Rational Numbers Matrix

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Authors: Roberto José Coelho de Araujo Dórea
Cited by: 0

Abstract

We present a proof of the Riemann Hypothesis (RH) based on the symmetry of the Rational Numbers Matrix Q. The matrix Q enumerates all rationals symmetrically around zero, enforcing E[Q] = 0 by geometric necessity. Primes, being strictly positive, exist only on one side of Q with no negative counterparts. The only valid perturbation of a prime is to another prime (e.g., 7 → 11), but even this breaks E[Q] = 0 since there is no "-7 prime" to compensate. If RH were false, off-critical-line zeta zeros would perturb prime distribution, violating E[Q] = 0. Since this symmetry is geometrically necessary, RH must be true.

Fields of Study & Subjects

Analytic Number Theory Research Advanced Mathematical Theories and Applications Advanced Mathematical Theories

Publication details

Journal / source
Zenodo (CERN European Organization for Nuclear Research)
Publication date
12 January 2026
Document type
Preprint