Freeze and exactly certify the first 512 lexicographic strict-five deletion cells around the locked degree-18 defect-10 seed using sparse maximum-recovery LP duals.

demand-aware loss-mask recovery LP certificate sharding

A fractional maximum-coverage LP upper-bounds how many post-deletion uncovered triples any exact-demand five-addition completion can recover; exact sparse scaled duals certify integer residual lower bounds cell by cell.

Hypothesis: Every strict five-delete/five-add exact-demand repair in lexicographic deletion ranks 0 through 511 leaves at least 11 triples uncovered, and all exact scaled-dual certificates can be independently replayed in under 60 seconds.

Test: Produce one exact sparse dual for each frozen rank, independently unrank every deletion and replay every inequality with Python big integers, redirect on any bound at most 10, reject six corruptions, and regenerate stable bytes.

Every legal distinct five-addition repair is feasible in the fractional recovery LP, so a feasible exact dual upper-bounds its recovered triples. Subtracting that upper bound from the post-deletion uncovered count and taking the ceiling gives a sound integer residual lower bound. Independent big-integer replay validates the bounded claim, while its narrow local scope prevents promotion to a covering-number result.

• For every lexicographic five-block deletion rank from 0 through 511 around the locked degree-18 seed, every strict outside-seed exact-demand five-addition completion leaves at least 14 triples uncovered.
• The exact integer residual-bound histogram on these 512 cells is {14:2,15:1,16:10,17:17,18:41,19:86,20:153,21:133,22:56,23:12,24:1}.
• The 512 cells are disjoint from the prior immutable 256-cell LP corpus.
• The maintained exact range remains 54 <= C(15,5,3) <= 55.

• Producer experiment 20260811-201751-4fa7d4 generated 512 duals with certificate SHA-256 eb33f70bbb9c432c51cef2acdeb6b3dbb17cc441d1c773b82e2267ec969f8521.
• Independent experiment 20260811-201824-50d0a5 returned valid=true after unranking ranks 0..511 and replaying 626773 inequalities.
• Mutation experiment 20260811-201834-ea490c rejected rank, deletion, coefficient, objective, residual and missing-row corruptions.
• Regeneration experiments 20260811-201904-5ad30e and 20260811-201930-dffbdd reproduced certificates, deterministic gzip, toolchain, and all stable summary/control fields.
• Overlap experiment 20260811-202011-8b0b1a found zero overlap with the prior 256-cell corpus.
• Final manifest experiment 20260811-202211-9e6fea passed every frozen SHA-256 entry.

• .proof-experiments/20260811-201751-4fa7d4: producer generated 512 exact sparse duals; minimum residual bound 14.
• .proof-experiments/20260811-201824-50d0a5: independent checker replayed ranks 0..511 and 626773 inequalities.
• .proof-experiments/20260811-201834-ea490c: all six mutations were rejected.
• .proof-experiments/20260811-201904-5ad30e and 20260811-201930-dffbdd: stable artifacts regenerated byte-identically.
• .proof-experiments/20260811-202011-8b0b1a: zero overlap with the prior 256-cell corpus.
• .proof-experiments/20260811-202211-9e6fea: final frozen manifest passed.

checkers/check_degree18_demand_recovery_lp_lex_shard_v1.py imports neither the producer, NumPy, SciPy, nor a solver. It independently combinatorially un-ranks each deletion, reconstructs all geometry and eligible blocks, and replays every sparse dual constraint, objective, residual, histogram and hash using Python arbitrary-precision integers.

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

• Exact LP proof logging -> predict small replayable local exclusion shards -> observed 512 cells and 626773 inequalities in a 248169-byte canonical packet.
• Canonical rank sharding from exhaustive search -> predict collision-free union-ready coverage without risky symmetry -> independently observed exact ranks 0..511 and zero overlap with the prior sample.

