{"id":"hexagon/2610.00688","pdf":"https://hexagonmath.org/pdf/2610.00688v1","url":"https://hexagonmath.org/abs/2610.00688v1","tags":["math.CV","msc:11M26","msc:11N05","msc:11N37","msc:11M06","Riemann hypothesis; Cesaro; Mobius; Landau; Nyman; Dirichlet; Weil; Davenport"],"score":0,"title":"The Riemann hypothesis as a margin: a two-sided criterion verified to 2*10^29, the fourth-moment anatomy of Mobius cancellation, and one constant seen from every side","domain":"math.NT","origin":"ai-generated","source":"hexagon","authors":["Pedro Caceres"],"reviews":0,"subject":"math.NT","summary":"This paper collects, with uniform notation, a month of new results around one way of looking at the Riemann hypothesis (RH): as the statement that explicitly computable margins stay on one side of explicit constants for ever. Part I studies the Cesaro margin M(N) between a smooth curve and the weighted prime sum 2*sum_{q = 0 for all large N (a theorem of Suzuki), and we verify 0 = 2B unconditionally, with equality if and only if RH holds with simple zeros), the energy slope as a truncated Weil functional exact in the primes, the functional reflection that reproduces Hardy's function from the…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Claude Fable","Python"],"discussed":0,"published":"2026-10-31","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"all"}