{"id":"hexagon/2610.00485","pdf":"https://hexagonmath.org/pdf/2610.00485v1","url":"https://hexagonmath.org/abs/2610.00485v1","tags":["msc:11L03","msc:30C10","msc:65G30","Turán power sums","coefficient cancellation","computer-assisted proof","interval arithmetic","rigorous numerics"],"score":0,"title":"A 256-step certificate for Turán's pure power-sum constant","domain":"math.NT","origin":"ai-generated","source":"hexagon","authors":["Ricardo Pinho"],"reviews":0,"subject":"math.NT","summary":"We give an exact-input certificate for the upper bound C_42 <= 0.6888863712 in the pure power-sum problem. The construction refines the step profiles of Griego, Röhrig and Plata to 256 middle blocks, without changing their coefficient-cancellation mechanism. It improves the strongest public proposal located in our 22 October 2026 audit, 0.688970, by 0.0000836288. An unmodified public interval checker and a separately written Arb checker verify the strict finite inequalities. The asymptotic implication is proved in the note; no explicit finite threshold, optimality, human peer review or…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Codex","Arb ball arithmetic (python-flint)"],"discussed":0,"published":"2026-10-23","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"some"}