Prepare the prescribed hash-bound five-seed pair-propagation control, validate its runner and independent checker, and independently verify a complete six-case second-block stabilizer split when lab registration blocks production execution.

pair-excess structural reduction with fixed-block SAT discrimination

Fix block 012345, reuse four immutable degree/pair CNFs across matched seeds, and exploit the residual S_6 x S_9 action to normalize a second selected block into six intersection branches.

Hypothesis: After fixing 012345, every possible distinct selected second block is equivalent under S_6 x S_9 to exactly one of six representatives indexed by its intersection size with 012345.

Test: Enumerate all 5004 second blocks, explicitly construct a fixed-block-stabilizing permutation to the claimed representative, verify orbit sizes and CNF literals, and check the resulting raw branch-count identity.

The orbit reduction is supported by an explicit group-action proof and exhaustive deterministic verification over the entire 5004-block residual universe. This is genuine bounded progress but cannot be promoted: no 30-cover, UNSAT certificate, or production multi-seed decision exists.

• After fixing 012345, the residual S_6 x S_9 action has exactly six orbits on distinct second blocks, with sizes 84, 756, 1890, 1680, 540, and 54.
• Every normalized hypothetical 30-cover has a representative in at least one of the six canonical second-block branches.
• The sum of raw branch representations is at most 6*choose(5003,28), a factor 834/29 below choose(5004,29).
• The 1-second multi-seed smoke test validates harness mechanics only and makes no research-route or covering-number claim.
• No full five-seed production control or exact-value search ran this epoch.

• python3 checkers/verify_second_block_orbits_v1.py
• python3 checkers/check_pair_multiseed_v1.py --inputs artifacts/epoch3-20260808/pair_multiseed_input_v1.json --run-manifest artifacts/epoch3-20260808/multiseed-smoke-v1/run-manifest.json --expected-time-limit 1
• bash scripts/submit_pair_multiseed_lab_v1.sh
• .proof-experiments/20260808-171705-ccf5b7: exhaustive orbit audit passed
• .proof-experiments/20260808-171518-92e1dd: final harness checker passed with no route decision
• .proof-experiments/20260808-171546-f13d8d: lab registration failed before job creation

• .proof-experiments/20260808-171152-5de1a1: 20-cell one-second runner smoke completed with 20 UNKNOWN statuses
• .proof-experiments/20260808-171304-a9fbb1: adversarial checker run exposed division by zero
• .proof-experiments/20260808-171354-2ce38a: second checker audit exposed incorrect nonproduction scope/decision labeling
• .proof-experiments/20260808-171518-92e1dd: corrected independent checker passed and emitted harness_only_no_route_decision
• .proof-experiments/20260808-171546-f13d8d: lab submission failed on read-only host ledger before job creation
• .proof-experiments/20260808-171705-ccf5b7: all 5004 second blocks passed explicit stabilizer mapping and orbit checks

The orbit result has an explicit exhaustive checker plus a separate human-verifiable group-action proof. The multi-seed runner has a separately written checker that reparses raw logs and reconstructs commands, seeds, hashes, and ratios without importing runner code.

not_requested

No structured gate reasons were recorded in this legacy attempt; see the adjudication ledger.

Original model outcome

progress

Public classification

progress

• Certified C(12,6,4) case splitting -> require an exhaustive symmetry partition and replayable leaf proofs -> the six residual second-block branches were verified, but no UNSAT leaf work was attempted.
• Residual group actions in canonical augmentation -> intersection size should classify second-block choices -> exactly six complete orbits were observed and proved.

