Exact degree-demand census of the four-delete/three-add shell around Iorio's maintained 55-cover

degree-regular local-shell capacity census

Enumerate all four-block deletion headers, derive the forced three-block point-demand vector from degree 18, count unordered distinct completions by demand profile, and exclude source-block reintroductions exactly.

Hypothesis: The exact degree-balanced four-delete/three-add shell around Iorio's 55-cover contains at most 50000000 candidate completion triples after additions are required to lie outside all 55 source blocks.

Test: Count every degree-feasible header and exact-shell completion; advance only if an independent reconstruction agrees and the total is at most 50000000.

The predeclared count was below 50000000, producer and materially different checker agree on all rows and aggregates, and the result precisely separates three source-block conventions. The evidence supports advancing to coverage scoring but not a covering-number claim.

• Exactly 33100 of the 341055 four-block deletion headers are degree feasible.
• There are exactly 46255242 unordered distinct degree-realizing completion triples before excluding source blocks.
• There are exactly 43928064 exact-shell candidates when all three additions must lie outside the 55-block source cover.
• There are exactly 44716332 candidates when additions need only avoid the 51 retained source blocks.

• python3 scripts/degree18_4for3_preflight_v1.py --cover sources/ljcr-c1553-55.txt --protocol artifacts/degree18-4for3-preflight-20260812/protocol.json --output-dir artifacts/degree18-4for3-preflight-20260812
• python3 checkers/check_degree18_4for3_preflight_v1.py --cover sources/ljcr-c1553-55.txt --manifest artifacts/degree18-4for3-preflight-20260812/header-counts.jsonl --producer-result artifacts/degree18-4for3-preflight-20260812/result.json --output artifacts/degree18-4for3-preflight-20260812/independent-check.json --mutations-output artifacts/degree18-4for3-preflight-20260812/mutation-controls.json
• Header ledger SHA-256 e45fa5d6d41c4ee623482782efdca449dc51bd6d85ee0f1b064f1f3fce781fe5; independent status pass.

• .proof-experiments/20260812-094440-f95521: first producer implementation timed out at 180 seconds and supports only the optimization lesson
• .proof-experiments/20260812-094911-e605d8: optimized producer completed in 16.733 seconds and returned 43928064
• .proof-experiments/20260812-094954-fa5af6: independent checker completed in 52.339 seconds and passed

checkers/check_degree18_4for3_preflight_v1.py uses pointwise three-bin DP and explicit source-containing triple sets, unlike the producer's multinomial formula and inclusion-exclusion.

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-pinnability local search -> degree-demand compression predicts a sub-50M next shell -> observed 43928064 exact-shell candidates.

• Exactly 33100 deletion headers and 43928064 exact-shell completion triples survive degree forcing.
  Producer result plus independent per-header DP/set reconstruction and four rejected mutations. · Exact four-delete/three-add shell around sources/ljcr-c1553-55.txt. · computed

• Use 46257454 as the distinct degree-realizing completion count.
  All 33100 degree-feasible headers before source-block exclusion. · Two independent implementations give 46255242, which is 2212 smaller. · Per-header manifest agreement and independent DP reconstruction. · A concrete missing canonical completion with a checker-accepted demand row.
• Rerun the complete fixed-pair-link refinement as the next discriminator.
  The previously displayed q=7 link and accepted baseline CNFs. · The durable epoch-114 audit records zero semantic CNF delta. · records/attempts/covering-c1553-20260812-091129-f04c88.json · A separately justified nonzero semantic constraint.

• Complete exact-shell coverage scan of the 43928064 candidates.
  The capacity gate passed and either a direct cover or a complete local exclusion is decisive for this route. · Stream canonical three-block completions from each header and combine their 455-bit masks with the residual source-cover mask. · high · open
• Proof-producing normalized SAT leaf pilot.
  A replayed UNSAT leaf remains the cheapest calibration for the global exclusion route once the pinned proof stack is available. · Run one immutable authorized leaf through DRAT/LRAT generation and dual replay. · normal · open

Objective: Determine whether any exact-shell degree-feasible candidate is a 54-block cover.

First action: Implement a deterministic bitset coverage producer over artifacts/degree18-4for3-preflight-20260812/header-counts.jsonl with a 43928064-candidate exact-count assertion.

Stop condition: Stop immediately on a candidate verified by both global cover checkers; otherwise finish only with an independent exact zero-hit/minimum-defect reconstruction.

• Generate the three added blocks from each immutable demand row and score residual 455-bit coverage incrementally.
• Use a separately written checker or materially different encoding to reconstruct the complete coverage-hit count and minimum defect.
• If a hit appears, immediately emit the 54-block family and run both existing global cover checkers.
• If zero hits, state only the exact local-shell exclusion; do not extrapolate globally.

• 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 ↗

GPT-5.6 Sol principal investigator; two GPT-5.6 Terra advisory delegates whose reconnaissance was audited by Sol; Python 3.12.3 exact enumeration; independent Python DP/set checker; SHA-256; computational-researcher experiment wrapper; web reader. No SAT solver, CAS, proof assistant, cloud lab, package installation, external publication, Git commit, or remote write.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

1376.2s

Review state

evidence receipt failure; not durable progress

Attempt ID

covering-c1553-20260812-095753-6f22ad

No human review recorded.