2026-07-21 19:53 UTCgpt-5.6-sol · high

Cold-review the mandatory segment-33 boundary of the checkpointed 656-host supplied-class embedding census before authorizing further computation.

Progress

The mandatory segment-33 review passed. All 33 artifacts reconcile; six positive hosts contain twelve exact embeddings and eight distinct boundary vectors; fresh VF2 regenerated every positive mapping stream; both exact graph checkers accepted all eight graphs; and four mutations failed. The remaining 623 hosts are untouched, no block was emitted, and 43 <= R(5,5) <= 46 is unchanged.

Strategy and discriminator

complete known-class boundary blocking

Enumerate every induced embedding of the fixed source-record-21 order-30 core into each supplied order-42 graph and complement, expand every row-lex-compatible residual order, and retain exact 426-bit boundary pullbacks for a future complete supplied-class block.

Hypothesis: The canonical 33-host census prefix is hash-consistent; fresh VF2 exactly regenerates every positive mapping stream and an empty control; every saved pullback reconstructs; all distinct vectors pass two exact five-set checkers; and four corruptions are rejected.

Test: Independently parse the corpus, verify the segment receipt and every saved object, cold-regenerate the six positive VF2 mapping streams, cold-enumerate host 0, replay all saved pullbacks, run two exact K5 checkers, and inject four mutations.

Rationale

The production receipt satisfies its resource gates, while the cold audit closes the principal archive weakness for every positive host in the reviewed prefix. This supports continuing the bounded control census but nothing stronger.

Claims requiring scrutiny

Canonical supplied hosts 0 through 32 have complete production profiles whose saved object hashes, summaries, checkpoint entries, and total byte count reconcile.
Exactly six reviewed hosts contain the fixed order-30 core; each has two induced embeddings, for twelve embeddings total.
Those embeddings yield eight distinct 426-bit boundary vectors.
Fresh NetworkX VF2 reproduces the exact sorted mapping-stream digest for every positive reviewed host.
The eight reconstructed graphs contain neither a 5-clique nor an independent 5-set under two exact checkers.
No claim is made about the remaining 623 hosts or the completeness of the supplied 656 classes.

Evidence and scope

Segment-33 durable receipt SHA-256 be5bd6c50ee33ea761ad8324949142ac19fe119387d063293ac65e53ce273114.
Cold-audit JSON SHA-256 4bfbbedcc0dd23a688431969693274915e19c892f56c3b84139f43f04a872c98.
Cold-audit checker SHA-256 69d01e8bd189498c70390404de034b354023ffe2fae812ee7c287c64b7c46687.
Eight-graph artifact SHA-256 4e99010340746b1c2ffdd81fec3da6b51342891d8cd906d8669fe1ac27053bcf.
Experiment record SHA-256 f0e89bcdf5d91ba5db08a8da207385d90f8a5e7ec2dc103495d664c1a8af92e2.

Computational experiments

.proof-experiments/20260721-194331-020393: initial 63.642-second prefix audit passed object, pullback, three-empty-host, dual-checker, and mutation controls.
.proof-experiments/20260721-194527-481cfe: strengthened 139.167-second audit additionally cold-regenerated all six positive VF2 mapping streams exactly.

Independent checker

checkers/known_class_embedding_tranche_audit.py imports neither production enumerator, independently parses graph6, verifies the checkpoint/manifest/object chain, cold-regenerates positive VF2 streams, replays every saved map and residual order, reconstructs full graphs, invokes independent Python and C five-set checkers, and rejects four mutations.

Contribution gate

not_requested

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

Original model outcome: progress
Public classification: progress

Cross-domain transfers tested

None recorded.

Established facts

The segment-33 census prefix covers canonical supplied hosts 0 through 32 exactly once and all saved hashes and byte counts reconcile.
Standalone cold audit and durable segment receipt. · Exactly the first 33 supplied source hosts. · computed
Hosts 11, 17, 18, 19, 20, and 24 each have exactly two fixed-core embeddings under both production paths and fresh cold VF2.
Six exact cold mapping-stream digest comparisons. · Those six supplied hosts under the fixed source-record-21 core. · computed
The twelve embeddings produce eight distinct valid Ramsey(5,5,42) labelled graphs.
Independent pullback reconstruction plus direct-combinations Python and recursive-bitset C checkers. · The eight retained vectors from canonical hosts 0 through 32. · computed

Ruled out in this epoch

Treat the reviewed 33-host prefix as a complete supplied-class block.
The current fixed-core boundary census. · Only 33 of 656 supplied host representations have been processed. · Checkpoint next_host is 33 and total_hosts is 656. · Complete and cold-audit all 656 canonical hosts.
Accept stored NetworkX summaries alone as offline proof of the second complete mapping stream.
The current per-host archive format. · The full NetworkX streams are not retained in host artifacts. · Production driver inspection; cold regeneration was required for the six positive hosts. · Retain complete second-path sidecars or cold-regenerate every positive stream.

Open leads

Complete the checkpointed 656-host supplied-class embedding census.
It is the direct prerequisite for one sound supplied-class boundary block and continues well above declared resource thresholds. · Resume lab-ramsey-r55-872a7c3ee855 from next_host 33 and review the next immutable tranche. · high · open
Deletion-minimize one certified two-orbit raw K5-clause core.
This remains a distinct structural challenger if the census loses correctness, feasibility, or decision value. · Test the predeclared at-most-20-origin threshold on one retained slice. · normal · open

Continuation checkpoint

Objective: Complete and independently validate all 656 supplied host profiles before emitting any block.

First action: After the continue review is applied, inspect /root/proof-factory/state/labs/jobs/lab-ramsey-r55-872a7c3ee855.json and confirm resumption from next_host 33 with unchanged input hashes.

Stop condition: Redirect on any implementation or cold-replay mismatch, host timeout, throughput below 0.001 host/s, segment artifact growth above 200 MB, or loss of decision value.

Next moves

Apply the continue review to lab-ramsey-r55-872a7c3ee855 and resume from next_host 33.
At the next completed-awaiting-review boundary, inspect the immutable receipt, progress hash, manifest hash, logs, throughput, and artifact growth before issuing another decision.
Queue future strengthened cold audits through the checkpointed lab because the observed runtime exceeded two minutes.
Before any block or residual SAT, finish all 656 hosts, regenerate every positive mapping stream, cold-enumerate at least 32 stratified empty hosts, replay every tied-row pullback, and rerun both graph checkers.

Citations

Tool disclosure

GPT-5.6 Sol served as principal investigator. Two supplied GPT-5.6 Terra delegates provided advisory challenger/prior-art and experiment-verification memos; Sol independently audited all relied-on claims and promoted scoped summaries with hashes. No new subagent was spawned. Deterministic tools were Python 3.12.3, NetworkX 3.3, GCC 13.3.0, SHA-256, the existing Python and C exact graph checkers, the computational-researcher experiment harness, and web access for current primary-source review. No SAT solver, CAS, proof assistant, package installation, system change, external publication, or remote account was used.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration: 925.5s
Review state: not a result claim
Attempt ID: ramsey-r55-20260721-195309-1f8700

Human review ledger

No human review recorded.