• Every exact-demand strict five-addition completion for lexicographic deletion ranks 0..511 has residual defect at least 14.
  certificates.jsonl SHA-256 eb33f70bbb9c432c51cef2acdeb6b3dbb17cc441d1c773b82e2267ec969f8521 and independent-check.json valid=true after 626773 inequalities. · Exactly 512 labelled deletion cells around seed SHA-256 3e83de2272aaf5fa18b6167ba384ac6722bd4f03d49c6b1ca3979e98c3f80462; strict outside-seed exact-demand five additions. · computed
• The complete residual-bound histogram on the shard ranges from 14 through 24 with the recorded counts.
  Producer result and independent histogram reconstruction agree exactly; regeneration stable fields match. · The same frozen 512-cell shard. · computed
• The current shard is disjoint from the prior 256-cell LP certificate corpus.
  overlap-audit.json valid=true, overlap_count=0, with both certificate hashes recorded. · Only comparison against the immutable epoch-95 256-cell corpus. · computed

• Reach residual defect at most 13 by strict exact-demand five-addition completion after deleting any rank 0..511 cell.
  All legal completions in those 512 labelled deletion cells around the locked seed. · Every cell has an independently replayed LP-dual integer residual lower bound at least 14. · independent-check.json valid=true and hash-bound certificates.jsonl. · A demonstrated LP-duality/sign error, rank omission, geometry mismatch, certificate corruption, or change to the seed/move model.
• Repeat the injected complete fixed-pair-link strengthening as a new discriminator.
  All 5460 link-only requirements in the four canonical degree-18 CNFs and the earlier 754-target relaxation. · Epoch 70 found zero semantic CNF delta, while the complete necessary relaxation retained every target. · artifacts/pair-link-cnf-delta-audit-20260811/independent-check.json and artifacts/type4-complete-pair-link-gate-20260809/independent-check.json. · A new labelled semantic constraint with independently checked positive formula delta and non-subsumption.

• Approval-gated complete strict-five recovery-LP census for the locked seed.
  The first disjoint shard has exact coverage, compact certificates, fast replay and minimum residual 14, making a complete local exclusion operationally feasible, though not globally decisive. · After approval, freeze the complete 3089-shard rank manifest, union checker, checkpoint/progress schema and stop thresholds before submitting any lab job. · normal · open
• Globally complete proof-producing SAT with independently audited positive semantic delta.
  This is the terminal negative route; stale pair-link constraints add no information, so a new cut or decomposition must first show non-subsumption and matched benefit. · Audit one proposed cut against the baseline clause semantics, then run one paired proof-emitting cube only if the delta is positive. · high · open
• Constructive exact-degree search beyond strict five-for-five moves.
  A 54-cover is the shortest terminal certificate, while the local LP evidence only freezes one radius-five basin around a defect-10 seed. · Specify a bounded radius-six or ejection-chain neighborhood with incremental exact deltas and require an independently replayed defect below 10. · high · open

Objective: Choose between approval-gated complete local classification and a more globally valuable terminal-route pilot.

First action: If approval is granted, draft and independently validate the 3089-shard union protocol without launching it; otherwise audit one proposed global SAT semantic cut for positive non-subsumed delta.

Stop condition: Do not launch the census without approval; redirect the SAT route if semantic delta is zero or matched telemetry does not improve by the predeclared threshold.

• Do not extrapolate the ranks 0..511 histogram to the other deletion cells, other seeds, other move radii, or the global covering problem.
• Do not rerun the fixed-pair-link strengthening without an independently checked positive semantic delta.
• Obtain explicit approval of the local full-census claim, shard manifest, checkpoint/progress schema, compute cap and union checker before any lab submission.
• If full-census approval is absent, select between a positive-semantic-delta global SAT proof-smoke and a bounded radius-six constructive search by matched expected validated uncertainty reduction.

• https://www.coveringrepository.com/systems.aspx?k=5&t=3&m=-1 ↗
• https://ljcr.dmgordon.org/cover/show_cover.php?k=5&t=3&v=15 ↗

OpenAI Codex (GPT-5-based) acted as the Sol principal for synthesis, protocol design, implementation and audit. Two gpt-5.6-terra delegates supplied advisory reconnaissance only; their roles and source hashes are preserved in sources/advisory/terra-epoch97-recon-20260811.json and their agreement was not treated as validation. Deterministic computation used CPython 3.12.3, NumPy 2.1.3, SciPy 1.14.1 with HiGHS via scipy.optimize.linprog, standard-library arbitrary-precision integers, gzip, SHA-256 and GNU sha256sum. No CAS, proof assistant, SAT solver or external human validator was used this epoch.

Duration

1085.7s

Review state

evidence receipt failure; not durable progress

Attempt ID

covering-c1553-20260811-202932-51235f

No human review recorded.