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-have no accepted theoretical origin. We present the Universal Generative Principle (UGP): the Perfect Self-Containment (PSC) foundational principle uniquely selects a single integer seed (1,73,823) at ridge level n=10, and a deterministic arithmetic cascade generates the Category-A structural backbone of the SM parameter spectrum. The framework is complementary to QFT: it fixes the numerical constants that a QFT Lagrangian takes as input. The Category-A derivation chain is machine-checked in Lean 4 with zero sorry and the standard Mathlib axiom signature; all sectors are classified by a five-status claim taxonomy (machine-certified, MDL-optimal, partially-derived, calibrated, and exploratory; :status). Headline results: (1) Bare gauge couplings g_1^2, g_2^2, g_3^2 are Lean-certified exact rationals; the blind evaluation _s(M_Z) = 0.11822 sits at +0.24 of PDG 2024, pre-committed 43 days before the first PDG comparison (Appendix app:alpha_s_precommit). (2) Nine charged-fermion masses at 0.293\% RMS with zero active parameters at prediction time; a 1000-permutation null confirms arithmetic structure. (3) Neutrino mass-squared ratio m^2_21/ m^2_31 = 0.0294 at 0.16 from NuFIT 6.0, parameter-free, from Braid Atlas b-values and the structural exponent 29/9. (4) Cosmological constant from the derived model bit-length L_model = _2(2000/3) at 0.31 from Planck 2018 (H_0 is the sole external input). (5) Higgs quartic = phi/(4)\!(1+IPT-12c_H+1) is machine-certified (Category A_Lean; SpivackGTEUnification,SpivackSRRG); with v_PSC=246.16 GeV, this gives m_H = 125.2499 GeV (-0.0003 PDG 2022), closing the prior -2.08 tension. The lepton seed b_L_1=73 of this triple is doubly certified: the GTE cascade formula G(N_c)=N_c^4-(N_c^2+1)/2-N_c and the Frobenius prime chain F(n)=n^4-n^2+1 independently yield 73 at n=N_c=3, with agreement provably unique at n=3 (fgci\_unique\_at\_nc, UgpLean.Universality.FrobeniusChain, 17 theorems, zero sorry). Preregistered falsification tests for JUNO, DUNE, CMB-S4, and LEGEND-1000 are listed in :falsifiability.