The Intrinsic Action Integral Equations as First Principles: Axiomatic Derivation of Quantum Chromo-Electrodynamics and the Standard Model with Complete Proofs

This paper establishes a new axiomatic system based on the intrinsic action integral equations and their dual forms as first principles. Starting from three fundamental axioms, we systematically derive all core features of Quantum Chromo-Electrodynamics (QCED) and the Standard Model of particle physics using rigorous mathematical tools: Lie algebras, differential geometry, path integral quantization, anomaly cancellation, renormalization group, and Kaluza–Klein compactification. The derivation yields the gauge group SU (3)c ×SU (2)L ×U (1)Y , the charge operator Q = T3 + Y /2, the high-energy boundary condition sin2 θW (MU ) = 1/(1 + 4π2), the chiral representation of one fermion generation, the Higgs mechanism with W/Z masses, the real orthogonality of CKM and PMNS matrices, the geometric origin of CP violation (relative rotation angle Ω), and the necessary embedding into the grand unified group U (1, 3)×U (1, 3). Moreover, the axiom system naturally predicts proton decay lifetime τp ≈ 2×1037 years, axion dark matter (ma ∼ 10−10 eV, Ωah2 =0.12), and Majorana neutrino mass mν ∼ 0.03 eV. All results are strict theorems proved from the axioms without extra assumptions. The high-energy boundary condition for the weak mixing angle is derived by combining the five-dimensional compactification with a numerical renormalisation-group fit to low-energy data, eliminating any algebraic inconsistency. This framework provides a geometric first- principles foundation for physics.