Algebraic Closure of the Standard Model: 26 Parameters from p2 − p = 1

The algebraic condition p2 − p = 1, whose positive root is the golden ratio φ = (1 + √5)/2,uniquely fixes the five constants of the Energy–Space Displacement (ESD) covariant scalar–tensor action. From these constants and the single dimensionful anchor me = 0.5110 MeV(itself derived from the D-field bridge in Ref. 1), we derive closed-form expressions for twenty-six free parameters of the Standard Model: three gauge couplings (sin2 θW , αs, αEM), twelvefermion masses, four CKM mixing parameters, four PMNS mixing parameters, the Higgs vac-uum expectation value, the Higgs boson mass, and θQCD. Every prediction is a closed-formexpression in φ and ln φ multiplied by rational group-theoretic coefficients, with no adjusteddimensionless parameters beyond the single dimensionful anchor me. In the fermion mass sec-tor, the formulas depend on integer generation indices whose integer-valuedness is the testableresonance prediction; the nine indices satisfy four structural rules and are reducible to twounexplained integers (Nµ = 11 and Nd − Nu = 1) that are targets of Paper 3.The mean deviation from measured values is 0.25% across all 26 parameters, with a root-mean-square deviation of 0.40% and a maximum single-parameter deviation of 0.9% (δPMNSCP ).Incorporating the golden phason—the standard quasiperiodic strain of the underlying quasicrys-tal lattice—reduces the mass-sector RMS from 0.33% to 0.003%, a 121× improvement with tworesidual degrees of freedom (Section 4.5). The framework makes several falsifiable predictions: amassless lightest neutrino (mν1 = 0, normal hierarchy), P mν = 59 meV, and precise correctionsto v and mH testable at next-generation colliders.A companion paper established the ESD gravitational closure 1; the present work extendsthe framework to the particle-physics sector.