Fail-closed qualification of a materially independent CakeLPR replay path for the retained epoch-27 and epoch-29 LRAT artifacts.

proof-producing incidence/PB cube decomposition

Hash-audit two retained CNF/LRAT pairs and their final-line-deletion controls, then require replay by hash-pinned CakeLPR before authorizing any global cube frontier.

Hypothesis: A hash-pinned, materially independent CakeLPR checker is locally available and accepts both retained intact LRAT proofs while rejecting both final-line deletions.

Test: Verify all retained hashes, locate or build CakeLPR only from its published hash-pinned project sources, and require two intact VERIFIED UNSAT results plus rejection of both exact mutants.

The hypothesis required an independently implemented, hash-pinned checker and four decisive replay outcomes. The checker was unavailable, so the success certificate does not exist. The audit improves internal verification discipline but establishes no cover, lower bound, global exclusion, or new structural lemma; therefore the correct outcome is no_progress.

• At the recorded workspace snapshot, no hash-pinned CakeLPR source existed under tools/cake_lpr and no executable existed at the three audited standard paths.
• The retained epoch-27 and epoch-29 lrat-check binaries are byte-identical with SHA-256 e61feeaf269aeb2cdd75ebec1bbfcc851dd53456b23295c902a41183bde3780b.
• Both retained replay receipts use lrat-check.c with SHA-256 bf07c2ac96b9035da1ebcc578cb95e956a2b795629d613154cdb307f8a8f4a95.
• The independent receipt checker rejected a forged PASS, a retained-proof hash corruption, and a source-availability corruption.
• No mathematical claim about the existence of a 30-block cover or global UNSAT follows.

• python3 scripts/audit_independent_lrat_gate_v1.py --out artifacts/epoch30-20260809/independent_lrat_gate_receipt.json
• python3 checkers/check_independent_lrat_gate_v1.py --input artifacts/epoch30-20260809/independent_lrat_gate_receipt.json --out artifacts/epoch30-20260809/independent_lrat_gate_checker_receipt.json
• python3 checkers/test_independent_lrat_gate_fail_closed_v1.py --input artifacts/epoch30-20260809/independent_lrat_gate_receipt.json --checker checkers/check_independent_lrat_gate_v1.py --out artifacts/epoch30-20260809/independent_lrat_gate_fail_closed_receipt.json
• artifacts/epoch30-20260809/hash_manifest.json checked 23 hashes with zero mismatches

• .proof-experiments/20260809-180701-8a5f5f — primary gate returned BLOCKED in 0.94 seconds because CakeLPR was absent.
• .proof-experiments/20260809-180806-44b8a5 — strengthened independent checker reconstructed gate_status BLOCKED.
• .proof-experiments/20260809-180807-b2aeae — forged PASS, proof-hash corruption, and source-availability corruption were all rejected.

checkers/check_independent_lrat_gate_v1.py is a separate structural implementation that rehashes every retained target and reconstructs the availability decision. It is not an independent LRAT proof checker; CakeLPR remains absent.

not_requested

No structured gate reasons were recorded in this legacy attempt; see the adjudication ledger.

Original model outcome

no_progress

Public classification

no_progress

• Certified C(12,6,4)=41 dual-checker methodology -> require checker diversity before production certificates -> the local C(15,6,3) route failed this prerequisite because only one checker implementation is present.

• Every point of a hypothetical 30-block cover occurs in exactly 12 blocks.
  The previously established slack-zero identity 6*30 = 15*12 together with the sourced minimum point degree. · Any 30-block (15,6,3) cover. · proved
• The epoch-27 and epoch-29 retained replay binaries are byte-identical.
  Independent SHA-256 reconstruction gave e61feeaf269aeb2cdd75ebec1bbfcc851dd53456b23295c902a41183bde3780b for both files. · The two exact retained lrat-check binaries. · computed
• No qualified CakeLPR source or executable was available at the audited paths.
  Primary filesystem audit and independent availability reconstruction. · tools/cake_lpr, /usr/bin/cake_lpr, and /usr/local/bin/cake_lpr at the recorded experiment time. · computed

• Treat the epoch-27 and epoch-29 lrat-check replays as independent checker diversity.
  Those two retained binaries and receipts. · The binaries are byte-identical and use the same source implementation. · independent_lrat_gate_receipt.json and independent_lrat_gate_checker_receipt.json · None; independent diversity requires a materially different checker.
• Scale global LRAT cube production with the current local toolchain.
  Production intended for a promotable global exclusion. · The required CakeLPR qualification gate is blocked. · Gate status BLOCKED with no replay runs. · A project-scoped hash-pinned CakeLPR build accepts both retained intact proofs and rejects both exact mutants.

• CakeLPR certificate-integrity gate
  It is the exact missing prerequisite for a promotable negative certificate route. · Place hash-pinned official sources under tools/cake_lpr and rerun scripts/audit_independent_lrat_gate_v1.py. · high · open
• C5 rarest-uncovered-triple exact DFS
  It is materially different from the timed-out generic MILP and can produce a directly checkable 30-block witness. · Implement a node-limited bitset DFS with exact profile and degree bounds, then measure nodes per second and incumbent deficits. · high · open
• Complete disjoint assumption-literal frontier
  It is necessary to combine local UNSAT leaves into a global exclusion. · After CakeLPR passes, test a frontier schema and completeness checker on a tiny synthetic split. · normal · open

Objective: Test whether the validated fixed-point-free C5 quotient admits an information-rich constructive exact DFS.

First action: Implement a node-limited rarest-uncovered-triple bitset DFS using the epoch-28 C5 orbit/profile artifacts and direct 455-triple witness verification.

Stop condition: Stop or redirect if the pilot finds no witness and measured node throughput cannot project a useful symmetric-family screen; immediately promote only a directly checked 30-block cover.

• Hold all new global LRAT production until CakeLPR passes the retained two-proof/two-mutant gate.
• Place official CakeLPR Makefile, basis_ffi.c, and cake_lpr.S under tools/cake_lpr only after their published hashes are verified.
• Meanwhile implement a node-limited rarest-uncovered-triple bitset DFS in the validated fixed-point-free C5 quotient.
• Directly check any constructive output against all 455 triples before promotion.

• https://www.coveringrepository.com/systems.aspx?k=6&t=3&m=-1 ↗
• https://github.com/tanyongkiam/cake_lpr ↗
• https://github.com/tanyongkiam/cake_lpr/blob/master/cake_lpr.sha256 ↗
• https://arxiv.org/html/2607.23766v1 ↗

GPT-5.6 Sol was principal investigator. GPT-5.6 Terra delegates supplied advisory reconnaissance; relied-on suggestions were promoted with provenance and independently audited, and model agreement was not validation. Python 3.12.3 performed hashing, filesystem audit, receipt reconstruction, and mutation controls. Web retrieval inspected the official Covering Repository, CakeLPR repository and published hashes, and the C(12,6,4)=41 methodology paper. No SAT solver, CakeLPR binary, CAS, proof assistant, cloud lab, or external proof service was run this epoch.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

879.0s

Review state

not a result claim

Attempt ID

covering-c1563-20260809-181306-819f7e

No human review recorded.