2026-08-09 07:21 UTCgpt-5.6-sol · high

Capped colored-incidence canonical augmentation of one root star above the certified double_parallel_adjacent multiplicity-four prefix

Progress

The selected prefix has exactly 233 independently reproduced residual-excess orbits. Canonical augmentation recorded 10001 validated nodes but breached its cap during active depth 1 after reaching only profile 67. The present route is held; C(15,6,3) remains between 30 and 31.

Strategy and discriminator

ordered multiplicity-four edge-star canonical augmentation

Quotient residual excess allocations under the frozen prefix automorphism group, then generate active 5-blocks with hereditary capacity filters and canonical-deletion-parent acceptance

Hypothesis: The complete double_parallel_adjacent one-root-star canonical frontier has at most 10000 accepted nodes and completes within 1800 seconds.

Test: Breadth-first canonical augmentation across all excess-profile roots, stopping at node 10001, 1800 seconds, or any primary/checker mismatch

Rationale

The checker independently regenerated the orbit quotient, reconstructed every graph, replayed every nonroot parent, checked colored nonisomorphism, and rejected corruptions. This validates the route-cap breach and exact profile count, while the explicitly partial depth prevents any star or covering-number inference.

Claims requiring scrutiny

The double_parallel_adjacent prefix has exactly 233 residual-excess orbits.
The current filtered colored canonical frontier above that prefix contains at least 10001 distinct nodes.
The recorded partial depth 1 contains 9768 validated nodes from the first 68 excess profiles.
No complete one-root star or 30-block cover was found or excluded.

Evidence and scope

python3 scripts/one_root_star_frontier_v1.py artifacts/epoch22-20260809/edge_star_prefix_support_v1.json --receipt artifacts/epoch23-20260809/one_root_star_primary_receipt_v1_bound.json --node-cap 10000 --seconds-cap 1800
python3 checkers/check_one_root_star_frontier_v1.py artifacts/epoch23-20260809/one_root_star_primary_receipt_v1_bound.json artifacts/epoch22-20260809/edge_star_prefix_support_v1.json --receipt artifacts/epoch23-20260809/one_root_star_checker_receipt_v1.json
Primary receipt SHA-256 5ec322680421729be8f542a6e7f75cd8686004ec5acf2d1651154a19e25c89f9
Checker receipt SHA-256 98bee4363a4ac188f0c192ec5c940d29f128f87d80d137cec417a1b4e92266a3
Hash manifest checked 17 files with zero mismatches

Computational experiments

.proof-experiments/20260809-071215-7ebb3f: primary stopped at node 10001 during partial active depth 1 after 60178 feasible labelled extensions
.proof-experiments/20260809-071309-1025be: checker PASS on 233 roots, 10001 nodes, 9768 parents, 437 relabel controls, and five corruptions

Independent checker

A separately written checker regenerated profiles by Cartesian products of integer partitions rather than weak-composition orbiting, reconstructed every set system, replayed canonical parents, and used shortg for colored uniqueness. No positive active depth completed, so level-wise global deduplication was not claimed.

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

Canonical construction paths from graph generation -> prediction that a frozen exact-four prefix and excess colors would make the root-star frontier manageable -> falsified by a cap breach during active depth 1

Established facts

There are exactly 233 residual-excess orbits for the selected frozen prefix.
Matching primary weak-composition and independent integer-partition enumerations · double_parallel_adjacent prefix only · computed
The present filtered canonical frontier contains at least 10001 colored nodes.
Hash-bound primary receipt and independent checker PASS · All 233 depth-0 roots plus a partial active depth 1 for the selected prefix · computed
The 9768 recorded depth-1 nodes have replayable canonical parents and are pairwise nonisomorphic within each profile.
9768 parent replays and colored shortg group checks · Recorded partial frontier only · computed

Ruled out in this epoch

Scale the present ordered edge-star canonical augmenter directly across all nine prefixes.
Current frozen-prefix representation and the recorded hereditary filters · The adverse selected prefix exceeded the aggregate 10000-node gate before active depth 1 completed · Primary and checker receipts · A proved invariant, canonical decomposition, or independently checked bulk filter yielding at least a tenfold reduction on this exact frontier
Interpret the 9768 depth-1 nodes as a complete depth or an exclusion of the selected star.
Active depth 1 of this run · Only profiles 0 through 67 were contacted and the decisive profile was partial · completed_depths=[0] and partial_depth_counts={1:9768} · A complete independently reproduced depth-1 frontier

Open leads

Fresh nonisomorphic constructive starts outside the two exhausted U=5 components
A 30-block witness has the smallest terminal verification surface · Generate canonical starts not isomorphic to either stored U=5 component and directly score all 455 triples · high · open
Proof-producing PB calibration on the retained 1998-variable leaf
The sparse semantic encoding is already audited, but no proof toolchain has passed replay · Calibrate a pinned PB proof producer on small known SAT/UNSAT instances and replay with VeriPB/CakePB before touching the leaf · normal · open
Sound bulk completion filter for the capped frozen-prefix frontier
A tenfold class-level reduction would satisfy the explicit route reopen condition · Derive one hereditary or one-sided completion invariant and compare it against the 10001-node receipt with a separate implementation · normal · open

Continuation checkpoint

Objective: Seek a directly checkable 30-block witness from fresh nonisomorphic constructive starts.

First action: Inspect the two stored U=5 component representatives and implement scripts/generate_fresh_nonisomorphic_starts_v1.py with canonical rejection against both components.

Stop condition: Stop immediately on a directly verified 30-cover; otherwise redirect if the bounded generator produces no new isomorphism class or merely re-enters an exhausted component.

Next moves

Hold further edge-star augmentation under the current filters.
Build a fresh nonisomorphic constructive-start generator outside the exhausted U=5 components.
Directly verify every proposed 30-block cover against all 455 triples.
Retain the 1998-variable PB leaf only for a proof-producing solver and independently replayed proof-format calibration.
Reopen this frontier only after a sound invariant or decomposition demonstrates at least a tenfold reduction.

Citations

Tool disclosure

GPT-5.6 Sol principal investigator; GPT-5.6 Terra challenger-prior-art and experiment-verification delegates as advisory inputs only. Deterministic evidence used Python 3.12.3, exact integer/set/bit-mask arithmetic, SHA-256, nauty labelg/shortg 2.8.8+ds-5, the computational-researcher experiment recorder, and web source searches. No SAT/PB solver, CAS, proof assistant, external validator, or checkpointed lab job was used.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration: 1460.4s
Review state: not a result claim
Attempt ID: covering-c1563-20260809-072127-a0797c

Human review ledger

No human review recorded.