{"id":"openai-math/Single-fold-Diophantine-representations","pdf":"https://github.com/openai/math/blob/main/preprints/Single-fold-Diophantine-representations-September-24-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Single-fold-Diophantine-representations-September-24-2026","tags":["logic","diophantine-equations","computability","hilbert-tenth-problem"],"score":0,"title":"Single-fold Diophantine representations","domain":"Mathematical logic","family":"242","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.LO","summary":"Every recursively enumerable set of natural-number tuples has a polynomial Diophantine representation with exactly one complete auxiliary tuple for each member. This proves the single-fold conjecture and, consequently, the finite-fold conjecture.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-24","reactions":{},"formalized":true,"family_title":"Single-fold Diophantine representations and undecidability under an at-most-one-solution promise"}