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 specification consistent with physical self-containment, with every Z_N x Z_M alternative eliminated by exhaustive machine proof. The selection acts twice, in sequence: MDL first selects an arithmetic seed, whose deterministic cascade emits the three-generation orbit, and the orbit's parity shadow plus MDL then interpolate exactly one multilinear rule --- p itself, making the polynomial a derived structure of the underlying arithmetic rather than an independently chosen object (machine-certified in Lean 4, zero sorry); Rule 110 universality follows as a corollary. Two unification theorems tie the architecture together. The diagonal of p factors through a single master quadratic x^2+x-1 (discriminant equal to the family count N_fam = 5) whose real root 1/phi seeds the Higgs vacuum expectation value and whose GF(7) rootlessness forces Rule 110 universality and vacuum uniqueness --- the electroweak scale and the computational floor are two arithmetic completions of one machine-certified equation. And the same MDL principle operates at three nested, non-circular levels --- theory selection, field dynamics, and event adjudication --- the Three-Level MDL Unification, with the non-circularity machine-certified. 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 x 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 0.295% 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. Conceptually, spacetime geometry is not fundamental but emergent from the Phi_MDL field via MDL-Lovelock coupling; the vacuum Ricci-flatness is certified at Level 1 by the CMCA algebraic structure, not assumed. 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. The adjudication mechanism is classified exactly: its decision-theoretic restriction to the self-referential diagonal has Turing degree precisely 0' --- quantum measurement operates at the halting degree, never requiring oracle access above the first Turing jump. 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; the baryon asymmetry eta_B = 6.109 x 10^-10 matches at +0.15 sigma (Planck 2018 CMB+BBN); and the Z_7 domain-wall sector is resolved dynamically --- walls form at the ordering crossover T_G ~0.70 GeV and are annihilated by the canonical coupling bias before nucleosynthesis, leaving zero surviving defect network as a parameter-free falsifiable prediction. All four standard inflation motivations (flatness, horizon homogeneity, spectral tilt, relic suppression) are discharged from first principles without an inflationary epoch. The past hypothesis --- the observed low-entropy initial state --- is a theorem of MDL-minimality, not a separately imposed boundary condition. The Wheeler-DeWitt frozen-formalism problem dissolves because the DPP clock tau_c provides a background-independent computational time order at Level 1, prior to Level-3 spacetime emergence. 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 a solar splitting Delta m^2_21 = 7.37 x 10^-5 eV^2, consistent with NuFIT 6.0 at ~1 sigma and to be sharpened by JUNO. All central results are machine-certified in Lean 4 with zero sorry and zero custom axioms across nearly 400 modules of the ugp-lean library. The Standard Model is not a coincidence. It is a theorem.