{"id":"openai-math/Bounded-Step-Walks-on-Gaussian-Primes","pdf":"https://github.com/openai/math/blob/main/preprints/Bounded-Step-Walks-on-Gaussian-Primes-September-26-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Bounded-Step-Walks-on-Gaussian-Primes-September-26-2026","tags":["number-theory","gaussian-primes","graph-theory"],"score":0,"title":"Bounded-Step Walks on Gaussian Primes","domain":"Number theory","family":"028","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.NT","summary":"We prove the Gaussian moat conjecture: no infinite walk through distinct Gaussian primes can have bounded steps. More strongly, for each fixed finite step bound, the connected components of the Gaussian-prime graph have uniformly bounded size. This bound applies to every starting prime, including primes on the coordinate axes, and is nonexplicit. The proof constructs a finite periodic sieve obstruction using geometric sampling and information-theoretic estimates.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-26","reactions":{},"formalized":true,"family_title":"Uniformly bounded components of Gaussian-prime graphs"}