Qualified deterministic checkpoint/restart and deletion-parent ownership for two canonical internal-edge chunks of the exact depth-four pair-surplus prefix ledger.

checkpointed canonical pair-surplus augmentation

Partition the 62437-profile S4 x S11 quotient by 61 canonical internal weighted graphs, materialize exact residual-degree tables per chunk, hash-bind completion state, and validate orbit totals and deletion parents with a separate Burnside encoding.

Hypothesis: A generic internal-edge-orbit producer can materialize orbit indices 16 and 38 with byte-identical clean versus interrupted/resumed outputs, and an independent encoding will recover every canonical profile and deletion parent.

Test: Run one clean two-chunk materialization, interrupt a matched run after the first chunk, resume it, require byte identity, then independently recompute Burnside totals and every deletion parent while rejecting mutations and changed checkpoint scope.

Two materially different counting/validation mechanisms agree on exact selected totals and every record, the restart path is byte-identical to a clean run, and fail-closed controls passed. The evidence has no quantified force outside the two selected depth-four chunks and cannot settle the covering number.

• Internal pair-surplus depth-four orbit 16 has exactly 2548 canonical profiles and orbit 38 has exactly 2 under the declared S4 x S11 quotient.
• Protocol pair-surplus-depth4-internal-orbit-chunks-v1 resumes the selected two-chunk run byte-identically after an intentional one-chunk stop.
• All 2548 refactored orbit-16 records agree exactly with the epoch-106 ledger on keys, tables, orbit sizes, weights, deletion parents, and owners.

• Clean producer experiment 20260812-044246-d60f79: PASS_SELECTED_COMPLETE, 2550 profiles in 8.503 seconds.
• Interrupted experiment 20260812-044304-5dc1e9: CHECKPOINT_STOP and exit 2 after one chunk; resume 20260812-044320-734278 completed in 0.428 seconds.
• Independent experiment 20260812-044328-af5032: PASS_INDEPENDENT, byte identity, exact 2548+2 counts, and three mutations rejected.
• Binding experiment 20260812-044354-c9ba4b rejected selection drift; baseline experiment 20260812-044447-be729e matched all 2548 prior records.

• .proof-experiments/20260812-044246-d60f79: clean selected run, PASS_SELECTED_COMPLETE with 2550 profiles.
• .proof-experiments/20260812-044304-5dc1e9: intentional one-chunk stop, exit 2 and no final manifest.
• .proof-experiments/20260812-044320-734278: resumed remaining chunk, byte-identical final digest.
• .proof-experiments/20260812-044328-af5032: PASS_INDEPENDENT and three semantic mutations rejected.
• .proof-experiments/20260812-044354-c9ba4b: changed-scope checkpoint rejected before final output.
• .proof-experiments/20260812-044447-be729e: all 2548 orbit-16 records match epoch 106.

checkers/check_pair_surplus_depth4_checkpoint_gate_v1.py uses stabilizer Burnside polynomial DP rather than producer table enumeration and reconstructs every selected record and deletion parent; checkers/compare_depth4_checkpoint_baseline_v1.py separately checks exact baseline preservation.

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 link/orbit decomposition for C(12,6,4) -> predict that content-addressed ownership chunks can support an exhaustive C(15,6,3) partition -> selected chunks passed restart and parent validation, but no terminal cover leaf has been reached.

• The selected depth-four internal-orbit chunks 16 and 38 contain exactly 2548 and 2 S4 x S11 profiles.
  Producer chunks plus independent stabilizer Burnside totals in artifacts/epoch108-20260812/checkpoint-independent-check.json. · Degree-feasible depth-four pair-surplus prefixes for internal orbit indices 16 and 38. · computed
• Clean and interrupted/resumed outputs are byte-identical for both selected chunks and the final manifest.
  PASS_INDEPENDENT receipt and SHA-256 bfc5d21bd0d8be0fd2d32187375bc6aad842501889bcaed0a65e81f5c1eddef9 for both manifests. · Protocol v1 with selection 16,38 and the frozen epoch-102 parent source. · computed

• Resume a checkpoint under a changed internal-orbit selection.
  Changing selection 16,38 to 16,39 under protocol v1. · The canonical binding hash changes and the producer raises checkpoint binding before writing a final artifact. · .proof-experiments/20260812-044354-c9ba4b/experiment.json · A versioned protocol migration with an explicit, independently checked equivalence map.
• Treat the orbit-16 refactor as new mathematical content.
  All 2548 orbit-16 records. · They match the epoch-106 ledger field-for-field and are a replication control. · artifacts/epoch108-20260812/checkpoint-baseline-match.json · None; only the checkpoint mechanism, added chunks, or later complete union can be new progress.

• Complete checkpointed depth-four ownership union.
  The exact expected total is 62437 and segmented restart is now qualified; this is the smallest missing global ownership prerequisite. · After human approval and checker generalization, submit all 61 chunks to the checkpointed lab and reconcile the content-addressed union. · high · open
• Proof-producing incidence/PB decomposition.
  It remains a materially distinct negative route, but cannot satisfy the verification contract without a pinned emitter and two qualified replayers. · On toolchain availability, require accept/reject mutation qualification on a toy contradiction before compiling any genuine cube. · normal · open

Objective: Qualify and, only after approval, execute the complete 61-chunk depth-four ownership materialization.

First action: Review artifacts/epoch108-20260812/continuation-checkpoint.json and obtain human approval or rejection of its exact lab job shape.

Stop condition: Stop or redirect on nonapproval, source/hash drift, any union total other than 62437, duplicate, parent mismatch, byte instability, accepted mutation, or budget breach.

• Obtain human approval or rejection of the exact full 61-chunk lab scope recorded in artifacts/epoch108-20260812/continuation-checkpoint.json.
• Before submission, generalize the checker to validate a complete 61-chunk union and require exactly 62437 distinct profiles.
• If approved, submit the checkpointed producer/checker with 100000-record, 1-GiB, and 900-second segment limits; redirect on any mismatch.
• Compile no SAT/PB cover leaves until the complete ownership union passes independent validation.

• https://ljcr.dmgordon.org/cover/show_cover.php?v=15&k=6&t=3 ↗
• https://arxiv.org/abs/2607.23766 ↗

GPT-5.6 Sol acted as principal investigator. Two GPT-5.6 Terra delegates supplied advisory prior-art and verification memos; Sol re-audited all relied-on claims, and model agreement was not validation. Python 3.12.3 executed the exact producer and two deterministic checkers under run_experiment.py with seed 0 and enforced memory/time caps. Web access checked the maintained LJCR table, arXiv:2607.23766, and targeted novelty queries. No SAT/PB solver, CAS, proof assistant, cloud lab, external proof service, or human validator was used this epoch.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

1128.8s

Review state

evidence receipt failure; not durable progress

Attempt ID

covering-c1563-20260812-045208-844dd5

No human review recorded.