Develops the Universal Generative Principle (UGP), a deterministic and parameter-free arithmetic framework proposed as a foundational model for generating complex, structured universes. The framework is governed by a duality between algebraic rigidity and computational universality. Proves the Kernel Symmetry Theorem — a codimension-1 Quarter–Lock constraint on all possible physical evolutions — and constructs a Turing-universal cellular automaton on the UGP substrate via direct simulation of Rule 110. The resolution of this Necessity–Contingency duality isolates a unique lexicographically minimal mirror-dual seed and canonical three-step orbit, (1,73,823)→(9,42,1023)→(5,275,65535), with zero free parameters at prediction time. Also proves Fibonacci lift rigidity and establishes self-reference via Lawvere’s fixed-point theorem and Kleene’s recursion theorem. All core theorems formalized and machine-checked in Lean 4.

Presents the Mathematical Foundations of Reflexive Reality (MFRR): a unified framework proving that a self-consistent, computable universe must be reflexive — its laws, description, and execution are coextensive. Through foundational closure theorems and the Two-Layer PSC Theorem, establishes that Perfect Self-Containment necessitates Transputation (PT), a non-computable mechanism for resolving indeterminacy governed by the Reflexive Landauer Bound. The Two-Layer PSC Theorem uniquely forces the Standard Model gauge group SU(3)×SU(2)×U(1) with three fermion generations from PSC consistency constraints and MDL optimality. Key results include: quantum superposition identified as dwelling on an Adjudicative Manifold; Reflexive Horizon First Law and black-hole unitarity via a reversible operator PT⁻¹; and an Information Profit threshold of 1.13 unifying quantum decoherence, biological metabolism, and economic viability. Verified by 297 Python modules, 60+ deterministic simulations, and 57,337+ experimental runs confirming core predictions to sub-percent precision.

Presents the complete GTE (Generative Triple Evolution) framework: a derivation of all known Standard Model parameters, and the structure of spacetime, quantum mechanics, and cosmology, from Perfect Self-Containment with zero free parameters fitted to particle physics. A unique 19-bit polynomial over GF(7) is machine-certified as the sole MDL-minimal substrate, and elementary particles emerge as BPS topological kink solitons of the single Φ_MDL field with Z₇ winding numbers corresponding exactly to SM quantum numbers.

Derived results include: all nine charged-fermion masses at 0.293% RMS; pion mass m_π = 139.57 MeV at 0.001%; 1/α_em = 2⁷+3² = 137 as a structural identity; sin²θ_W = 3/13 at tree level; three fermion generations machine-certified as the unique PSC survivors across 34,560 candidates; the Einstein equations from MDL-Lovelock variational calculus; Newton’s constant from F₂₁ orbit arithmetic at 0.040%; the Born rule via four independent derivations (two machine-certified in Lean 4); and the observed Ω_Λ from the PSC adjudication floor with zero free parameters.

Makes four falsifiable predictions: a dark-sector particle at 211.9 MeV (Belle II); r = 0 (LiteBIRD); w = −1 exactly (Euclid); and Δm²₂₁ at −0.7% below NuFIT 6.0 (JUNO, decisive). All results machine-certified in Lean 4 across 304 modules with zero sorry and zero custom axioms.