Complete Foundation of Boundary Relativity Theory: A Unified Derivation of the Standard Model and General Relativity from Five Principles

This preprint presents the complete foundational framework of Boundary Relativity Theory (BRT), a zero-free-parameter unification program that aims to derive the Standard Model and General Relativity from five pre-theoretical principles: non-negativity, self-consistency, coordinate invariance, analyticity, and minimality. Starting from these principles, the paper derives a projector-valued nonlinear sigma model with target space Gr (4, 15), establishes 21 theorems, and formulates the unified BRT field equation δΓₑffP/δP (x) =0. Within this framework, the Einstein equation, Yang-Mills equation, Dirac equation, the Higgs mechanism, and the cosmological constant are derived from a single variational principle. The manuscript further presents zero-parameter derivations of all three PMNS lepton mixing angles from a single mass-matrix diagonalization, an FRW cosmology with Ω_Λ = 13/19 and w = -1, the Schwarzschild solution as an exact vacuum solution, and a derivation of the Weinberg angle from the Cartan-Root-Trace decomposition of u (k), yielding sin²θW (f) = 3/13 and sin²θW (MZ) = 0. 23153 after Standard Model RG running. In total, 22 precision predictions are reported. According to the manuscript, current observational data are consistent with these predictions. The work also discusses the UV structure of the theory in terms of Grassmannian compactness, the projector constraint P² = P, lattice regularizability, and gravitational UV completion via the Bekenstein bound. Files included: Main preprint PDF Source manuscript / supporting text This upload is intended as the first public preprint release of the complete BRT foundation. Future revisions should be released as versioned updates. Keywords Theory of Everything; Quantum Gravity; Unified Field Theory; Standard Model; General Relativity; Boundary Relativity Theory; Zero-Parameter Theory; Fundamental Constants; Grassmannian Sigma Model; Sakharov Induced Gravity; Electroweak Mixing Angle; PMNS Matrix; Neutrino Mixing; Cosmological Constant; UV Completion