A constraint graph of open conjectures: proven logical relations, exact model counts, and auditable conditional consequences

A versioned registry of proven implications and incompatibilities between mathematical conjectures, represented as signed Boolean clauses with exact model counts. Version 12 strengthens the twin-prime packing result to an unconditional bound for every window with x >= y and 3 <= y <= 378, and proves under Dickson that the first actual crossing is exactly 379. It gives complete revised proofs that the Cochrane-Dressler gap conjecture implies infinitely many non-Wieferich primes, including liminf W_2(X)/log X >= 1/(2 log 2), and the existential-window Erdos-Woods conjecture, hence the existing Woods arithmetic-definability consequence. It also proves CD implies a uniform perfect-power gap bound C-B >= c_delta C^(1/12-delta), and therefore Pillai finiteness with all bases and exponents at least 2. The constructions and counting methods have established precedents; the exact CD implications were not located in the checked sources, and worldwide priority is not established. A ten-candidate research batch is documented with primary-source dossiers, structured records from Fable 5.1 main reviews invoking Opus 5 proof-review agents, where completed, and explicit integration outcomes, including unsuccessful or unresolved cases. Current numerical graph statistics and batch outcomes are generated from the release data in release_facts.json and the note. The curated standalone atlas works offline, with full-registry search and embedded proofs. The source bundle retains historical notes, proof notes, certificates, archived graph baselines, historical audits, structured review records, and reproducible build tools. Prepared with the assistance of OpenAI Codex and Anthropic Claude systems; actual review-model identities are recorded in the run artifacts. The author is responsible for the publication. CC BY 4.0.