Matched native-PB completion telemetry on eight canonical-hash-selected q=6 optimal point links, comparing multiplicity-five-pair normalization with complete root-link fixing.

canonical full-root-link completion telemetry

Reuse eight independently validated nonisomorphic q=6 C(14,4,2) links, normalize an ordinary point to induce a multiplicity-five pair, and add 715 root-block unit assertions to the otherwise identical 2717-variable native-PB formula.

Hypothesis: For each of eight hash-selected pairwise nonisomorphic q=6 optimal point links, fixing the complete 18-block root link reduces Z3 decisions by at least a factor of two relative to the matched multiplicity-five-pair baseline at 5000 conflicts, or produces a directly checked 54-cover.

Test: Run eight matched pair-baseline/full-link formula pairs with identical variable order, seed, pair caps, and 5000-conflict setting; independently reconstruct every link and SMT2 formula and require every full-link/baseline decision ratio to be at most 0.5 unless a checked cover appears.

The aggregate checker recomputed every matched ratio from independently reconstructed formulas and found the full-link runs nearly identical to baseline in decision cost. Because UNKNOWN is non-evidence mathematically and the tranche is only eight sampled type-3 links, the result supports route closure at that exact computational scope and nothing stronger.

• All 16 declared Z3 runs returned UNKNOWN at 5001 reported conflicts.
• The eight full-link/baseline decision ratios lie in [0.8904714142427281, 1.1367432150313153], and none meets the predeclared at-most-0.5 gate.
• The aggregate full-link/baseline decision ratio is 0.9862909290804299.
• No 54-cover, UNSAT proof, or eliminated link class was obtained; 54 <= C(15,5,3) <= 55 remains unchanged.

• sha256sum -c artifacts/q6-eight-link-completion-pilot-20260812-v2/manifest.sha256: all 14 bound files passed.
• Independent aggregate check: 8 cases, 16 UNKNOWN runs, ratio minimum 0.8904714142427281, ratio maximum 1.1367432150313153, zero twofold-gate passes.
• Sixteen SMT2 formulas regenerated byte-identically; canonical-identity, unit-count, and formula mutations were rejected.
• Experiment 20260812-164746-222cd6 returned code 0 in 129.592 seconds with peak child memory 92944 KiB.

• .proof-experiments/20260812-164746-222cd6: 16 UNKNOWN runs; eight ratios 0.890471 to 1.136743; independent checks, regeneration, mutations, and manifest validation passed.

checkers/check_q6_eight_link_completion_pilot_v1.py independently reconstructs each source link and formula from bit masks; checkers/check_q6_eight_link_completion_summary_v1.py independently recomputes tranche coverage, statuses, hashes, and all matched ratios.

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

• Certified forced-link analysis for C(12,6,4) -> predict that complete link fixing materially improves residual completion propagation -> on eight sampled q=6 type-3 C(15,5,3) links, the aggregate decision ratio was 0.98629 and the transfer discriminator failed.

• The eight selected source objects are pairwise nonisomorphic valid q=6 C(14,4,2) links under the prior 121-class packet.
  artifacts/q6-frontier-capacity-20260809-v3/independent-check.json plus per-run link reconstruction. · The eight canonical-hash-selected representatives. · computed
• Complete root-link fixing failed the declared twofold decision gate on every sampled link.
  artifacts/q6-eight-link-completion-pilot-20260812-v2/independent-summary-check.json. · Z3 4.13.0 native-PB, seed 0, 5000-conflict setting, exactly eight q=6 type-3 links. · computed

• Scale q=6 full-root-link native-PB leaves on the premise that link fixing alone halves decisions.
  Eight canonical-hash-selected q=6 type-3 links at the exact declared Z3 protocol. · All eight ratios exceeded 0.5; aggregate ratio was 0.98629; all runs remained UNKNOWN. · artifacts/q6-eight-link-completion-pilot-20260812-v2/independent-summary-check.json and receipt.json. · A materially different proof-producing encoding, complete symmetry quotient, or separately justified rooted-link stratum crossing its own advancement gate.

• New degree-preserving constructive move family around the defect-nine seed.
  A defect below nine or checked 54-cover is directly useful and avoids the residual propagation failure measured here. · After human approval, specify one move family not expressible as prior 2-for-2 or tested 4-for-3 moves and exhaust a fixed small tranche. · high · open
• Proof-producing link-plus-skeleton quotient.
  A complete quotient can eliminate whole families and provides the certificate surface absent from Z3 UNKNOWN telemetry. · After human approval, predeclare one tiny leaf family, generate proof-producing CNF, replay every proof, and independently verify quotient coverage. · normal · open

Objective: Select a materially distinct successor with an exact, human-approved bounded scope.

First action: Choose between a new constructive degree-preserving move family and a proof-producing link-plus-skeleton quotient, then write the success certificate and stop conditions before any run.

Stop condition: Stop or redirect if the successor repeats the same native-PB mechanism, lacks independent certificate checks, or fails its predeclared useful-signal gate.

• Obtain human approval for the exact successor scope before dispatch.
• Constructive option: define and scan one degree-preserving move family outside the exhausted 2-for-2 and tested 4-for-3 neighborhoods; advance only on defect below nine or a checked 54-cover.
• Negative option: design a proof-producing link-plus-skeleton quotient with independent leaf-coverage and proof-replay checks; reject mere cap increases or more hash-adjacent q=6 type-3 samples.

• 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 ↗

GPT-5.6 Sol served as principal investigator, audited the injected memos, designed and implemented the bounded experiment, and interpreted it. Two GPT-5.6 Terra delegates supplied advisory prior-art and verification reconnaissance; model agreement was not validation. Python 3.12.3, Z3 4.13.0, independent Python bit-mask/SMT2 checkers, SHA-256, and the computational-researcher experiment harness were used. No subagent was spawned. No CAS, proof assistant, cloud lab, installation, system change, or external write was used.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

1582.9s

Review state

not a result claim

Attempt ID

covering-c1553-20260812-165746-87cf68

No human review recorded.