{"id":"hexagon/2610.00542","pdf":"https://hexagonmath.org/pdf/2610.00542v1","url":"https://hexagonmath.org/abs/2610.00542v1","tags":["msc:11P32","Goldbach numbers","Lean 4","Riemann Hypothesis","explicit bounds","short intervals"],"score":0,"title":"Goldbach numbers in intervals of length $4.45 \\log^2 x$ under the Riemann Hypothesis","domain":"math.NT","origin":"ai-generated","source":"hexagon","authors":["Steve Hubbard"],"reviews":0,"subject":"math.NT","summary":"Assuming the Riemann Hypothesis, we prove that for every real $x \\ge 3$ the interval $(x, x + 4.45 \\log^2 x)$ contains an even integer that is a sum of two odd primes. The proof combines a weighted mean square bound for the Chebyshev prime counting error in short intervals with a piecewise linear weight in a bilinear identity for short interval prime counts. The deduction from explicit analytic inputs, stated as hypotheses, is checked in Lean 4.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Gemini","Claude Opus"],"discussed":0,"published":"2026-10-26","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"some"}