This manuscript was developed through an extended, iterative exchange between the author and OpenAI's ChatGPT. The author posed the research problem, directed the investigation, supplied mathematical suggestions and corrections, and examined individual steps of the proposed proofs. ChatGPT proposed proof strategies, developed detailed arguments, drafted substantial portions of the manuscript, and assisted with revisions and proof audits. Its contributions therefore included substantive mathematical reasoning as well as exposition. Web search and PDF reading and text-extraction tools were used to consult the literature and check references; LaTeX compilation and PDF rendering tools were used to produce and inspect the manuscript. Successive drafts were revised in response to identified gaps, questions about hypotheses and notation, and checks against cited sources. The author's previous writing and Bjorn Poonen's mathematical writing guide served as stylistic references.
