Exact point-isomorphism classification of every defect-preserving endpoint in the complete saved-sixteen degree-preserving 2-for-2 census.

isomorphism-quotiented defect-10 plateau graph

Reconstruct all 115 defect-10 endpoint occurrences from the independently checked 626349-neighbor ledger, canonicalize their point-block incidence graphs, and independently verify all class memberships and nonisomorphisms by exhaustive point-map search.

Hypothesis: Every one of the 115 defect-preserving endpoints is point-isomorphic to one of the sixteen saved classes.

Test: Canonicalize all 115 reconstructed endpoints and independently search for exact point maps to the sixteen saved representatives and among every proposed new class.

The source neighbor ledger was already independently checked as complete. All new endpoint families were reconstructed directly and hash-checked. Nauty produced the classification, while a materially different exhaustive point-map checker validated all positive memberships and all required negative comparisons. Semantic mutations failed closed and regeneration was byte-identical.

• The 115 defect-10 endpoints of the complete saved-sixteen degree-preserving 2-for-2 census comprise exactly 91 distinct labelled families.
• Exactly 24 endpoint point-isomorphism classes lie outside the sixteen saved classes.
• The sixteen saved classes are not closed under legal degree-preserving defect-nonincreasing 2-for-2 moves.
• The known local degree-18 defect-10 plateau contains at least forty point-isomorphism classes.

• sha256sum -c artifacts/degree18-2for2-plateau-closure-20260812/manifest.sha256 passed for every listed file.
• The final reproducibility run returned 0 in 34.368 seconds with seed 0 and a 2048 MB limit.
• The independent checker reconstructed 115 occurrences, supplied 115 exact point maps, and completed 384 new-vs-saved and 276 pairwise-new nonisomorphism tests.
• Three semantic mutations were rejected and endpoints.jsonl and result.json regenerated byte-identically.

• .proof-experiments/20260812-015650-a8caef: a tightened control failed closed because the chosen target-label mutation was semantically only a valid renaming; the mutation was replaced by a genuinely false saved-class assignment.
• .proof-experiments/20260812-020030-872466: final producer, independent classifier, corrected semantic mutations, and regeneration all passed; exactly 24 outside classes.

checkers/check_degree18_2for2_plateau_closure_v1.py imports no producer code and does not call nauty. It reconstructs all endpoint families, exhausts pair-codegree-compatible point maps, replays each positive map over all 54 blocks, and performs all 660 required representative nonisomorphism tests.

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

• Graph canonicalization of block-design incidence structures -> predict that a complete local-move frontier can be quotiented exactly before further search -> observed 91 labelled endpoints collapsing to 39 endpoint classes, including 24 new classes.

• The complete one-step defect-10 frontier from the sixteen saved classes contains 115 occurrences and 91 distinct labelled families.
  Hash-bound endpoint reconstruction from all 626349 candidate-ledger rows. · Legal degree-preserving 2-for-2 moves from the sixteen saved classes. · computed
• Twenty-nine endpoint occurrences form exactly 24 point-isomorphism classes outside the saved sixteen.
  115 positive maps, 384 new-vs-saved tests, and 276 pairwise-new tests. · The classified one-step endpoint set. · computed
• The known local defect-10 plateau contains at least forty point-isomorphism classes.
  The prior sixteen independently separated classes plus 24 new classes independently separated from them and one another. · Known saved classes and their complete one-step defect-preserving frontier. · computed

• The sixteen saved defect-10 classes are closed under legal degree-preserving defect-nonincreasing 2-for-2 motion.
  Their complete one-step frontier. · Twenty-nine endpoint occurrences form 24 classes outside the saved sixteen. · artifacts/degree18-2for2-plateau-closure-20260812/independent-check.json · None; the closure statement is falsified.
• Repeat the proposed complete fixed-pair-link relaxation as a new discriminator.
  All 395 saved signatures and 754 targets in the prior complete gate. · The complete prior gate retained every target, and the later CNF audit found zero new clauses. · artifacts/type4-complete-pair-link-gate-20260809/independent-check.json and artifacts/pair-link-cnf-delta-audit-20260811/independent-check.json · A genuinely new pair-count, labelled-subset, or skeleton constraint that adds independently verified information.

• Complete neighborhood tranche for the 24 new plateau classes.
  This exactly satisfies the previous route's reopen condition and can either produce defect below 10 or quantify further frontier growth. · Extract 24 representatives and run the complete incidence-signature replacement producer plus independent universe-scan checker. · high · open
• Replayable DRAT/LRAT throughput control on a normalized SAT branch.
  The four normalized branches remain the globally complete exclusion route, but scale-up needs measured proof-production and replay throughput. · Run one fixed small cube with proof logging, DRAT conversion, LRAT replay, and measured bytes and conflicts per second. · normal · open

Objective: Determine whether the 24 new classes contain a descending 2-for-2 edge or further expand the finite plateau frontier.

First action: Extract the first full family for each plateau-new target from endpoints.jsonl and create a hash-bound 24-representative protocol.

Stop condition: Stop for immediate validation on defect below 10; close only if the complete new frontier introduces no outside class; checkpoint and compare routes if more than 48 further classes appear.

• Extract one representative for each plateau-new-01 through plateau-new-24 into a hash-bound manifest.
• Adapt the epoch-104 complete producer and independent universe-scan checker to those 24 representatives.
• Validate immediately if any neighbor has defect below 10; otherwise classify the next defect-10 frontier against all known forty classes.
• If more than 48 further classes appear, checkpoint the breadth-first frontier and compare its measured value with normalized-branch DRAT/LRAT proof throughput before another tranche.

• https://www.coveringrepository.com/systems.aspx?k=5&t=3&m=-1 ↗
• https://ljcr.dmgordon.org/cover/show_cover.php?k=5&t=3&v=15 ↗
• https://arxiv.org/abs/math/9502238 ↗
• https://doi.org/10.1002/jcd.3180030404 ↗
• https://arxiv.org/abs/2607.23766 ↗

GPT-5.6 Sol principal audited route status, designed and implemented the discriminator, executed it, and interpreted the evidence. Two GPT-5.6 Terra delegates supplied bounded advisory reconnaissance; their agreement was not validation. Python 3.12.3 reconstructed and checked set systems. Nauty/dreadnaut 2.8.8 canonicalized incidence graphs. An independently written exhaustive point-map checker validated all class claims. SHA-256 bound the packet. Web search checked maintained status and bounded prior art. No SAT solver, CAS, proof assistant, package installation, lab job, external publication, Git commit, or remote write was used.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

1419.7s

Review state

evidence receipt failure; not durable progress

Attempt ID

covering-c1553-20260812-020605-5dd8c5

No human review recorded.