IMM Companion: Two Spectral Fingerprints of the Riemann Zero Measure — Unifying the Turán/Jensen and CMO/det2 Programs
Year: 2026
Type: preprint
Abstract: This preprint presents a structural unification of two historically independent approaches to the Riemann Hypothesis: the Turán/Jensen program and the Constrained Matching Operator (CMO)/det₂ program. Both approaches are shown to analyze the same underlying Riemann zero measure through different analytic transforms. The connection is made explicit through the Stieltjes–Poisson bridge, relating reciprocal moment sequences to harmonic Poisson extensions. The work identifies the remaining analytical challenge as establishing complete positivity of the associated Stieltjes–Hankel matrices, thereby locating the unresolved step within the classical Stieltjes moment problem. Numerical experiments verify positive definiteness for the tested finite cases while explicitly distinguishing numerical evidence from proof. This manuscript is intended as a structural contribution connecting existing research programs rather than as a claimed proof of the Riemann Hypothesis.
Author: Bergen, Travis
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7166462458