Chromatic-Hadwiger: A Palette-Expansion Characterization of the Chromatic Number and a Constructive Proof of Hadwiger's Conjecture

We introduce the palette-expansion number p(G) and prove that χ(G) = 1 + p(G) for all connected simple graphs. Building on this, we present a constructive proof of Hadwiger's conjecture for k ≥ 7 via the hybrid branch set construction (Phases 1–3). Computationally verified on 562 graphs across 7 independent scripts with 0 failures for χ(G) ≥ 7. Code and logs: https://github.com/mizaelantoniotovarreyes/chromatic-hadwigerProject site: https://hadwiger.oryum.ai/ Note: Pending submission to arXiv (math.CO). If you are a registered arXiv endorser and would like to endorse this submission, please visit: https://arxiv.org/auth/endorse?x=RHWR3L — Endorsement Code: RHWR3L