Hadron Mass Spectrum Arithmetic Operator on Primes

A zero-parameter formula M = (D/163) × γₙ GeV relates particle masses to imaginary parts of non-trivial Riemann zeta zeros, where D ∈ 24, 32 are lattice dimensions (Leech lattice for the QCD sector, E₈ structure for the electroweak sector) and 163 is the largest Heegner number. Applied to the PDG 2025 database, the formula resolves 82 particles above spectral threshold with R² = 0. 99998 and MAPE = 0. 69%, with zero continuous free parameters. Seven parameter-free mass ratios Mᵢ/Mⱼ = γₙᵢ/γₙⱼ (mean deviation 0. 060%, p 5σ (arXiv: 2602. 02252) are mapped to consecutive zeros n = 8, 9, 10 with errors 0. 6–2. 6%. The Weinberg angle sin²θW is reproduced to 0. 018% accuracy from a zero ratio. The QCD freeze-out temperature Tfreeze = k ln 2 = 102 MeV is confirmed by ALICE data. The framework is built on a self-adjoint arithmetic operator Ĥₐrith defined from cumulative prime sums, whose spectrum converges to the Riemann zeros with exponential bounds (Theorem A) and is made exact via a Newton–Raphson map (Theorem B). A derivation of the Riemann Hypothesis is presented as a consequence of three independent spectral obstructions (convergence, spacing, completeness), formalized in Theorem 5. 17. The derivation is logically complete and awaits independent peer verification. Additional structures include: a complete effective Lagrangian with Zeta-Higgs potential and Feynman rules; electroweak consistency including the W mass from the j-invariant; a LeClair–Mussardo scattering interpretation via Bethe ansatz; an exact information conservation law verified to 10⁻¹⁴ on 29 transitions; and a thermal derivation of the QCD crossover temperature Tc = 155 MeV (lattice QCD: 156. 5 ± 1. 5 MeV). Falsifiable predictions are pre-registered for LHCb, BESIII, ALICE, KATRIN, and DUNE.