The Complete GTE Framework: Standard Model, Gravity, Quantum Mechanics, and Cosmology from Phi_MDL

The Standard Model of particle physics contains approximately twenty-five numerical parameters --- gauge couplings, fermion masses, mixing angles, the Higgs sector, the cosmological constant --- that the theory treats as measured inputs with no theoretical origin. This monograph presents the complete GTE (Generative Triple Evolution) framework: a derivation of all known SM parameters, and the structure of spacetime, quantum mechanics, and cosmology, from a single foundational principle with zero free parameters fitted to particle physics. The starting point is Perfect Self-Containment (PSC): the requirement that a universe has no external selector for its laws. Presentation Invariance (PI≡MDL) terminates the meta-level regress of law selection and forces selection by the Minimum Description Length principle. The MDL principle then uniquely identifies p(L,C,R) = C+R-CR-LCR over GF(7): a 19-bit polynomial is the sole MDL-minimal substrate consistent with physical self-containment, with every Z_N × Z_M alternative eliminated by exhaustive machine proof. The framework has a two-level architecture. At Level 1, p defines the Chiral Minkowski Cellular Automaton (CMCA): a discrete algebraic certificate that encodes the structural constraints of SM physics through Rule 110 Turing universality and Z_7-winding arithmetic. The CMCA plays a novel and surprising role: not as the physical substrate --- no cellular automaton can replicate Lorentz symmetry exactly at the continuum --- but as an algebraic proof system that certifies which structures must exist in the field theory. At Level 2, the physical substrate is Phi_MDL: a single Z_7-symmetric Klein-Gordon gauge field on R^(3,1) with internal symmetry group F_21 = Z_7⋊Z_3, the unique non-abelian group of order 21. Elementary particles are not points: they are BPS topological kink solitons of Phi_MDL, carrying Z_7 winding numbers that correspond exactly to SM quantum numbers. This is what "one field" means: all matter, forces, spacetime, and quantum mechanics emerge from a single field equation. From this architecture, the complete SM spectrum is derived without free parameters. Particles: three fermion generations are machine-certified as the unique PSC survivors across 34,560 candidates; all nine charged-fermion masses reproduce at 0.293% RMS; the pion mass m_pi = 139.57 MeV matches PDG at 0.001%; neutrino mass-squared ratios agree at 0.16 sigma. Forces: 1/alpha_em(0) = 2^7 + 3^2 = 137 (tree-level structural identity; QED running closes the 0.026% gap to the measured 137.036); the Weinberg angle sin^2(theta_W) = 3/13 at tree level, closed to +0.038 sigma by two-loop corrections; strong CP theta_QCD=0 by three independent machine-certified proofs, requiring no axion (falsifiable prediction: any axion detection by ADMX, CASPEr, or BabyIAXO at any mass would refute GTE); QCD asymptotic freedom from b_0 = 7 = |Z_7|. Spacetime and gravity: 3+1 dimensions forced by the Dimensional Protocol Principle (machine-certified); the Einstein equations G_mu_nu = 8 pi G T_mu_nu derived from MDL-Lovelock variational calculus; Newton's constant G_N = m_tau^2/M_Pl^2 at 0.040% from F_21 orbit arithmetic, with no gravitational input. The quantum mechanical and cosmological sectors complete the derivation. The Born rule P(k) = |c_k|^2 is derived via four independent routes --- two machine-certified in Lean 4 with zero sorry and zero custom axioms --- and is not postulated. Quantum measurement is replaced by transputation: a formally characterized non-computable branch-selection mechanism proved necessary by the Physical Incompleteness Theorem. This theorem machine-certifies that no algorithm can decide all computational outcomes of a PSC-consistent universe --- a Turing-Rice analogue of Goedel's theorem applied to physics --- forcing objective quantum randomness and making deterministic completions internally inconsistent with PSC. In the cosmological sector, the classical cosmological constant Lambda=0 exactly from Z_7 symmetry; the observed Omega_Lambda in [3pi/14, 0.6899] follows from the PSC adjudication floor with zero free parameters, bracketing Planck 2018; the CMB spectral tilt n_s = 1 - ln(2)/(2pi^2) = 0.96488 agrees at +0.004 sigma; and the baryon asymmetry eta_B = 6.109 x 10^-10 matches at +0.15 sigma (Planck 2018 CMB+BBN). GTE makes falsifiable predictions distinguishing it from the SM: a dark sector particle at 211.9 MeV (Belle II); r=0 (LiteBIRD); w=-1 exactly (Euclid); and Delta m^2_21 at -0.7% below NuFIT 6.0 (JUNO, decisive). All central results are machine-certified in Lean 4 with zero sorry and zero custom axioms across 326 modules of the ugp-lean library. The Standard Model is not a coincidence. It is a theorem.