2026-08-12 13:35 UTCgpt-5.6-sol · high

Exact S_13 capacity census for the distinct two-link local-completion prefilter, with a maintained-cover semantic control and independent VF2/orbit-stabilizer reconstruction.

No Progress

The stale fixed-pair rerun was rejected. The distinct two-link capacity gate passed: exactly 94 unmarked union-13 six-triple types and 3770 ordered-distinct-mark types were independently validated. No residual kernel was solved, so 54 <= C(15,5,3) <= 55 remains open.

Research-policy redirect

Evidence receipt creation failed; durable progress is withheld.

Strategy and discriminator

two-link local-completion prefilter

Encode each six-triple shared family as a bicolored incidence graph, add two ordered distinct marked points, quotient by S_13, and independently account for every labelled family and marked orbit.

Hypothesis: The number of S_13-isomorphism types (H,a,b), where H consists of six distinct triples with union 13 and a != b are ordered, is at most 100000, and both residual-link formulas accept the pinned 55-cover control.

Test: Generate every unmarked H canonically, expand all 156 ordered markings, batch quotient them, and require an independent orbit-stabilizer/VF2 checker to reproduce the labelled-family and marked-orbit counts.

Rationale

The producer uses nauty canonical generation while the checker uses VF2, explicit automorphism actions, and orbit-stabilizer accounting against an independent inclusion-exclusion total. Agreement, exact orbit coverage, four rejected mutations, and byte-identical regeneration support the finite classification but not residual feasibility or the global covering number.

Claims requiring scrutiny

There are exactly 94 S_13-isomorphism types of six distinct triples whose union is all 13 points.
There are exactly 3770 S_13-isomorphism types after adding two ordered distinct marked points.
The pinned Iorio 55-cover validates each proposed 12-block residual-link formula for endpoints (1,15), with coincident marks [6,6].

Evidence and scope

python3 /root/proof-factory/skills/computational-researcher/scripts/run_experiment.py --name two-link-local-completion-capacity-v1 --timeout 180 --seed 1553 --memory-mb 1024 -- python3 scripts/run_two_link_local_completion_capacity_v1.py --protocol protocols/two-link-local-completion-capacity-v1.json --output-dir artifacts/two-link-local-completion-capacity-20260812
python3 checkers/check_two_link_local_completion_capacity_v1.py --protocol protocols/two-link-local-completion-capacity-v1.json --artifact-dir artifacts/two-link-local-completion-capacity-20260812
sha256sum -c artifacts/two-link-local-completion-capacity-20260812/manifest.sha256

Computational experiments

.proof-experiments/20260812-132536-5b501d: complete packet passed in 54.822 seconds at 49912 KiB peak child memory; exact marked-type count 3770

Independent checker

check_two_link_local_completion_capacity_v1.py does not use nauty canonical forms to establish the count: it verifies unmarked nonisomorphism with VF2, enumerates automorphism actions, checks the 13!/|Aut(H)| sum against inclusion-exclusion, reconstructs every ordered-pair orbit, and maps every canonical row exactly once.

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

Forced-link certified covering proofs -> classify local link interfaces before global SAT -> the interface has only 3770 exact types, making a proof-producing pilot feasible.
Orderly graph generation -> replace labelled hypergraph traversal with incidence-graph orbits -> 1690383234540 labelled marked objects compress to 3770 independently covered types.

Established facts

The six-distinct-triple full-union universe on 13 points has 10835789965 labelled families and 94 S_13-orbits.
Inclusion-exclusion plus pairwise VF2 and the exact orbit-stabilizer sum · All six-element subsets of C([13],3) with union [13] · computed
Adding an ordered distinct pair of marked points produces exactly 3770 S_13-orbits.
Explicit automorphism pair orbits and one-to-one canonical-row coverage · The complete marked shared-family universe · computed
The Iorio (1,15) control satisfies both residual degree and unshadowed-pair conditions with marks [6,6].
Independent tuple reconstruction from sources/ljcr-c1553-55.txt · Semantic control only · computed

Ruled out in this epoch

Repeat the complete fixed-pair-link 754-target relaxation as a new discriminator.
All 5460 labelled requirements across the four canonical degree-18 CNFs and the earlier 754 type-4 targets · The audit found 4890 existing clauses, 570 fixed-block tautologies, and zero non-subsumed additions; the earlier gate retained every target. · artifacts/pair-link-cnf-delta-audit-20260811/result.json and artifacts/type4-complete-pair-link-gate-20260809/independent-check.json · A genuinely new labelled correlation not already present in baseline coverage clauses

Open leads

Stratified exact residual-link kernel pilot on the 3770 marked types
It is the cheapest test of actual pruning power after the capacity gate passed · Generate one kernel from tuples, independently check its semantics, then solve types at shared-degree and pair-shadow extremes with checked models/proofs · high · open
Proof-producing normalized global PB/SAT pilot
It remains globally decisive if a replayable proof stack shows useful throughput · Run one fixed-cap normalized branch with proof output and independent replay after the local pilot · normal · open

Continuation checkpoint

Objective: Measure local-kernel pruning power and replayable proof cost on the exact 3770-type universe.

First action: Create a tuple-based CNF/PB encoder for one residual 12-block family and a checker independently enumerating all 715 four-subsets, 13 degree targets, and unshadowed pairs.

Stop condition: Redirect on semantic disagreement, proof replay failure, zero pilot rejections, or projected exhaustive cost beyond a checkpointed resource cap.

Next moves

Do not rerun the closed 754-target fixed-pair relaxation.
Build and independently semantic-check one 715-variable residual-link kernel.
Run a deterministic stratified pilot from the 3770 types using shared-degree and pair-shadow extremes; require checked models and replayed UNSAT proofs.
Submit a complete all-type job only if the pilot rejects types and measured proof cost fits a checkpointed resource plan.

Citations

Tool disclosure

Codex (GPT-5), acting as the Sol principal, rejected the stale fixed-pair rerun, audited the formulas, designed and implemented the experiment, executed it, and interpreted the result. GPT-5.6 Terra delegates supplied advisory prior-art and experiment-verification memos only; model agreement was not counted as validation. CPython 3.12.3, NetworkX 3.3 VF2, and nauty 2.8.8+ds-5 performed deterministic generation, canonicalization, independent checking, mutation tests, and regeneration. No SAT solver, CAS, proof assistant, or checkpointed lab job was used. Web search rechecked the maintained LJCR entry and primary forced-link precedent.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration: 1442.0s
Review state: evidence receipt failure; not durable progress
Attempt ID: covering-c1553-20260812-133504-a1169c

Human review ledger

No human review recorded.