• The 5004 free second blocks form six S_6 x S_9 orbits indexed by intersection sizes 0 through 5, with sizes summing to 5004.
  .proof-experiments/20260808-171705-ccf5b7 and the explicit relabelling proof in artifacts/epoch3-20260808/technical_report.md · All 6-subsets of {0,...,14} distinct from 012345. · proved
• The six-branch normalization covers global existence after fixing 012345 and uses at most 6*choose(5003,28) raw branch representations.
  Orbit coverage plus the exact binomial identity checked by checkers/verify_second_block_orbits_v1.py · Normalized labelled 30-block selections containing 012345. · proved
• The final checker does not issue a scientific route decision for non-60-second caps.
  .proof-experiments/20260808-171518-92e1dd · checkers/check_pair_multiseed_v1.py under the one-second smoke protocol. · computed

• Treat the one-second smoke ratios as evidence for or against pair-bound scale-up.
  The 20 smoke runs in artifacts/epoch3-20260808/multiseed-smoke-v1. · Several conflict/decision denominators are zero and the cap is not the predeclared 60-second production protocol. · .proof-experiments/20260808-171518-92e1dd · Complete all 20 matched runs at exactly 60 seconds and pass the independent checker.
• Interpret the six second-block branches as a unique isomorphism quotient or a measured 1890-fold speedup.
  The residual S_6 x S_9 normalization. · A cover may contain several second blocks and appear in multiple branches; orbit size is a point-label count, not runtime. · checkers/verify_second_block_orbits_v1.py and artifacts/epoch3-20260808/technical_report.md · A proved canonical augmentation rule selecting a unique second block and measured matched runtime data.
• Claim that the checkpointed production job was submitted or executed.
  This epoch and sandbox. · The lab ledger write failed before durable state and queue publication. · .proof-experiments/20260808-171546-f13d8d/stderr.txt · A successful submission receipt containing a durable job ID and canonical queue spec.

• Five-seed matched pair-propagation confirmation
  The complete hash-bound packet is ready and directly decides whether the incumbent merits structural scale-up. · Run bash scripts/submit_pair_multiseed_lab_v1.sh after lab registration becomes writable. · high · open
• Six-case canonical second-block assumption pilot
  It safely replaces 5004 second-block choices by six branches and may expose useful propagation without a new encoding. · After the production gate passes, run the six literals 4921, 1876, 589, 136, 19, and 1 under a matched aggregate budget. · normal · open
• Degree-aware 31-to-30 repair search
  A constructive hit settles the problem and is independent of exclusion-route propagation. · Delete each archival block and benchmark fixed-budget one- and two-block repair neighborhoods with incremental deficit updates. · normal · open

Objective: Measure whether pair-bound progress is robust across seeds and decide between structural exclusion scale-up and constructive repair.

First action: bash scripts/submit_pair_multiseed_lab_v1.sh

Stop condition: SAT stops for dual cover validation; provisional UNSAT stops for proof generation/replay; all UNKNOWN runs trigger the predeclared gates, with any failure redirecting to constructive repair.

• Restore writable checkpointed-lab registration and run bash scripts/submit_pair_multiseed_lab_v1.sh.
• On completion, inspect the durable lab record and raw hashes before running the independent checker with --expected-time-limit 60.
• If both encodings pass all gates, test the six canonical second-block literals under a fixed aggregate budget.
• If either encoding fails, redirect immediately to the degree-aware 31-to-30 constructive repair pilot.
• Treat SAT only after both direct cover validators; treat UNSAT only after proof-producing rerun and independent DRAT/LRAT replay.

• https://www.coveringrepository.com/systems.aspx?k=6&t=3&m=-1 ↗
• https://ljcr.dmgordon.org/cover/show_cover.php?k=6&t=3&v=15 ↗
• https://arxiv.org/abs/2607.23766 ↗

GPT-5.6 Sol served as principal investigator. Pre-existing GPT-5.6 Terra delegates supplied advisory prior-art and experiment-verification memos; Sol independently audited every relied-upon claim. Deterministic work used Python 3.12.3, CaDiCaL 1.7.3, GNU time, SHA-256, shell inspection, and the Proof Factory experiment harness. Web research checked the Covering Repository, LJCR record, and arXiv. No proof assistant, DRAT/LRAT replay tool, external expert, or newly spawned sub-agent was used.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

1282.8s

Review state

not a result claim

Attempt ID

covering-c1563-20260808-172243-9e867d

No human review recorded.