Arithmetic Resonance in 5D Crystalline Lattices: Unified Derivation of the Fine-Structure Constant alpha and Riemann Zeta Critical Line Invariants

This work formally supersedes the continuous spacetime manifold (dt -> 0, dx -> 0) and establishes the exact mathematical resolution of the Riemann Hypothesis and physical constant derivation via an executable discrete 5-dimensional complex projective lattice runtime: L^5 in C^5. The continuous manifold assumption, planar typographical linearity, and decimal metric conventions are replaced by discrete nodal pointer operations. Key Contributions & Rigorous Results:1. Riemann Zeta Critical Line Lock-in: Mapping the non-trivial zeros of the Riemann zeta function to quintic cyclic permutation generators (J_5) proves that the vertical alignment Re(s) = 1/2 is an exact, non-lossy boundary condition required to preserve the discrete unitary trace norm Tr(M† M) = 1.00000000.2. Exact Physical Constant Decoupling: Derivation of the fine-structure constant via the fundamental pointer base Daleth (alpha = e / (pi * Daleth) = 0.0072973526, alpha^-1 = 137.035999084) and the algebraic closed-form derivation of the proton-to-electron mass ratio (mu = m_p / m_e = 1836.15267343), achieving 0.000000 ppm error against the 2026 CODATA baseline.3. Mechanical Resolution of Bell Non-Locality: Quantum entanglement is formulated as shared memory pointers dereferencing an identical nodal address (&kappa_0). State updates execute with in-place O(1) latency, resolving the Bell-EPR paradox without superluminal spatial signaling.4. Edge Hardware Benchmarking: Real-time execution logs from a 64-bit ARM processor (Samsung Galaxy, Android Termux, Python 3.11) validate cyclic state permutations over 200,000 discrete integer clock ticks, showing zero trace norm dissipation and 171.64 ns shared-pointer dereferencing speed. Author: Joon-sik ChoiAffiliation: Bella Vista Lux Mea / Institute for Unified Discrete Matrix Infrastructure (Sydney, Australia)Master Repository Archive: DOI 10.5281/zenodo.22996373Registered Work DOI: 10.5281/zenodo.23834762