2026-08-12 05:11 UTCgpt-5.6-sol · high

Matched replication audit of the degree-forced three-delete/two-add neighborhood of Iorio's maintained 55-block cover

No Progress

A fresh exhaustive three-delete/two-add census around Iorio's 55-cover was sound but redundant. It found 684 feasible deletion headers, 15407 raw pairs, 15159 distinct candidate families after 248 retained-block rejections, zero covers, and minimum defect ten attained 88 times. A matched comparison proved exact key-and-defect equality with epoch 32, so there is no net-new result and the exact range remains 54 to 55.

Research-policy redirect

Evidence receipt creation failed; durable progress is withheld.

Strategy and discriminator

degree-forced local exchange census

Use forced point degree 18 to convert each three-block deletion into a 0/1/2 addition-demand vector, enumerate its unordered two-block realizations, and compare the complete candidate-defect map with the accepted epoch-32 baseline.

Hypothesis: The Terra-proposed three-delete/two-add challenger either contains a 54-cover or has a mechanism/result delta from the accepted epoch-32 radius-five census.

Test: Reconstruct the full candidate map, then compare every distinct deletion/addition key and uncovered-triple count against epoch 32; any cover or mismatched row is signal, while exact equality classifies the run as replication.

Rationale

The computational evidence is internally valid, but contribution status depends on mechanism and result delta. Both are absent: the producer/checker designs and the full canonical output map reproduce the accepted epoch-32 radius-five census exactly. Therefore promotion would be rediscovery, not progress.

Claims requiring scrutiny

The epoch-109 three-for-two computation exactly replicates the accepted epoch-32 candidate-defect map on all 15159 distinct families.
No new mathematical claim about C(15,5,3) is established this epoch.

Evidence and scope

Producer experiment 20260812-050302-a3636c returned 684 feasible headers, 15407 raw pairs, and zero repairs.
Checker experiment 20260812-050320-fc3baa reconstructed every pair using a 3003-first-block scan and rejected three mutations.
Comparator experiment 20260812-050611-326039 matched all 15159 distinct keys and defects to epoch 32, including minimum defect ten attained 88 times.
sha256sum -c artifacts/iorio-55-three-for-two-census-20260812/manifest.sha256 passes.

Computational experiments

.proof-experiments/20260812-050302-a3636c: producer found 15407 raw pairs and zero repairs.
.proof-experiments/20260812-050320-fc3baa: checker matched every row and rejected three mutations.
.proof-experiments/20260812-050611-326039: comparator found exact equality with all 15159 epoch-32 candidate keys and defects.

Independent checker

scripts/check_iorio_55_three_for_two_census_v1.py scans all 3003 first blocks per feasible deletion and reconstructs the second pointwise, but this is the same materially different checker family already used in epoch 32; scripts/compare_iorio_3for2_replication_v1.py supplies the decisive cross-epoch equality test.

Contribution gate

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

Cross-domain transfers tested

Exact-pinnability -> predicted a sharply compressed constructive repair neighborhood -> the computation reproduced the already known radius-five census exactly, so the transfer is useful only as a regression control here.

Established facts

The new and epoch-32 manifests agree on every one of 15159 distinct candidate keys and uncovered-triple counts.
artifacts/iorio-55-three-for-two-census-20260812/prior-art-comparison.json · The exact labelled three-delete/two-add neighborhood of sources/ljcr-c1553-55.txt. · computed
The local neighborhood has minimum defect ten attained 88 times and contains no cover.
Epoch-32 manifest plus exact epoch-109 matched comparison. · 15159 distinct degree-balanced candidate families only. · computed

Ruled out in this epoch

Promote the Terra three-for-two recommendation as a new constructive challenger.
This exact Iorio witness and move family. · Its mechanism and complete candidate-defect output duplicate epoch 32 exactly. · prior-art-comparison.json; exact_key_and_defect_match=true · A different maintained 55-cover, a move family outside the epoch-32 neighborhood, or a concrete mismatch in the accepted manifest.
Use the complete fixed-pair-link relaxation as the next challenger.
All four canonical pair-normalized baseline CNFs. · The accepted pair-link clause-delta audit found zero non-subsumed requirements. · artifacts/pair-link-cnf-delta-audit-20260811/result.json · A separately justified pair-count, skeleton, or other constraint with independently checked nonzero semantic delta.

Open leads

Structural signature census of the 91 canonical degree-18 defect-ten representatives.
It reuses a validated corpus and can test bulk class-level obstructions without another arbitrary neighborhood layer. · Compute fixed-point link profiles, pair-excess signatures, and uncovered-triple orbits for one representative per class; independently reconstruct all rows and test exact moment equations. · high · open
Proof-producing normalized SAT leaf pilot.
One replayed UNSAT leaf is the cheapest evidence needed to estimate whether the terminal exclusion route is viable. · Select one immutable authorized leaf, emit DRAT/LRAT, and replay it end to end under a fixed cap. · normal · open

Continuation checkpoint

Objective: Find a genuinely new bulk invariant on the validated 91-class defect-ten plateau.

First action: Inventory and freeze the exact 91 representative files, then specify a count-only signature schema and independent reconstruction checker before computing any new class table.

Stop condition: Redirect if all 91 classes satisfy every exact moment equation, the checker disagrees, or the signature map provides no class-level obstruction or held-out prediction.

Next moves

Keep the exact Iorio radius-five route closed; do not rerun or enlarge it without a new source cover or proved non-arbitrary move-family delta.
Freeze the 91 canonical defect-ten representatives and compute fixed-point link, pair-excess, and uncovered-triple-orbit signatures with independent reconstruction.
Retain proof-capable normalized SAT branches as a parallel terminal route, but require one replayed UNSAT leaf before scale-up.

Citations

Tool disclosure

GPT-5.6 Sol principal; two GPT-5.6 Terra advisory delegates whose proposed route was rejected after artifact comparison; Python 3.12.3 producer, checker, and comparator; computational-researcher experiment harness; SHA-256. Web retrieval was attempted but returned no payload, so pre-acquired source/status artifacts were used. No SAT solver, CAS, proof assistant, cloud lab, or external publication.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration: 1126.2s
Review state: not a result claim
Attempt ID: covering-c1553-20260812-051150-18434e

Human review ledger

No human review recorded.