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Background: 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. Methods: Weextendthenon-Archimedeanamplitude formalism for open/closed p-adic strings, develop a spectral correspondence mapping Dedekind/Riemann zeros to eigenvalues of a Hermitian operator H, and introduce a learning framework (Corridor Zero/One) for reconstructing spacetime spectra. Additional sections explore the arithmetic–holographic connection, spectral geometry, and cosmological implications. Results: The expanded 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 Beken stein bound dynamically. Conclusions: The 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.