Sharp Nonnegative Hadamard Powers on the Six-Vertex Wheel

This preprint proves the exact positive exponent set {1} union [2,infinity) for entrywise nonnegative positive semidefinite matrices supported on the six-vertex wheel C5+. The analytic proof covers singular matrices and zero allowed edges and describes strictness in the positive-rim rank-three family. Exact and outward checks accompany the sources. The technical supplement contains quantitative gap bounds, certified neighborhoods and counterexamples to stronger proposed methods. The arbitrary-graph GKR problem and longer odd-rim wheels remain unresolved. Consolidated preprint edition 1.0, dated 5 November 2026. The main PDF and its source/certificate archive form one article. The accompanying technical supplement belongs to this article. Conceptual origin and AI assistance. The initial idea and conceptual starting point of this investigation are based on the framework of the original geometric paper by Christos Panorias and Kostandina Theodhori, Canonical Parametric Representation of Plane Euclidean Geometry (DOI: 10.5281/zenodo.23837735). This attribution concerns the conceptual origin and methodological organization of the research; every mathematical premise required by the present proofs is stated explicitly here. OpenAI ChatGPT/Codex assisted verification of calculations, editorial polishing and selected, delimited arguments during proof development, including substantive mathematical reasoning in those arguments. Christos Panorias is the sole named author and retains responsibility for reviewing, adopting and submitting the mathematical claims and final text. Research preprint for scholarly scrutiny. Independent peer review, proof-assistant formalization and worldwide priority are not certified.