Exhaustive breadth-first degree-preserving 2-for-2 expansion from the 24 newly validated defect-10 point-isomorphism classes, followed by exact point-isomorphism classification against the known 40-class frontier.

isomorphism-quotiented defect-10 plateau graph

Enumerate every labelled-incidence-preserving two-block replacement from one representative per class, score exact triple coverage, and quotient the defect-preserving endpoints by point isomorphism.

Hypothesis: At least one of the 24 new defect-10 class representatives has a legal degree-preserving 2-for-2 neighbor with at most nine uncovered triples.

Test: Enumerate and independently reconstruct every legal nonidentity degree-preserving 2-for-2 neighbor of the 24 representatives; read the exact minimum defect and, if it remains ten, classify every defect-10 endpoint against the known 40 classes.

The producer result was reproduced by a materially different exhaustive replacement enumeration and full 455-triple recomputation. Classification was independently replayed without nauty using exact point maps and exhaustive nonisomorphism tests. Mutation controls and byte-identical regeneration passed. The scope is local and cannot imply a global covering bound.

• Across the complete legal degree-preserving 2-for-2 neighborhoods of the 24 declared new defect-10 classes, there are exactly 937,780 legal nonidentity moves and the minimum uncovered-triple count is ten.
• The 142 defect-10 endpoint occurrences comprise 105 distinct labelled families; 80 occurrences form exactly 51 point-isomorphism classes outside the previously known 40.
• The independently validated local defect-10 plateau therefore contains at least 91 point-isomorphism classes.
• No 54-block cover or exclusion of 54 was obtained; 54 <= C(15,5,3) <= 55 remains open.

• python3 scripts/degree18_2for2_repair_census_v1.py --protocol protocols/degree18-2for2-frontier24-census-v1.json --output-dir artifacts/degree18-2for2-frontier24-census-20260812
• python3 checkers/check_degree18_2for2_repair_census_v2.py --protocol protocols/degree18-2for2-frontier24-census-v1.json --artifact-dir artifacts/degree18-2for2-frontier24-census-20260812 --output artifacts/degree18-2for2-frontier24-census-20260812/independent-check.json
• python3 scripts/classify_degree18_frontier24_endpoints_v1.py --protocol protocols/degree18-frontier24-endpoint-classification-v1.json --output-dir artifacts/degree18-frontier24-endpoint-classification-20260812
• python3 checkers/check_degree18_frontier24_endpoints_v1.py --protocol protocols/degree18-frontier24-endpoint-classification-v1.json --artifact-dir artifacts/degree18-frontier24-endpoint-classification-20260812 --output artifacts/degree18-frontier24-endpoint-classification-20260812/independent-check.json
• Both manifest files replay with sha256sum -c; five census mutations and three classification mutations were rejected; both packets regenerated byte-identically.

• .proof-experiments/20260812-023943-56ad94: extracted 24 deterministic representatives; independent extraction check passed in 20260812-023934-84d165.
• .proof-experiments/20260812-024040-d1711c: generated 937,780 legal moves in 102.071 seconds; minimum defect ten.
• .proof-experiments/20260812-025819-d7eb32: independent universe scan reproduced all rows and minimum defect ten in 91.951 seconds.
• .proof-experiments/20260812-024748-1287d1: classified 142 endpoints into 51 outside classes in 8.204 seconds.
• .proof-experiments/20260812-024822-d1803c: nauty-free independent classification passed in 8.954 seconds.
• .proof-experiments/20260812-025958-b6d219 and 20260812-024848-4cb960: five census and three classification mutations rejected.
• .proof-experiments/20260812-025022-9179f0 and 20260812-024919-719916: census and classification regenerated byte-identically.

check_degree18_2for2_repair_census_v2.py uses an all-3003-block first-member scan and full 455-triple unions, unlike the producer's direct signature partitions and deltas. check_degree18_frontier24_endpoints_v1.py never calls nauty or imports producer code; it exhausts pair-codegree-compatible point maps and replays all 54 blocks.

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 canonical augmentation -> quotient a local-search frontier by exact point isomorphism -> observed 24 input classes expanding to 51 new classes, so the quotient controls duplication but not branching.
• Cube-and-conquer stop rules -> predeclare a frontier-width ceiling before another breadth-first tranche -> observed 51 > 48 and redirected without scaling.
• Covering-link analysis from C(12,6,4) -> predict fixed-point links expose forced degree profiles -> next bounded test is a (14,4,2) link catalog, not yet observed.

