Deterministic 256-node pilot of a joint two-cut, four-cell residual-block profile relaxation on the epoch-62 root-link survivors, followed by independent exact dynamic-program replay.

two-cut regional block-profile feasibility

Compress residual 5-blocks by their compositions across four cells induced by two tight cuts, impose exact regional degrees and ten aggregate pair demands, and independently replay infeasibility by exact eight-layer reachability.

Hypothesis: At least 26 of 256 deterministically sampled epoch-62 survivors have an infeasible joint two-cut profile relaxation.

Test: Solve all 256 frozen profile systems exactly and require at least 26 UNSAT cases, with every UNSAT case independently unreachable in a looser exact DP and every SAT model directly validated.

Every real completion maps into the profile system, and the independent DP found no reachable state for the 11 blockers even after loosening that system. This supports the exact local exclusions. The incomplete source frontier, untested degree types, and failed efficiency gate prevent any global lower-bound or candidate claim.

• Every genuine eight-block completion of a four-block root-link prefix satisfies the stated two-cut regional profile system.
• Exactly 11 nodes in the frozen 256-node sample are infeasible even after deleting profile-availability bounds.
• All 245 remaining sampled nodes have directly validated feasible profile assignments, which are not claimed to be actual completions.
• The blocker key-list SHA-256 is 2ea5cf745a0230e159b94acdb090f3b0f372374d84e08f400661d8cf9ff714ed.
• The 11/256 rejection rate failed the frozen 26-node continuation gate.
• The maintained covering-number range did not change.

• python3 scripts/two_cut_profile_pilot_v1.py --source artifacts/epoch19-20260809/root_link_canonical_primary_receipt.json --old-receipt artifacts/epoch62-20260810/root_link_subset_capacity_primary_receipt.json --out artifacts/epoch64-20260810/two-cut-profile-primary.json
• python3 checkers/check_two_cut_profile_pilot_v1.py --source artifacts/epoch19-20260809/root_link_canonical_primary_receipt.json --old-receipt artifacts/epoch62-20260810/root_link_subset_capacity_primary_receipt.json --result artifacts/epoch64-20260810/two-cut-profile-primary.json --out artifacts/epoch64-20260810/two-cut-profile-checker.json
• sha256sum -c artifacts/epoch64-20260810/SHA256SUMS
• Primary receipt SHA-256 b898d0661dbdb1e360355389134aeebd6e6db4611ed029fd7d3a950f847448f2.
• Checker receipt SHA-256 4f07af561a706cb3651380b6c513aabd00d768d123af881c30a94bf3b0f31fc1.

• .proof-experiments/20260810-201533-dd9ce2: primary Z3 4.13.0 run completed in 56.179 seconds with 245 SAT, 11 UNSAT, and no UNKNOWN.
• .proof-experiments/20260810-201811-901c18: independent checker completed in 59.103 seconds, validated 245 models, replayed 11 looser DP exclusions, and rejected four mutations.
• .proof-experiments/20260810-201514-62670b: failed before research output because installed Z3 rejected generator-valued Sum arguments; corrected by materializing lists.
• .proof-experiments/20260810-201741-cad834: failed before DP because tuple/list JSON normalization disagreed; corrected with a type-normalized reconstruction.

checkers/check_two_cut_profile_pilot_v1.py is separately written and uses set-based graph reconstruction, subset-combination cut generation, direct SAT-model arithmetic, and ordered eight-block exact DP. For UNSAT replay it deliberately omits the primary profile-capacity constraints.

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

• Cut-capacity inequalities -> prediction that coupling two cuts would reject at least 26 sampled separate-cut survivors -> 11 were rejected, so the transfer is sound but below scale.
• State aggregation from resource-constrained scheduling -> cap accumulated pair coverage at demand and memoize equal partial states -> all 11 local UNSAT cases were replayed exactly in 59.103 seconds.
• Constructive local-search diversification -> prediction that fresh nonisomorphic starts combined with larger-support transitions may escape a support-two plateau -> not tested this epoch and retained as the next discriminator.

