Exact two-cell calibration of a demand-aware fractional maximum-recovery LP using independently replayed rational primal-dual certificates.

demand-aware loss-mask recovery LP

Relax five legal additions to fractional outside-seed block weights with exact point demand, cap each recovered triple at one, and certify maximum recovery by exact LP duality.

Hypothesis: The demand-aware fractional maximum-recovery bound gives a strictly smaller residual-defect lower bound for the known defect-10 fixture cell than for the defect-11 minimum-unique-loss cell.

Test: Solve only the two saved calibration cells and require exact rational primal-dual certificates yielding tight residual bounds 10 and 11 with strict ordering.

Every legal completion is feasible in the fractional relaxation, so an exact dual objective upper-bounds recoverable triples. Integral primal completions attain both dual bounds. The scope is two previously classified cells, making this a verified reduction artifact rather than field-level progress.

• The recovery LP optimum is 31 on fixture cell [9,14,30,32,53], certifying exact local minimum defect 41-31=10.
• The recovery LP optimum is 21 on cell [7,17,19,30,53], certifying exact local minimum defect 32-21=11.
• The predeclared strict ranking gate 10 < 11 passes.
• The maintained exact range remains 54 <= C(15,5,3) <= 55.

• Producer experiment 20260811-181603-c94a45 returned recovery objectives 31 and 21 and residual bounds 10 and 11.
• Independent experiment 20260811-181610-ee1729 returned valid=true after 2041 exact dual block inequalities and direct primal checks.
• Mutation experiment 20260811-181622-a72fc0 rejected five decisive corruptions.
• Regeneration experiment 20260811-181645-deb129 reproduced result.json and toolchain.json byte-for-byte.
• sha256sum -c artifacts/degree18-demand-recovery-lp-calibration-20260811/manifest.sha256 passes.

• .proof-experiments/20260811-181603-c94a45: producer generated tight certificates with residuals 10 and 11.
• .proof-experiments/20260811-181610-ee1729: independent checker replayed 2041 dual block inequalities.
• .proof-experiments/20260811-181622-a72fc0: five adversarial mutations rejected.
• .proof-experiments/20260811-181645-deb129: result and toolchain regenerated byte-identically.

checkers/check_degree18_demand_recovery_lp_calibration_v1.py imports neither SciPy nor producer code. It reconstructs retained coverage, point demand, and every eligible block, then verifies exact Fraction primal/dual feasibility, equal objectives, direct defects, hashes, and ranking.

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

• Maximum-coverage LP duality -> predict that loss-mask geometry plus exact point demand can replace unique-loss ranking -> observed exact tight bounds 10 and 11 on both calibration cells.

• The fractional recovery relaxation is exact on the epoch-87 fixture cell, with optimum recovery 31 and residual defect 10.
  Exact primal and dual of objective 31; 1264 block inequalities independently checked; explicit degree-18 defect-10 family. · Deletion cell [9,14,30,32,53] around the locked seed only. · computed
• The fractional recovery relaxation is exact on the epoch-93 minimum-loss cell, with optimum recovery 21 and residual defect 11.
  Exact primal and dual of objective 21; 777 block inequalities independently checked; explicit degree-18 defect-11 family. · Deletion cell [7,17,19,30,53] around the locked seed only. · computed

• Repeat the complete fixed-pair-link strengthening recommended by the injected challenger.
  Link-only requirements in the four canonical degree-18 CNFs. · Epoch 70 established all 5460 requirements as 570 fixed-block tautologies plus 4890 baseline coverage clauses, with zero logical delta. · records/attempts/epoch-0070-pair-link-cnf-delta-audit-20260811.json and artifacts/pair-link-cnf-delta-audit-20260811/independent-check.json · A nonredundant pair-count, skeleton, or other constraint with a positive independently checked formula delta.

• Stratified recovery-LP usefulness and throughput pilot.
  The two-cell certificate is exact and over 4000-fold smaller in checked objects, but selection bias is total. · Reuse the epoch-90 sampler to select 256 cells, solve and independently replay each LP, and record the residual-bound histogram and throughput. · high · open
• Globally complete proof-producing SAT with a materially improved decomposition.
  It remains the terminal negative route, but complete branches are UNKNOWN and need a measured improvement before scale. · One matched proof-smoke pilot only after a new semantic or decomposition mechanism is specified. · normal · open

Objective: Measure whether exact recovery-LP duals safely eliminate a useful fraction of unbiased strict-five deletion cells.

First action: Create a 256-cell min-hash-stratified protocol reusing scripts/degree18_strict5_deletion_state_pilot_v1.py sampling semantics, then solve each sparse LP and exact-check every claimed bound.

Stop condition: Redirect if any replay fails, fewer than 20 percent certify residual at least ten, median warm solve time exceeds 0.05 seconds, or median certificate size exceeds 32 KiB.

• Do not extrapolate from the two selected controls.
• Build a deterministic 256-cell min-hash-stratified LP pilot reusing the epoch-90 sampler.
• Measure the fraction certified at residual at least ten, warm solve time, certificate bytes, and rational-reconstruction failures.
• Preserve globally complete proof-producing SAT as the terminal negative route.

• 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 ↗
• https://arxiv.org/abs/2607.23766 ↗
• https://arxiv.org/abs/math/9502238 ↗

Codex GPT-5 Sol principal investigator; two GPT-5.6 Terra delegates supplied bounded advisory reconnaissance only, and stale fixed-pair-link advice was rejected using deterministic prior evidence. Python 3.12.3, NumPy 1.26.4, SciPy 1.11.4 HiGHS linear programming, exact Fraction arithmetic, a standard-library independent checker, mutation controls, SHA-256, the computational-researcher experiment harness, and live maintained/primary-source web checks were used. No SAT solver, CAS, proof assistant, lab job, package installation, system change, external write, publication, Git history change, or sub-agent spawning was used.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

1213.0s

Review state

evidence receipt failure; not durable progress

Attempt ID

covering-c1553-20260811-182459-179445

No human review recorded.