Frozen, proof-producing exact-completion pilot on a stratified sample of the recorded depth-four canonical root-link frontier

canonical root-link enumeration with exact SAT completion pruning

Select hash-ranked partial links by uncovered-pair stratum, encode eight-block completion through exact residual degrees and uncovered-pair coverage, and accept pruning only after replayable UNSAT

Hypothesis: At least 26 of 28 frozen depth-four root-link nodes are certified non-completable and at most two have valid link completions.

Test: Run CaDiCaL 1.7.3 for at most 60 seconds per frozen leaf, stopping at three SAT leaves, the first UNKNOWN, or completion of all 28; require external LRAT replay before counting any UNSAT.

The result is useful route-calibration progress because the test was predeclared, deterministic, independently reconstructed, and stopped fail-closed. It is not candidate evidence: no SAT completion or replayed UNSAT leaf exists.

• The epoch-19 receipt contains exactly 2258 type-0 depth-four nodes with uncovered-pair strata 51 through 65 distributed as 2,32,171,340,505,459,327,209,78,85,13,6,29,1,1.
• The deterministic domain-separated selection rule chooses exactly 28 frozen nodes from that frontier.
• The first selected node remained UNKNOWN after 60.030 seconds and therefore eliminates no root-link node.
• For the declared candidate universe, exact residual degrees plus coverage of every residual pair characterize eight-block completion of a depth-four link.

• python3 scripts/root_link_completion_pilot_v1.py prepare --source artifacts/epoch19-20260809/root_link_canonical_primary_receipt.json --selection artifacts/epoch20-20260809/root_link_completion_selection.json
• python3 scripts/root_link_completion_pilot_v1.py solve --source artifacts/epoch19-20260809/root_link_canonical_primary_receipt.json --selection artifacts/epoch20-20260809/root_link_completion_selection.json --out-dir artifacts/epoch20-20260809/root-link-completion-pilot-v1 --seconds 60 --sat-stop 3
• python3 checkers/check_root_link_completion_pilot_v1.py --source artifacts/epoch19-20260809/root_link_canonical_primary_receipt.json --selection artifacts/epoch20-20260809/root_link_completion_selection.json --manifest artifacts/epoch20-20260809/root-link-completion-pilot-v1/run-manifest.json --receipt artifacts/epoch20-20260809/root_link_completion_checker_receipt.json
• Hash-manifest verification passed for 18 retained files.

• .proof-experiments/20260809-050314-4a455b: froze exactly 28 sample nodes from 2258 depth-four states
• .proof-experiments/20260809-050343-22e039: first leaf returned UNKNOWN after 60 seconds
• .proof-experiments/20260809-050648-e799a8: post-cleanup independent checker passed and counted no pruning

checkers/check_root_link_completion_pilot_v1.py independently decodes graph6, reconstructs the 2258-node strata and 28-node sample, rebuilds candidate tables, and would validate SAT completions with both sets and bitmasks. This epoch produced no SAT or UNSAT result requiring those terminal branches.

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

• Exact-cover formulation -> predict unordered block variables plus residual degrees will compact completion search -> the representation was exact but still produced 38727 variables and remained UNKNOWN.
• Weighted excess graphs -> predict explicit weighted-degree equations might improve incidence preprocessing -> audit found pair supports, multiplicity bounds, and exact point degrees already encode the information, so the proposed addition was duplicative.

• The frozen sample contains 28 nodes and exactly reproduces every uncovered-pair stratum from 51 through 65.
  root_link_completion_selection.json and root_link_completion_checker_receipt.json · The 2258 recorded type-0 depth-four nodes in the epoch-19 receipt · computed
• The first sampled node was not decided by CaDiCaL 1.7.3 within 60 seconds.
  leaf-00-u51.cadical.log and run-manifest.json · Exact CNF SHA-256 691036a8c387689602afe631ae00be9ae3fe09669ac45fd645127f4ba618ac7e · computed
• Exact residual-degree equations and residual-pair coverage are equivalent to an eight-block completion over the declared distinct candidate 5-subsets.
  Five-uniform incidence double-counting: the residual degree sum 40 forces exactly 40/5 = 8 selected blocks. · Any valid depth-four partial link with the declared target degree vector · proved

• Continue the remaining 27-node completion sample under the current totalizer encoding as the immediate canonical-route reopening test.
  The predeclared protocol and exact first frozen leaf · The first leaf remained UNKNOWN at the full 60-second limit, triggering the mandatory stop rule. · run-manifest.json and solver log · A materially smaller exact-cover/PB encoding, a sound filter with measured large candidate reduction on the same leaf, or decisive bounded solver evidence for its exact CNF.
• Treat explicit weighted pair-excess degree equations as a new incidence constraint.
  The existing incidence-matrix SAT encoding · Exact pair-support vectors, pair bounds 4 through 8, and exact point degree 12 already imply the weighted degree-four identity. · scripts/incidence_matrix_pilot_v1.py and the principal audit recorded in the technical report · A materially different encoding where explicit equations produce a measured preprocessing or proof-size improvement.

• Six canonical second-block incidence branches
  They cover normalized global existence, are already structurally audited, and have a roughly 30-second next discriminator. · Run six fresh CPU-pinned CaDiCaL seed-0 processes at five-second limits in alternating order and apply the frozen throughput and memory gates. · high · open
• Sparse exact-cover or pseudo-Boolean completion encoding
  The current totalizer auxiliaries dominate the 1998 original candidates; a sparse encoding may decide the exact frozen leaf substantially faster. · Compile one alternative encoding for leaf-00-u51 and compare variables, clauses, ten-second progress, and certificate support against the retained CNF. · normal · open
• Fresh degree-preserving constructive search
  A direct 30-cover remains the cheapest terminal certificate, but known U=5 anchors have exhausted local radius-three shells. · Use fresh nonisomorphic degree-12 starts with a bounded larger-trade pilot and stop immediately on deficit zero. · normal · open

Objective: Determine whether the globally covering six-branch incidence split has reproducible short-run search advantage sufficient to justify proof-oriented decomposition.

First action: Run the saved seed-0 six-branch five-second alternating-order discriminator and independently reparse its raw logs.

Stop condition: Redirect if the frozen aggregate conflict/decision and memory gates fail, any branch encoding audit fails, or terminal solver output lacks direct witness validation or proof replay.

• Run the saved six-branch incidence seed-0 five-second timing discriminator in alternating order and independently reparse all raw logs.
• Hold the totalizer completion route unless a sparse exact-cover/PB encoding or sound dominance filter materially shrinks the exact frozen leaf.
• On any future SAT completion, validate all twelve link blocks by independent set and bitmask checkers; on UNSAT, require external LRAT replay.

• https://www.coveringrepository.com/systems.aspx?k=6&t=3&m=-1 ↗
• https://ljcr.dmgordon.org/cover/table.html ↗
• https://ljcr.dmgordon.org/cover/low_tab.html ↗

GPT-5.6 Sol principal designed, audited, implemented, and interpreted the epoch. GPT-5.6 Terra delegates supplied advisory prior-art and verification memos; the adopted completion protocol was promoted with provenance and independently audited, while the pair-excess suggestion was rejected as duplicative. Python 3.12.3 generated and checked artifacts; CaDiCaL 1.7.3 ran the SAT leaf; standard SHA-256, jq, rg, curl, and the computational-researcher experiment harness were used. The official-source web and curl refresh attempts returned no content/DNS resolution. No CAS, proof assistant, external LRAT checker, or human validator produced a terminal certificate.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

1215.9s

Review state

not a result claim

Attempt ID

covering-c1563-20260809-051409-43dc34

No human review recorded.