaustive bounded verification] 0 incidental hits across bounded message sets. - [unresolved] multi-coordinate / full-lattice / persistent reachability (z3 timeouts; no witness).
…iteria + report Reorganizes WAVELOCK_CURVATURE_CAPACITY_RESULTS.md to open with "Current Verdict - Phase CC-3" (verdict, test count, CI status, reachability, merge recommendation, allowed/forbidden claims). Phase 1 / CC-1 / CC-2 conclusions moved under a labeled "Historical results" section; the stale "z3 not installed" note is confined to the Phase-1 historical heading (z3/sympy are installed and used in CC-2/CC-3). History is preserved, not deleted. Appends the CC-3 research-only merge criteria (all met) and the 23-point final report. FINAL VERDICT: Merge research-only -- Candidate B survives the protocol- level singular audit; no security claim; unsafe for production pending Layer-3.
…tests test_cc3_reachability.py (12 tests): exact v_star and constant preimage c; round-0 unreachability bound; pinned 191-byte witness replays to psi_1[20]=v_star (exactly one singular cell); round-0 injection zeroed at the hit; singular-hit commitment sensitivity (digest changes); reference==optimized on the witness; normative-protocol constants and padding; all byte strings valid; version/domain separation; results-doc leads with Current Verdict - Phase CC-3 (stale-headline guard). CI workflow gains an explicit CC-3 reachability step. 205 fast tests pass.
run_audit.py now also runs vstar_one_round_preimages, vstar_message_solver, vstar_bounded_exhaustive, vstar_guided_search, vstar_collision_consequence (heavy/solver runs stay out of ordinary CI).
…cess) curvature_audit/artifacts/cc3_ci_status.json records the real CI result for PR #19 at the CC-3 head: the audit-fast job ran on both push and pull_request events and completed with conclusion SUCCESS (run ids 27788159667, 27788158440). Resolves blocker #2: the legacy combined-status API is empty BY DESIGN (Actions reports via check-runs, not commit statuses) -- so "no combined status" was not a CI failure; the check-runs pass. All ten required check categories are covered by CI steps. Fast suite: 205 passed. No workflow repair was needed (it triggers and passes); the workflow already filters paths to the curvature packages and audit.
rickyjreyes
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June 18, 2026 21:00
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Summary
A research track making the "curvature-capacity" intuition precise, implementing
path-binding candidates, and adversarially falsifying them. Design A
(
wavelock/pde_hash) is untouched; Phase 8J/8K, CC-Core-v0-A, and CC-Core-v1-Bpinned vectors are all preserved. Files only added.
Candidates
wavelock/curvature_capacity/):j_A = u + γuv + ηu² + ζv. Frozenbaseline (
docs/CC_CORE_V0_BASELINE.md).wavelock/curvature_capacity_v1/): linearj_B = u(1+γv). Currentprimary experimental candidate. Distinct
D_TAG/VERSION.Phase CC-3 — singular reachability & merge readiness
The singular value is
v_star = −γ⁻¹ mod p = 195225786(wherej_B(·, v_star) ≡ 0).docs/CC_CORE_V1_NORMATIVE_PROTOCOL.md): bytemessages, 192-byte blocks, rate-only injection (cells 0..63 + CAP), T=32 rounds/block.
ψ_0(m)is≤ 16,777,589or a fixed constant — all
< v_star. So no valid message reachesv_starbefore thefirst wave round (z3 UNSAT corroboration). The constant preimage
c·1(c=357959172)is likewise not message-reachable as
ψ_0.message with
ψ_1[20] = v_star(exactly one singular coordinate), replay-verifiedthrough reference == optimized. So coordinate reachability is YES at round 1.
wave-injection, but the same rate bytes already injected into C at absorption
(
C[c] += G·elem); round-1 injection is nonzero; 0/64 single-cell perturbationscollide and the cell-20 cubic has only one in-window root (no same-neighbour pair).
No valid-message structural collision found.
annealing count 0; 0 incidental hits across all bounded/structured messages).
Details:
docs/CC_CORE_V1_REACHABILITY_MODEL.md,docs/CC_CORE_V1_VSTAR_REACHABILITY.md.Artifacts:
vstar_one_round_preimages,vstar_message_solver,vstar_bounded_exhaustive,vstar_guided_search,vstar_collision_consequence,cc3_ci_status(all incurvature_audit/artifacts/).CI (actual, not "green locally")
GitHub Actions
audit-fastruns on PR #19 (push + pull_request events) and completeswith conclusion success on the CC-3 head (run ids 27788159667 / 27788158440;
cc3_ci_status.json). The legacy combined-status API is empty by design (Actionsreports via check-runs, not commit statuses) — that was the only "missing status", and
it is not a failure. 205 fast tests pass.
Research-only merge criteria — all met
Design A untouched ✔ · Candidate A frozen ✔ · explicit versioning ✔ · all fast tests
pass ✔ · actual CI checks pass ✔ · no valid-message structural collision ✔ ·
v_starround-0 unreachable + round-1 reachable-but-harmless ✔ · code isolated, no production
import ✔ · "no security claim" stated ✔ · PR labeled experimental ✔.
A Layer-3 hardness proof is not required to merge research-only, but is required
before any security/production claim. Next Layer-3 problem: a genuine lower bound on
second-preimage/collision cost (untouched for both candidates).
🤖 Generated with Claude Code
https://claude.ai/code/session_01BqTM7VZ2gMtmTmwLH6vx22