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 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; ). Headline results: (1)~Bare gauge couplings g_1^2, g_2^2, g_3^2 are Lean-certified exact rationals; the blind evaluation α_s(M_Z) = 0.11822 sits at +0.24σ of PDG~2024, pre-committed 43~days before the first PDG comparison (Appendix~). (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 Δ m^2_21/Δ m^2_31 = 0.0294 at 0.16σ 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 = log_2(2000/3) at 0.31σ from Planck~2018 (H_0 is the sole external input). (5)~Higgs quartic λ = φ/(4π) (1+IPT-1/2c_H+1 ) is machine-certified (Category~A_ Lean; ); with v_ PSC=246.16~GeV, this gives m_H = 125.2499~GeV (-0.0003σ PDG~2022), closing the prior -2.08σ 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 ( \_unique\_at\_nc, .Universality.FrobeniusChain, 17 theorems, zero ). Preregistered falsification tests for JUNO, DUNE, CMB-S4, and LEGEND-1000 are listed in .