Complete induced-core embedding and row-lex boundary-pullback enumeration for supplied source records 21 and 12, with complement record 21 as a negative control.

complete known-class boundary blocking

Enumerate every induced embedding of the fixed record-21 order-30 core, expand every tied-row-compatible residual order, and deduplicate exact 426-bit boundary pullbacks before emitting blocks.

Hypothesis: Every induced embedding and row-lex boundary pullback for source records 21 and 12 can be enumerated by two independent implementations within 30 seconds and 1 GiB per case, with identical exact streams and no embedding in complement record 21.

Test: Run custom graph6/bitset DFS and NetworkX graph6/VF2 exhaustive enumeration on records 21 and 12 plus complement record 21, then replay every map and vector with a third checker and two exact R(5,5) graph checkers.

Exact stream agreement and independent replay establish the mechanism only on its declared two-record scope; the unprocessed 654 hosts forbid any class-exclusion claim.

• Source record 21 has exactly two fixed-core embeddings producing one unique row-lex vector.
• Source record 12 has exactly two fixed-core embeddings producing two unique row-lex vectors.
• Complement record 21 has no induced embedding of the fixed core.
• Both enumerators and the independent replay checker agree on this scope.

• artifacts/known_class_embedding_bitset_pilot.json; SHA-256 794b281338a4dd5a126c7dd36d840fd1b0eabd9567e84311d777d0a03d2dccd9
• artifacts/known_class_embedding_networkx_pilot.json; SHA-256 1c83da22cf2585e52d4f4c58903f9057667d47ece954499baafc90a79eba3cc8
• artifacts/known_class_embedding_pilot_audit.json; SHA-256 dbc0fc380b19f0eef14f4021570e840d67e77f175f9b829168dfe292af966ab0
• artifacts/known_class_embedding_pilot_graphs.g6; SHA-256 249662ab7df7a7e3df9df82f214d910bcc4becfc1cd91a48031284ba7b6b5756

• .proof-experiments/20260721-182632-8096f2: custom enumeration passed in 11.576 seconds total
• .proof-experiments/20260721-182712-0ba9c4: VF2 enumeration passed in 57.953 seconds total
• .proof-experiments/20260721-183048-41afe5: independent replay passed in 5.988 seconds

checkers/known_class_embedding_pilot_audit.py imports neither enumerator, reparses graph6, validates every map and tied-row order, reconstructs pullbacks, compares exact streams, recovers historical controls, rejects mutations, and invokes independent Python and C graph checkers.

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

None recorded.

• Source record 21 has exactly two induced embeddings and one unique boundary vector.
  Two exact manifests and independent replay. · Fixed core embedded into source record 21 only. · computed
• Source record 12 has exactly two induced embeddings and two unique boundary vectors.
  Two exact manifests, replay, and stored candidate recovery. · Fixed core embedded into source record 12 only. · computed
• Complement record 21 contains no induced copy of the fixed core.
  Both enumerators emitted empty streams. · Complement record 21 only. · computed

• The complete-pullback mechanism is already infeasible on either named positive control.
  Records 21 and 12 under the two retained implementations. · All positive cases completed in 3.82–26.76 seconds and below 53 MiB. · The retained experiment records. · A reproducible timing or completeness defect.

• Reconcile all supplied-class pullbacks over 328 source records and their complements.
  This is the first sound prerequisite for bulk supplied-class blocking. · Build a checkpointed driver and submit it under the existing fail-closed gates. · high · open
• Use raw-origin proof-core compression if the corpus pass breaches a gate.
  It is a distinct structural route with a cheap kill condition. · Deletion-minimize one raw K5-clause set and stop if it exceeds 20 clauses. · normal · open

Objective: Produce or fail closed on a complete two-implementation pullback corpus for all 656 host representations.

First action: Generalize both enumerators into an atomic host-by-host checkpoint driver and submit it using /root/proof-factory/scripts/submit_lab.py.

Stop condition: Stop on stream mismatch, replay failure, per-host time at least 30 seconds, tied expansion above 100,000, or aggregate projection above 12 core-hours/20 GiB; never emit partial blocks or run residual SAT.

• Generalize both enumerators into atomic host-by-host checkpoint drivers.
• Submit the 328-source-plus-328-complement reconciliation to the checkpointed lab.
• Only after complete reconciliation, deduplicate and replay a global block stream before considering residual SAT.

• https://www.combinatorics.org/ojs/index.php/eljc/article/download/DS1/pdf/0 ↗
• https://users.cecs.anu.edu.au/~bdm/papers/r55.pdf ↗
• https://arxiv.org/abs/2409.15709 ↗

GPT-5.6 Sol was principal investigator. Supplied GPT-5.6 Terra challenger-prior-art and experiment-verification delegates were advisory and promoted with provenance; no new subagent was spawned. Sol audited the maintained survey and primary papers, wrote both enumerators and the replay checker, and ran all experiments. Tools were Python 3.12.3, NetworkX 3.3, GCC 13.3.0, exact Python/C graph checkers, jq, pdftotext, SHA-256, and the computational-researcher harness. No SAT solver, CAS, proof assistant, external publication, package installation, or system change was used.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

1368.6s

Review state

evidence receipt failure; not durable progress

Attempt ID

ramsey-r55-20260721-184001-fccb60

No human review recorded.