• Every actual residual completion induces a feasible two-cut profile satisfying the four classes of constraints in the lemma.
  Double-counting proof in artifacts/epoch64-20260810/two-cut-profile-lemma.md. · Every eight-block completion of a valid four-block partial 14-point 5-uniform root link. · proved
• Exactly 11 nodes in the deterministic sample are infeasible in the profile relaxation without availability bounds.
  Primary key digest and independent DP receipts in artifacts/epoch64-20260810/two-cut-profile-checker.json. · The exact 256 sampled nodes selected from the 2094 epoch-62 survivors. · computed
• All 245 primary SAT assignments satisfy every independently reconstructed profile constraint.
  artifacts/epoch64-20260810/two-cut-profile-checker.json. · The exact 245 sampled profile systems classified SAT. · computed
• The single-pair rejection rate is 11/256 = 4.296875%.
  Primary and checker receipts with matching UNSAT key digest. · The frozen sample and cut-selection rule only. · computed

• Scale the unchanged single-pair two-cut profile filter across all 2094 epoch-62 survivors.
  The frozen 256-node sample, 32-tightest-cut window, and first four-nonempty-cell pair rule. · Only 11 nodes were rejected, below the predeclared threshold of 26. · artifacts/epoch64-20260810/epoch-receipt.json and two-cut-profile-checker.json. · A proved multi-pair ownership or coverage rule, or materially stronger coupling, that independently rejects at least 10 percent on a fresh bounded sample.
• Use the epoch-20 file named leaf-00-u51.witness as a positive root-link completion control.
  That exact stored file. · Its entire solver result is c UNKNOWN, so it is not a witness. · artifacts/epoch20-20260809/root-link-completion-pilot-v1/leaf-00-u51.witness. · A directly checked twelve-block root-link completion with exact target degrees and complete pair coverage.

• Multi-anchor support-three constructive search.
  It combines independently generated degree-12 starts with a transition class larger than the closed support-two neighborhood and retains a direct witness path. · Compare support-two and exact support-three transitions under identical deterministic proposal budgets, recording deficit and canonical-state diversity. · high · open
• Certified multi-pair root-link profile portfolio.
  Multiple owned cut pairs could strengthen the local filter, but the unchanged single-pair mechanism failed its gate. · First prove an exactly-once pair-selection or dominance rule, then test a new 256-node sample with a 10 percent incremental gate. · low · open
• Canonical complete root-link catalogue with local residual blockers.
  A complete independently checked catalogue could turn local blockers into components of a global exclusion. · Measure canonical augmentation growth under a 10000-orbit cap and independently audit ownership before solving any completion leaves. · normal · open

Objective: Determine whether exact support-three plateau transitions improve constructive search across fresh nonisomorphic degree-12 starts.

First action: Audit scripts/generate_fresh_nonisomorphic_starts_v1.py and the epoch-23 fresh-start receipt, then freeze equal proposal counts for support-two control and exact three-block replacement challenger.

Stop condition: Stop on degree drift, duplicate blocks, direct-check disagreement, no deficit or canonical-diversity improvement under the matched cap, or projected runtime above two minutes without lab submission.

• Do not scan all 2094 survivors with the unchanged single-pair rule.
• Audit the fresh nonisomorphic degree-12 start generator and exact support-three allocation engine.
• Freeze matched proposal counts for support-two control and support-three challenger.
• Directly validate every zero-deficit state against all 455 triples.
• Use the checkpointed lab if the matched constructive experiment is expected to exceed two minutes.

• https://www.coveringrepository.com/systems.aspx?k=6&t=3&m=-1 ↗
• https://ljcr.dmgordon.org/cover/show_cover.php?v=15&k=6&t=3 ↗
• https://arxiv.org/abs/math/9502238 ↗

GPT-5.6 Sol served as principal investigator. GPT-5.6 Terra delegates supplied advisory prior-art and experiment-design reconnaissance only and were not treated as evidence or independent validation. Python 3.12.3 implemented the deterministic producer and checker; Z3 4.13.0 solved primary integer systems; a separately written Python exact dynamic program replayed every local UNSAT result; SHA-256 bound artifacts. Web search checked the Covering Repository/LJCR and arXiv sources. No CAS, proof assistant, SAT proof replayer, cloud lab, external proof service, or human validator produced a terminal certificate.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

1458.7s

Review state

evidence receipt failure; not durable progress

Attempt ID

covering-c1563-20260810-202657-fada5b

No human review recorded.