Exact pointwise residual-pair capacity prefilter over the complete 3770-row ordered-distinct-mark two-link corpus, guarded by an independent 41-skeleton scope audit.

two-link local-completion prefilter

For each marked shared six-triple interface and each residual side, derive exact point degrees d_z and unshadowed incident-pair demands q_z; reject the whole interface whenever q_z exceeds the maximum 3*d_z pairs coverable by d_z residual 4-set incidences.

Hypothesis: Exactly 1599 of the 3770 canonical ordered-distinct-mark interfaces violate q_z <= 3*d_z on at least one residual side, leaving 2171 survivors in 25 deterministic signature strata.

Test: Decode every canonical graph6 row into six triples twice, once with NetworkX and once with a custom standard-library graph6 decoder, and require exact per-row agreement, the predeclared 1599/2171/25 counts, rejected mutations, and byte-identical regeneration.

Each residual 4-set containing z covers at most three unshadowed pairs incident with z, making q_z <= 3*d_z a sound necessary condition. Two different decoders agree on every row and all fixed counts. The explicit branch audit prevents extrapolation to the global problem.

• In any scoped six-common-triple residual interface, q_z <= 3*(5+[z=mark]-h_z) for every side and point z.
• Exactly 1599 of the complete 3770 canonical ordered-distinct-mark interfaces violate this necessary condition; exactly 2171 survive and occupy 25 declared signature strata.
• The ordered-distinct-mark corpus applies to 38 of 41 pair-excess skeleton profiles; the omitted profiles are [3^5], [3^3,2^3], and [3,2^6].

• python3 /root/proof-factory/skills/computational-researcher/scripts/run_experiment.py --name two-link-point-capacity-prefilter-v1-receipt --hypothesis 'Exactly 1599 of the 3770 ordered-distinct-mark interfaces violate q_z <= 3*d_z on at least one residual side.' --expected-signal 'Independent reconstruction reports 1599 rejects, 2171 survivors, 25 survivor strata; mutations reject; regeneration is byte-identical; receipt binds every decisive local input.' --timeout 180 --memory-mb 1024 --source-url 'https://www.coveringrepository.com/systems.aspx?k=5&t=3&m=-1' python3 scripts/run_two_link_point_capacity_prefilter_v1.py --protocol protocols/two-link-point-capacity-prefilter-v1.json --output-dir artifacts/two-link-point-capacity-prefilter-20260812
• sha256sum -c artifacts/two-link-point-capacity-prefilter-20260812/manifest.sha256
• Final experiment 20260812-141102-967cdb: return code 0, 5.496 seconds, peak child memory 40576 KiB.

• .proof-experiments/20260812-140428-f62152: development run reproduced 1599/2171/25 but fail-closed packet comparison caught an omitted derived field in the checker; no claim accepted.
• .proof-experiments/20260812-141102-967cdb: final producer/checker/mutation/regeneration packet passed in 5.496 seconds with 40576 KiB peak child memory and bound all decisive local inputs in the manifest.

check_two_link_point_capacity_prefilter_v1.py uses a custom standard-library graph6 bit decoder rather than NetworkX, reconstructs all triples, shadows, degrees, violations, and strata from raw rows, and compares every ledger record. A separate regeneration checker byte-compares all producer outputs.

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

• Forced-link covering proofs -> preclassify exact local interfaces before SAT -> the point-capacity inequality eliminates 1599 complete marked interfaces without a solver.
• Degree-constrained set cover -> incident demand cannot exceed per-incidence capacity -> q_z <= 3*d_z is decisive on 42.414% of the scoped canonical corpus.

• The point-capacity inequality q_z <= 3*d_z is necessary on each residual side.
  Direct combinatorial proof in notes/two-link-point-capacity-lemma-20260812.md · Six-common-triple pair-multiplicity-six interface with the declared exact mark profile · proved
• Exactly 1599 of 3770 ordered-distinct-mark interface types violate the inequality; 2171 survive in 25 strata.
  Independent per-row reconstruction and receipt ffed4eabd236dc7acf7fb06f75c4c2e9e4fd1a54396acf44bdd16218c18398dc · Complete validated epoch-120 canonical corpus · computed
• The corpus covers 38 of 41 skeleton profiles and omits [3^5], [3^3,2^3], and [3,2^6].
  Exact partition and automorphism arithmetic in branch-scope-audit.json · All 41 loopless weighted-degree-two pair-excess skeleton partitions on 15 points · proved

• Treat an exhaustive solve of the 3770 ordered-distinct-mark corpus as a global exclusion of 54.
  All global completeness claims based only on that corpus · Three skeleton profiles require coincident-mark and/or doubled-edge interfaces absent from the corpus. · artifacts/two-link-point-capacity-prefilter-20260812/branch-scope-audit.json · Add independently canonicalized and checked triangle/coincident-mark and doubled-edge/seven-common-triple interface corpora and prove their union covers all 41 profiles.
• Send the 1599 capacity-rejected interfaces to SAT.
  The complete reject ledger · The proved one-sided inequality already excludes every row. · artifacts/two-link-point-capacity-prefilter-20260812/rejected-types.jsonl and independent-check.json · A counterexample to the capacity lemma or a per-row checker disagreement.

• Proof-producing 25-stratum residual-kernel pilot
  It tests exact feasibility and proof throughput on boundary-dominated survivors at bounded cost. · Generate two exact 715-variable kernels for each selected row and run the fixed 50000-conflict checked-model/replayed-proof protocol. · high · open
• Complete the two omitted interface forms
  Global completeness requires coincident-mark six-triple and doubled-edge seven-triple corpora. · Run count-only canonical capacity gates for B and C, with independent orbit-stabilizer checks, before any solver kernels. · normal · open

Objective: Measure exact residual-kernel pruning and proof cost on all 25 survivor strata while preserving the three-profile global scope guard.

First action: Implement scripts/two_link_residual_kernel_pilot_v1.py to consume survivor-strata.jsonl, emit two tuple-derived DIMACS files per selected row, and validate the Iorio mark-6 side control before any live solve.

Stop condition: Redirect on semantic disagreement, any UNKNOWN leaf, proof replay failure, all 50 kernels SAT, or projected exhaustive cost beyond a checkpointed resource plan.

• Generate canonical DIMACS for both residual sides of the 25 selected survivor rows and validate a frozen Iorio side-kernel semantic control.
• Run a fixed 50000-conflict pilot per kernel; directly check SAT tuple models and replay each UNSAT proof with pinned drat-trim. Stop on any UNKNOWN or if all 50 kernels are SAT.
• Canonicalize the coincident-mark six-triple and unmarked seven-triple interfaces before any global completeness claim.

• 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 ↗

GPT-5.6 Sol principal designed the lemma, implemented and audited the packet, and interpreted the result. Two GPT-5.6 Terra delegates supplied advisory prior-art/scope and experiment-verification memos; their claims were not treated as votes and the used counts were independently recomputed in the main workspace. Python 3.12.3, NetworkX 3.3, a separate standard-library graph6 decoder, SHA-256, jq for diagnostics, and the computational-researcher experiment harness were used. The inherited corpus was generated with nauty and independently validated in epoch 120. No SAT solver, CAS, proof assistant, or lab compute was used this epoch.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

1222.8s

Review state

evidence receipt failure; not durable progress

Attempt ID

covering-c1553-20260812-141511-862550

No human review recorded.