Denominator-cleared sparse integer encoding and two-implementation exact replay of the immutable 256-cell demand-recovery LP dual corpus.

demand-aware loss-mask recovery LP certificate compression

Clear one denominator per LP dual, store sparse scaled coefficients, replay every dual inequality with packed signed-int64 arithmetic, and independently reconstruct them with unbounded scalar integers.

Hypothesis: The denominator-cleared encoding exactly reproduces all 256 rational duals, replays all 373112 block inequalities under both packed and scalar integer arithmetic, and reduces canonical certificate bytes by at least 4x without exceeding signed 31-bit coefficients.

Test: Integerize the hash-bound epoch-95 corpus, require coefficient-for-coefficient equivalence, replay every inequality twice with materially different arithmetic, measure storage and time, reject nine corruptions, and regenerate certificate bytes.

Coefficient-level equality and two materially different exact replays establish preservation of the bounded certificates. The experiment adds no new certificate or mathematical scope, so it cannot change the covering-number bound.

• The sparse denominator-cleared encoding exactly represents all 256 epoch-95 rational dual certificates and preserves their residual-bound histogram.
• All 373112 source dual block inequalities pass guarded packed signed-int64 replay and independent unbounded scalar-integer replay.
• Canonical storage decreases from 1507709 to 118642 bytes; deterministic gzip occupies 20423 bytes.
• The maintained exact range remains 54 <= C(15,5,3) <= 55.

• Producer experiment 20260811-194445-7933e4 checked 256 cells and 373112 inequalities in 2.123224697075784 seconds with maximum coefficient width 9 bits.
• Independent experiment 20260811-194502-38817f returned valid=true after source-Fraction equality and complete scalar replay.
• Mutation experiment 20260811-194603-f162f7 rejected all nine corruptions.
• Regeneration experiments 20260811-194631-a067e1 and 20260811-194640-585062 reproduced compact JSONL, gzip, and toolchain byte-for-byte.
• Manifest experiment 20260811-194850-510a9d returned success for every frozen entry.

• .proof-experiments/20260811-194445-7933e4: producer passed every compression, coverage, width, timing, and overflow gate.
• .proof-experiments/20260811-194502-38817f: independent checker matched every source coefficient and replayed 373112 inequalities.
• .proof-experiments/20260811-194603-f162f7: nine mutations were rejected.
• .proof-experiments/20260811-194631-a067e1 and 20260811-194640-585062: compact projections regenerated byte-identically.
• .proof-experiments/20260811-194850-510a9d: frozen manifest replay passed.

checkers/check_degree18_demand_recovery_lp_integer_replay_v1.py imports neither producer nor NumPy. It reconstructs deletion geometry and eligible blocks, matches every coefficient to the source Fraction certificate, and checks dual constraints, objectives, residual ceilings, hashes, gzip, counts, and compression arithmetic with unbounded 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

• Proof-certificate integerization -> predict exact replay without Fraction overhead -> observed full agreement on 256 duals and 373112 inequalities.
• Sparse proof logging -> predict storage rather than mathematical reduction -> observed 12.708x canonical and 73.824x gzip compression with zero new cells classified.

• All 256 epoch-95 rational recovery-LP duals have exact sparse scaled-integer representations that pass complete dual replay.
  compact-certificates.jsonl SHA-256 7fca6c80840c1ee60bf1cad0532bc4c543ae5bb0972091911f58f21f445b26c7 and independent-check.json valid=true · Exactly the immutable 256-cell epoch-95 corpus. · computed
• The compact corpus occupies 118642 canonical bytes and 20423 deterministic gzip bytes while preserving the source histogram.
  result.json, independent-check.json, and regeneration-check.json · The fixed corpus and recorded Python 3.12.3 toolchain. · computed

• Repeat the complete fixed-pair-link strengthening as a new route.
  All 5460 link-only requirements in the four canonical degree-18 CNFs. · The complete audit classified every requirement as a fixed-block tautology or existing coverage clause; logical delta is zero. · artifacts/pair-link-cnf-delta-audit-20260811/independent-check.json · A new labelled semantic constraint with independently checked positive formula delta.
• Use verbose Fraction JSON as the only storage/replay format.
  The 256 epoch-95 certificates. · A source-equivalent sparse integer format is independently verified and 12.708x smaller canonically. · result.json and independent-check.json · A certificate outside the guarded integer envelope or failure of integer replay.
• Infer all-cell or global exclusion from the compressed pilot.
  The other 3162254 deletion cells and the global C(15,5,3) problem. · Compression preserves the same 256 local certificates and adds no mathematical coverage. · Protocol scope and one-to-one source coefficient checks. · A complete all-cell census or proved global reduction connecting these cells to every 54-cover.

• Approval-gated segmented full deletion-cell recovery census.
  Replay and storage gates pass strongly, but production coverage and global usefulness remain unmeasured. · Draft an immutable chunk map, checkpoint/progress schemas, bounded chunk pilot, and exact union checker; do not submit the full job before approval. · high · open
• Globally complete proof-producing SAT with a positive semantic delta.
  This remains the terminal negative route; prior branches are UNKNOWN and link-only additions are redundant. · Specify one new semantic cut or decomposition, prove nonzero formula delta, and run a matched proof-smoke pilot. · normal · open
• Constructive exact-degree search beyond closed radius-five neighborhoods.
  A 54-cover is the shortest terminal certificate and the current seed has defect 10. · Design a radius-six or ejection-chain family and stop unless an independently replayed state beats defect 10. · normal · open

Objective: Compare the approval-gated recovery census with genuinely terminal constructive and SAT routes.

First action: Present the full-census chunk and validation scope for approval; if not approved, specify a new radius-six move family and below-defect-10 stop gate.

Stop condition: Hold recovery scale-up on withheld approval, failed coverage, replay mismatch, or impractical production; redirect constructive work that cannot beat defect 10 and SAT work with zero semantic delta.

• Do not report storage compression as elimination of any additional cell or global branch.
• Before an all-cell lab submission, obtain explicit human approval of the chunk manifest, checkpoint/progress schema, compute cap, independent union checker, and stop thresholds.
• If approval is absent, run a genuinely new radius-six/ejection constructive pilot or audit a global SAT encoding with positive semantic delta.
• Preserve the compact format and scalar checker as reusable certificate infrastructure.

• 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 ↗

Codex GPT-5 Sol acted as principal investigator. Two GPT-5.6 Terra delegates supplied bounded advisory route-selection and verification-design memos; their agreement was not evidence. Sol independently audited all decisive artifacts. Deterministic work used Python 3.12.3, NumPy 1.26.4, standard-library Fraction and arbitrary-precision integers, gzip, SHA-256, mutation testing, and the computational-researcher experiment harness. Live web checks used the maintained LJCR record and exact-phrase searches. No SAT solver, CAS, proof assistant, lab job, package installation, system change, external write, publication, or newly spawned sub-agent was used.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

1055.7s

Review state

evidence receipt failure; not durable progress

Attempt ID

covering-c1553-20260811-195459-b1dfb1

No human review recorded.