Certified nonexistence of a 20-vertex graph with consecutive Laplacian spectrum

Abstract

Pre-publication exact certificate archive, independently checkable verification code, canonical results, and companion manuscript for the nonexistence of a simple graph on 20 vertices with Laplacian spectrum {0,1,...,19}. The frozen certificate archive has SHA-256 1eeda59a36dc835ec0efd3dc741d985145054af0d72e77f59e84f9cb63461206, and two fresh offline replays produced the identical canonical-result SHA-256 735fa3da7b587ebd6ae44ca732bdf69b401bbf2db53ea0234a7e28e60b19a1c2. AI systems assisted drafting, code generation, testing, and review; the named human author curated and executed the exact verification and remains responsible. No prompts or chat transcripts are included. The result has not yet undergone external human peer review, and a DOI records identity and preservation rather than mathematical endorsement.