A Nonmonotone Real-Rootedness Set for Symmetric Imaginary Shifts

Abstract

AI Research Artifact. This work presents an exact rational degree-8 polynomial whose symmetric imaginary-shift real-rootedness set is neither an interval nor an up-set. The explicit witness and candidate proof were materially model-generated. Version 0.1.3 replaces mental-state and submission-decision wording with action-based authorship and accountability language and aligns Zenodo and arXiv metadata. The theorem statement, proof arguments, polynomial, and exact certificates are unchanged from version 0.1.2.