A Deterministic Number-Theoretic Framework for the Standard Model Parameter Spectrum

The Standard Model's 25 free parameters — gauge couplings, fermion masses, mixing angles, and the cosmological constant — are experimentally measured inputs with no accepted theoretical origin. We present the Universal Generative Principle (UGP): a deterministic number-theoretic framework in which three axioms — locality, symmetry, and compression (minimum description length) — uniquely select a single integer seed, and a rigid arithmetic cascade from that seed generates the Category-A structural backbone of the Standard Model parameter spectrum — exact bare gauge-coupling rationals, canonical fermion triples, quantum-number assignments, and several parameter-free mass-ratio predictions. Calibrated, scale-anchored, and partially derived sectors are explicitly separated throughout by a five-status claim taxonomy (A_ Lean, A_ MDL, A/D, B, D; ). The framework is complementary to QFT rather than a replacement: it fixes the numerical constants that a QFT Lagrangian takes as input, leaving QFT to supply the scattering dynamics. The Category-A derivation chain is machine-checked in Lean 4 with zero sorry and the standard Mathlib axiom signature; physics-bridge and A/D sectors are explicitly disclosed (companion formalization paper ). How it works. The ridge level n=10 is pinned by three independent arithmetic certificates: ridge minimality (the smallest level admitting a prime-locked mirror-dual survivor pair, Lean: n10\_is\_minimal\_admissible\_ridge); global asymptotic sparsity (for all n, the joint "mirror-dual survivor with b_1=73" constraint forces n=10, Lean: asymptotic\_sparsity\_universal); and a divisor-count certificate (the ratio (R_n)/D_1 = 15/8 unique to n=10 on [5,20], Lean: ckm\_theta23\_ratio\_uniqueness).... Supplementary information (supplementary_information.pdf) is bundled as a second file in this Zenodo record. EPIC_051 update (2026-05-15): Level 1 Higgs mass closure — using the self-consistent EW VEV v = 2M_W/g2(M_W) = 246.27 GeV derived from the same two-loop g2 running that closes OP(viii), the Higgs mass prediction improves from 124.2 GeV (-9.1 sigma) to 124.971 GeV (-2.08 sigma, Grade C). Structural VEV derivation (grade [A-]): v_PSC = 246.16 GeV (-0.024% from v_PDG), via PSC entropy framework, formalized in SrrgLean.VEVProof.* (4 modules, zero sorry, conditional on one named open axiom: psc_ew_entropy_maximization). Round G1 update (2026-05-16): PSCEntropyDuality axioms discharged; one named open axiom remains; grade [A-] unchanged. EPIC_052 update (2026-05-16): neutrino seesaw formalization — NeutrinoMassRatio.lean Phase 2 complete in ugp-lean (all 5 theorems, zero sorry); tight bound |R − 0.02936| < 0.0001 and NuFIT 1% comparison certified; supplementary Table S3 updated.