A constraint graph of open conjectures: proven logical relations between unproven statements, with exact model counts

A registry ('constraint graph') whose vertices are named open statements of mathematics and theoretical computer science and whose edges are published theorems relating two of them: the two cannot both hold, cannot both fail, or one implies the other. Each edge is a signed 2-clause, so the registry is a 2-CNF whose satisfying assignments are the truth-value patterns still permitted by known theorems. Version 11 holds 644 relations between 676 canonical statements, each with a citation and a verifier log. The note describes how the edges were collected (literature-search agents, adversarial verification with relation correction, canonicalisation) and what the graph shows: three mutually disconnected continents (complexity theory; number theory with harmonic analysis; set theory), a small set of hubs, a resolution closure of derived clauses, no forced literal and no contradiction, and exact counts of remaining labelings (2^193.2, 2^92.9 and 2^50.6 for the three continents). Own results: the exact twin-prime crossing y0 = 379 for the Hensley-Richards mechanism with the table of minimal diameters of admissible packings of twin pairs; ten composite incompatibilities with their prior-art status; and the certificate mechanism used as one edge type. The model count is proposed as the progress measure for the registry. Files: note.pdf/note.tex (the note), edges.json (the registry), aliases.json (canonical statements), nodes.json, registry.md (tables, derived clauses, model counts), graph_min.html (interactive graph of the named statements; open in a browser), build.py (regenerates the derived files), verifier_results.jsonl (verifier transcripts), certificates and checker data. Prepared with the assistance of AI systems (Claude, Anthropic); the author is responsible for the content. CC BY 4.0.