SIDE QUEST 09 / COMPUTATIONAL MATHEMATICS / CERTIFIED SEARCH
The strongest branch of the solver repository is no longer a speculative search. It is an expert-review-ready certification package that extends several published finite verification frontiers in graph labeling.
The current expert packet certifies that every tree with 2 ≤ n ≤ 23 is super edge-magic. The research record lists 17 as the standing published all-tree bound. The claim is computational, independently checked, and still pending specialist bibliographic confirmation and human review.
The current package certifies the odd-graceful conjecture for every tree through n = 24, compared with a standing published bound of 12 in the repository's prior-art audit. Exact certificate streams and independent counting/checking are the core evidence.
Every unicyclic graph with at most 19 vertices, except the cycle exceptions Cn with n ≡ 1 or 2 mod 4, is certified graceful. The repository records the previous exhaustive bound it could verify as n ≤ 9; this remains subject to the same expert prior-art check.
Certificate streams are deterministically regenerable. A separately written Rust checker validates labelings, verifies pairwise non-isomorphic trees through canonical keys, and checks the census against Otter tree counts. The unicyclic result also has independent Python and Rust verification paths.
The cross-repository publication program labels the tree-labeling package level 11 and EXPERT_REVIEW_READY. That means the autonomous verification, regeneration, red-team and handoff work is complete. The remaining gates are human: specialist literature databases, expert review, authorship and AI-use disclosure decisions, and venue selection.
No structural proof for all orders is claimed. The result is narrower and more auditable: exhaustive finite verification over explicitly stated ranges, with one certificate per graph and independent checks that the graph census is complete.
The program separates discovery from acceptance. A search implementation may propose a labeling, but a different implementation checks it; regeneration tests remove dependence on one binary; negative controls and red teams target failure modes; and prior-art review determines whether the finite extension is actually new.
The mature package is frozen for expert review rather than continuously rewritten by agents. That is intentional: once the autonomous gates are closed, further changes should be driven by an error report, new prior art or human feedback.