2026-08-12 00:27 UTCgpt-5.6-sol · high

Construct explicit elementary signed 3-trades proving equality of the full and normalized residual integer incidence lattices.

No Progress

The twenty fixed-column occurrences across the four normalized branches comprise twelve distinct blocks. Each distinct block has an independently checked 16-term signed 3-trade with coefficient +1 on the target and all other terms among the 2991 retained columns. Therefore simultaneous twelve-column deletion leaves the integer incidence lattice unchanged. This closes only signed-lattice congruence filtering; the exact range remains 54 <= C(15,5,3) <= 55.

Research-policy redirect

Evidence receipt creation failed; durable progress is withheld.

Strategy and discriminator

residual integer-lattice trade certificates

For each deleted block, construct a 16-term alternating four-pair 3-trade having coefficient +1 on that block while avoiding every other deleted block.

Hypothesis: Deleting the union of the fixed blocks from all four complete multiplicity-five-pair normalized branches leaves the integer column lattice of W_{3,5}(15) unchanged.

Test: Find, for every distinct deleted block B, a signed 3-trade with coefficient +1 on B and no other term in the complete deleted union.

Rationale

Each certificate gives an integral kernel relation expressing its deleted target column as an integer combination of retained columns. Together they prove containment of the full lattice in the residual lattice; the reverse containment is immediate.

Claims requiring scrutiny

Deleting simultaneously the twelve distinct fixed columns used across the four complete multiplicity-five-pair normalized branches leaves the integer column lattice of W_{3,5}(15) unchanged.
Each separate five-column normalized residual lattice therefore equals the full integer column lattice.

Evidence and scope

Producer found twelve certificates after 136 structured candidates.
Independent checker reconstructed 192 signed terms and verified 5460 triple rows.
Four sign, pair-disjointness, deleted-union, and completeness mutations were rejected.
Regeneration was byte-identical with result SHA-256 9ccf245a1cbd811321509905ffadffd878253258fbc6dcc9d471520ff92e5df1.
sha256sum -c artifacts/residual-integer-lattice-trades-20260812/manifest.sha256 passed.

Computational experiments

.proof-experiments/20260812-002023-c43dac: twelve certificates found after 136 candidates.
.proof-experiments/20260812-002429-b08669: independent reconstruction accepted 192 terms and 5460 triple rows.
.proof-experiments/20260812-002429-c5fd5b: four material mutations rejected.
.proof-experiments/20260812-002055-65ab1e: byte-identical regeneration passed.

Independent checker

checkers/check_residual_integer_lattice_trades_v1.py imports no producer code; it independently reconstructs the branch union and every alternating trade, checks all signed triple incidences, verifies target uniqueness and unit coefficient, and proves both generator containments.

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

Inclusion-matrix trade theory -> predict that a deleted column may have a compact unit-coefficient kernel witness -> all twelve normalized columns had 16-term witnesses avoiding the entire deleted union.

Established facts

The twelve-block simultaneous residual integer lattice equals the full integer column lattice of W_{3,5}(15).
Twelve explicit unit-coefficient trade certificates independently checked on all 455 triple rows. · Signed integer coefficients after deleting the normalized twelve-block union. · proved
All four five-column normalized residual integer lattices equal the full lattice.
Each five-column set is contained in the simultaneously certified twelve-column set. · The four complete multiplicity-five-pair normalized branches. · proved

Ruled out in this epoch

Use a signed integer-lattice congruence caused by normalized fixed-column deletion to eliminate a complete pair-normalized branch.
All four branches, strengthened to simultaneous deletion of their twelve distinct fixed blocks. · Every deleted generator is an integer combination of retained columns. · artifacts/residual-integer-lattice-trades-20260812/result.json and independent-check.json · A nonlinear, nonnegative, bounded-coefficient, binary-distinctness, or deeper-cube invariant not implied by signed lattice membership.

Open leads

Exact legal 2-for-2 repair census over sixteen saved defect-ten isomorphism classes.
It is a complete finite constructive move family over a safely quotiented saved corpus and can either find an improvement or close the move family exactly. · Enumerate all degree-preserving two-block deletions and two-block insertions for each representative with a separate move checker. · high · open
Variable-length degree-preserving ejection chains.
Adaptive chains are materially different from previously tested fixed-size neighborhoods and directly target a 54-cover. · Specify the chain kernel and run one deterministic tranche accepted only on independently checked defect below ten. · normal · open

Continuation checkpoint

Objective: Determine whether any saved defect-ten isomorphism class admits an improving legal 2-for-2 repair.

First action: Extract the sixteen representative families and enumerate all legal degree-preserving 2-for-2 moves with an independently reconstructed move checker.

Stop condition: Close the move family if no representative has an improving move; stop immediately on checker disagreement; promote only a directly checked defect below ten.

Next moves

Extract the sixteen representatives from artifacts/saved-defect10-isomorphism-census-20260811/families.jsonl.
Exactly enumerate all legal degree-preserving 2-for-2 repairs for each representative.
Independently reconstruct every reported move and close the move family if no representative admits an improving move.
Run matched 4096-proposal constructive tranches only for classes with a reproducible positive repair signal.

Citations

Tool disclosure

GPT-5.6 Sol acted as principal investigator, audited the prior campaign state, designed and implemented the discriminator, and interpreted the result. Two GPT-5.6 Terra delegates supplied advisory reconnaissance promoted with provenance under sources/advisory; their agreement was not validation. Python 3.12.3 performed deterministic enumeration. A separately written Python checker, mutation tests, byte-identical regeneration, the computational-researcher experiment harness, and SHA-256 validated the packet. Web search checked maintained status and primary method sources. No SAT solver, CAS, proof assistant, lab job, package installation, system change, external write, publication, or Git operation was used.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration: 908.7s
Review state: evidence receipt failure; not durable progress
Attempt ID: covering-c1553-20260812-002722-e781db

Human review ledger

No human review recorded.