Paper 125E: A Single-Scale RH Criterion and Dark Visibility in the Primitive Möbius Slice Moving-Window Observability, an Explicit Diagonal Constant, and a Hidden Factor-Count Carrier
Year: 2026
Type: article
Abstract: A single primitive numerator, one denominator shell, and one block length suffice to encode theRiemann hypothesis in an explicit moving-window energy. We represent the arithmetic amplitudesby two real components, identify their energy with a compact moving-window transform, and recoverfixed smooth Möbius sums by a finite telescoping identity. A smooth multiplicative partition thengives a locally uniform continuation of the reciprocal zeta function. This proves that subpolynomialgrowth of the one-scale energy along dyadic scales is equivalent to the Riemann hypothesis, withoutan unproved passage from smooth sums to sharp partial sums. The diagonal has an unconditionallimiting constant of approximately 9.89144; the unresolved growth is in the signed interactionsbetween distinct denominators. A separate finite analysis groups all squarefree denominators by theiractual number of prime factors. Its real Gram matrix distinguishes a large sign-removed carrier fromthe much smaller Möbius combination and identifies a subordinate mode carrying most of the latterat the larger tested scales. Complete factor-count bookkeeping, signed contribution accounts, andrandomized controls delimit this visibility interpretation. The figures and full reproduction programsare embedded in the manuscript. The result is an exact criterion with finite operator diagnostics, nota proof of its required asymptotic bound or a uniquely physical explanation of prime cancellation.
Author: Sarnowski, Michael
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225810594
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