• The declared 24 class representatives have exactly 937,780 legal nonidentity degree-preserving 2-for-2 neighbors and minimum defect ten.
  Complete ledger plus independent all-3003-block reconstruction; SHA-256 manifest 4f7ce7d5332bc6f541eb5eb42f560de082fc5ac70cf741493c47869d7b30d0e6 · One-step 2-for-2 neighborhoods of plateau-new-01 through plateau-new-24 · computed
• The 142 defect-10 occurrences in that ledger comprise 105 labelled families and exactly 51 point-isomorphism classes outside the known 40.
  142 positive maps, 2,040 novel-vs-known exclusions, 1,275 pairwise-new exclusions; classification manifest c8dc865c02be2d55e55118ce4bbc3832cb5ec2168b1c12dc57af43d46b682877 · Defect-10 endpoints of the same complete local tranche · computed
• The independently validated local defect-10 plateau contains at least 91 point-isomorphism classes.
  Previously validated 40 classes plus 51 independently excluded new classes · Known campaign corpus only; not a complete global classification · computed

• Find a defect-below-10 family by one legal degree-preserving 2-for-2 move from any of the 24 new representatives.
  All 937,780 legal moves in the declared 24-class tranche · The exact minimum defect is ten. · Complete producer ledger and independent full reconstruction · A different starting class, a nonmonotone path, or a different trade size; rerunning this exact tranche is closed.
• The known 40 classes are closed under defect-preserving 2-for-2 moves from the 24 newly added classes.
  All 142 defect-10 endpoints in this tranche · Exactly 51 point-isomorphism classes lie outside the known 40. · Independent point-map and nonisomorphism checker · None; the closure claim is falsified.
• Continue breadth-first 2-for-2 expansion immediately.
  Resource-allocation decision after this tranche · The frontier grew by 51 classes, exceeding the predeclared 48-class stop without improving defect. · Hash-bound classification result and protocol threshold · A new invariant that eliminates classes in bulk or measured evidence that another tranche has greater expected value than structural/proof routes.

• Catalog fixed-point 18-block (14,4,2) links under forced degree profiles.
  In any 54-block cover each point has degree 18; its link covers every pair on 14 points, each link point has degree at least five, and total link degree 72 forces profile 7,5^13 or 6^2,5^12. A small catalog could prune global branches by whole link types. · Write a deterministic canonical augmentation protocol and first count isomorphism classes separately for the two profiles, with an independent pair-coverage and orbit checker. · high · open
• Measure normalized-branch DRAT/LRAT proof throughput.
  This is the terminal negative route, but scale-up remains blocked by UNKNOWN branches and unmeasured certificate throughput. · Select one immutable, already authorized canonical branch; demand UNSAT plus DRAT-to-LRAT replay within a fixed cap, otherwise hold proof-scale dispatch. · normal · open
• Test structural invariants on the 91-class local corpus.
  A discriminator that separates the 51 newly found classes or correlates with pair-excess skeletons could turn the expanded corpus into bulk pruning rather than another BFS layer. · Compute exact link-profile, pair-excess, and uncovered-triple orbit signatures for one representative per class and test whether any signature class is forbidden by global moment equations. · normal · open

Objective: Replace class-by-class local expansion with a fixed-point link classification that can prune whole global families.

First action: Prove in a protocol note that every point link has 18 four-blocks covering all pairs with degree profile 7,5^13 or 6^2,5^12, then estimate the labelled search and canonical-augmentation bottleneck before enumeration.

Stop condition: Redirect if the link catalog remains too large to couple to pair-excess skeletons, if an independent checker finds coverage disagreement, or if a matched normalized-branch proof pilot offers greater validated uncertainty reduction per CPU-hour.

• Hold another 2-for-2 BFS tranche because 51 new classes exceeded the predeclared 48-class stop.
• Prove and encode the fixed-point link lemma: each point link is an 18-block (14,4,2) covering whose link degrees are 7,5^13 or 6^2,5^12.
• Run a bounded isomorphism-class census of those link profiles and stop if the catalog is too large to couple to pair-excess skeletons.
• Compare that measured structural gate with an independently replayable normalized-branch proof-throughput pilot before allocating proof-scale compute.

• https://www.coveringrepository.com/systems.aspx?k=5&t=3&m=-1 ↗
• https://arxiv.org/abs/math/9502238 ↗
• https://arxiv.org/abs/2607.23766 ↗

GPT-5.6 Sol principal selected, implemented, executed, and interpreted the bounded discriminator. Two GPT-5.6 Terra delegates supplied pre-epoch advisory reconnaissance as challenger-prior-art and experiment-verification roles; their agreement was not counted as validation. Python 3.12.3 performed deterministic enumeration and checking; nauty/dreadnaut 2.8.8 canonicalized incidence graphs; a separately written exhaustive point-map checker provided independent classification; SHA-256 bound artifacts; web search checked current status and bounded prior art. No SAT solver, CAS, proof assistant, cloud lab, package installation, external publication, Git commit, or remote write was used.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

2189.1s

Review state

evidence receipt failure; not durable progress

Attempt ID

covering-c1553-20260812-030704-bc98f3

No human review recorded.