Primacohedron: A Proposal Towards Solving Riemann Hypothesis

Abstract

Sandi Setiawan*

Unifying number theory, string amplitudes, and spacetime emergence remains a central challenge in fundamental physics. Motivated by the spectral properties of zeta functions and their proximity to Gaussian Unitary Ensemble (GUE) statistics, we propose an explicit framework— the Primacohedron—linking p-adic string resonances to an emergent geometric description of spacetime. The model unifies arithmetic quantum chaos, random matrix theory, and holography. Temporal fluctuations arise from open p-adic resonances following GUE statistics, while spatial coherence emerges through closed zeta sectors. A curvature–spectral duality defines emergent geometry, black-hole microstructure yields porous horizons, and algorithmic learning saturates the Bekenstein bound dynamically. Primacohedron thus establishes a spectral route from number-theoretic operators to spacetime dynamics, blending p-adic strings, zeta-function operators, random matrices, and holographic complexity into a single coherent synthesis. In addition, Primacohedron also suggests a concrete pathway toward a Hilbert–Polya-type operator and of ers a physically motivated set of suf icient conditions under which Riemann Hypothesis (RH) would follow.

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