Deterministic 10000-cell min-hash-stratified pilot of exact residual-state memoization across strict five-deletion cells of the locked defect-ten degree-18 seed.

deletion-demand residual-state memoization

Identify cells only when their exact 15-coordinate insertion-demand vectors and retained 455-triple coverage masks coincide.

Hypothesis: The 10000 min-hash-stratified deletion cells collapse to at most 78 exact residual states, giving at least 128x compression.

Test: Regenerate 100 minimum-hash cells in each of 100 equal combinadic-rank strata, count exact state keys, and independently reconstruct sample membership and every key.

Exact-key equality is sound for reuse, but no sampled keys coincide. This falsifies the predeclared sample hypothesis and removes the rationale for scaling while implying nothing about unsampled cells or the global optimum.

• The locked seed is a simple 54-block family with point degrees 18^15.
• The sample contains exactly 10000 distinct deletion cells, 100 from each of 100 strata.
• All 10000 sampled cells have distinct exact residual states.
• Measured sample compression is exactly 1.0x and the 128x gate fails.

• Experiment 20260811-150844-9626e2 returned distinct_states=10000 and compression_gate_passed=false.
• Experiment 20260811-150913-cb1d3b checked all selection and state records with valid=true.
• Experiment 20260811-151112-80b0e3 rejected five adversarial mutations.
• sha256sum -c artifacts/degree18-strict5-deletion-state-pilot-20260811/manifest.sha256 passes.

• .proof-experiments/20260811-150844-9626e2: producer found 10000 singleton states.
• .proof-experiments/20260811-150913-cb1d3b: independent checker matched all records.
• .proof-experiments/20260811-151112-80b0e3: five mutations rejected.

check_degree18_strict5_deletion_state_pilot_v1.py imports no producer code; it uses complete per-stratum sorting instead of heaps and triple-count decrements instead of undeleted-mask ORs.

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 dynamic-programming memoization -> predict repeated residual states -> no repeats occurred in the stratified sample, so the transfer failed its cheapest discriminator.

• All 10000 sampled cells have pairwise distinct exact residual-state keys.
  Producer and checker agree on histogram {1:10000} and the multiset digest. · Protocol-v1 sample around the locked seed only. · computed
• Equality of the exact key is a sound completion-reuse relation.
  Equal demand gives identical degree constraints and equal retained coverage gives an identical objective for every common addition set. · Strict outside-seed five-addition completions from the fixed seed. · proved

• Scale the full exact demand/retained-coverage census under the 128x protocol.
  Protocol-v1 scale-up decision; not a claim about unsampled duplicates. · The checked sample has 10000 singleton keys versus the at-most-78 gate. · result.json and independent-check.json · A proved coarser equivalence or dominance relation with an independently checked material-compression pilot.

• Incoming-first coverage-aware exact-degree repair.
  Epoch 46 showed that degree closure is easy but outgoing-first moves damage coverage. Reverse the construction order and constrain loss directly. · Reproduce the epoch-87 boundary fixture, then run a tiny fixed anchor tranche and require independently checked defect below ten. · high · open
• Sound coverage-loss dominance bound.
  A one-sided recoverability bound could eliminate cells without requiring identical masks. · Derive and test the cheapest matching or LP bound on the fixed cell and a small control sample. · normal · open

Objective: Test materially new coverage-aware exact-degree repair geometry without reopening epoch-46's failed kernel.

First action: Specify additions-first missing-triple anchors and solve for outgoing blocks with identical point incidence and a hard unique-triple-loss budget.

Stop condition: Redirect if the kernel misses the boundary fixture, violates direct checks, duplicates epoch 46, or yields no defect-below-ten family in the fixed tranche.

• Do not run the full exact-state census without a new proved bulk reduction.
• Keep the epoch-46 ejection-chain protocol closed.
• Fixture-gate an incoming-first, loss-budgeted repair kernel.
• Hold global proof SAT until a new branch yields replayable LRAT or passes a matched gate.

• 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 acted as Sol principal, audited the injected Terra memos, corrected the advisory gate arithmetic, designed and executed the experiments, and interpreted the result. Two injected GPT-5.6 Terra delegates supplied advisory reconnaissance only; one memo was truncated/erroring and neither was treated as evidence. CPython 3.12.3 standard-library programs used arbitrary-precision bitsets and SHA-256. The experiment wrapper captured commands, limits, logs, versions, and hashes. Web search checked maintained sources and literature. No SAT solver, CAS, proof assistant, newly spawned sub-agent, package installation, or external write was used.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

1273.5s

Review state

evidence receipt failure; not durable progress

Attempt ID

covering-c1553-20260811-152022-2fadd6

No human review recorded.