Validated an exact S_12 destroyed-label row-order quotient for the retained source-record-21 frozen order-30 boundary, blocked the canonical source vector, and classified exactly one subsequent SAT model.

symmetry-normalized exact boundary repair

Remove the non-invariant Hamming counter, impose lexicographically nondecreasing 30-bit destroyed-to-core rows, exhaustively validate tied-row coverage, and permit one source-blocked SAT model.

Hypothesis: The row-order quotient retains every boundary orbit, including tied rows, and one source-blocked model can be exactly classified without resuming labelled CEGAR.

Test: Enumerate all 2^21 labelled four-core/three-destroyed graphs and the complete four-bit comparator truth table, verify the sorted source against the regenerated no-Hamming CNF, then run CaDiCaL once with seed 1 for 30 seconds.

The exhaustive and independent controls establish the exact scoped reduction, while supplied-corpus membership triggers the predeclared stop and forbids novelty or exclusion claims.

• The row-sorted quotient covers every S_12 destroy-label orbit in the fixed record-21 boundary.
• The quotient represents exactly 2^66*C(2^30+11,12) primary assignments.
• The one post-block model is a valid Ramsey(5,5,42) graph isomorphic to supplied source record 12.

• artifacts/novel42_lex_quotient_report.json; SHA-256 b3dba7917002fc7f49fdaefe25bc65e79a51f461878405f38233bd467f7e33ee
• artifacts/novel42_lex_quotient_cold_audit_v2.json; SHA-256 edcde85e7fff664770a7e26f32d531cab9cb338c5814842901cff132923ec7ab
• artifacts/novel42_lex_quotient/record-21-lex-source-blocked.cnf; SHA-256 92eb867d7e523e673de1b9ea2b848600abf793eacad0b59cce7861cfc94fbe41
• CHECKPOINT.md; epoch-16 replay instructions and continuation
• docs/novel42-lex-quotient.md; full formulation and scope

• .proof-experiments/20260721-172006-427f4a: exhaustive production gate passed; one SAT model found in 4.849 seconds
• .proof-experiments/20260721-172356-d34034: independent physical reconstruction and adversarial transposition audit passed

checkers/novel42_lex_quotient_audit.py imports no producer, independently reconstructs the raw and lex clauses, evaluates all 198913 clauses, validates graph semantics and record-12 isomorphism, and verifies that an unsorted destroy transposition preserves raw Ramsey clauses but is rejected by lex order.

not_requested

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

Original model outcome

progress

Public classification

progress

• Group-action canonicalization -> sorting core-neighborhood rows should retain an orbit representative despite ties -> exhaustive S_3 controls and the S_12 production/adversarial audits passed.

• The record-21 boundary row quotient is covering and has exact represented size 2^66*C(2^30+11,12).
  Production report and independent adversarial cold audit. · The declared fixed-core boundary only. · proved
• The one post-block model is valid and isomorphic to supplied source record 12.
  Two exact graph checkers, physical DIMACS evaluation, nauty, and NetworkX. · The exact predeclared seed-1 solve. · computed

• Continue the same quotient formula with an arbitrary larger individual-normal-form cutoff.
  This record-21 fixed core and primary-vector blocks. · The quotient is not a class block, and the first post-source-block model is another supplied class. · Production and cold reports. · A proved class-level block or canonical augmentation, an artifact defect, or a predeclared experiment that directly meets a field-progress gate.

• Compress a certified two-orbit exclusion into a raw K5-clause obstruction theorem.
  A first core of at most 20 clauses is the cheapest discriminator for the named structural-theorem gate. · Deletion-minimize one raw clause set with exact UNSAT checks and independently verify its five-set origins. · high · open

Objective: Test whether one certified two-orbit exclusion has a raw core of at most 20 clauses.

First action: Use the retained burden-zero slice artifacts to generate a raw-clause-only instance, then deletion-minimize with exact replay and independent origin mapping.

Stop condition: Stop on a core larger than 20 clauses, an origin-map failure, or non-replayable UNSAT; consider the 20-distance atlas only after the first threshold passes.

• Select one retained burden-zero two-orbit slice.
• Strip all auxiliary and symmetry structure to raw K5 clauses.
• Deletion-minimize with exact UNSAT checks and independently verify every surviving five-set origin.
• Stop immediately if the first core exceeds 20 clauses.

• https://www.cs.rit.edu/~spr/ElJC/sur.pdf ↗
• https://users.cecs.anu.edu.au/~bdm/papers/r55.pdf ↗

GPT-5.6 Sol was the campaign-designated principal. Supplied GPT-5.6 Terra literature-strategy and experiment-verification delegates were advisory; their artifacts were promoted with provenance. Sol independently audited the primary sources, corrected the comparator count, implemented and ran the producer, and wrote the cold checker. Deterministic tools were Python 3.12.3, GCC 13.3.0, CaDiCaL 1.7.3, nauty labelg, NetworkX 3.3, curl, pdftotext, jq, SHA-256, and the computational-researcher experiment harness. No new subagent, CAS, proof assistant, external publication, remote account, or system-level change was used.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

1874.8s

Review state

not a result claim

Attempt ID

ramsey-r55-20260721-173738-495bea

No human review recorded.