Geometric Constants of the 14‑Order Unified Field Theory: π, 7/19, 1/80 and the First‑Principle Derivation of Proton–Neutron Mass Spectra(V12)

Abstract This paper systematically establishes the geometric origin of fundamental mass constants within the axiomatic framework of the 14‑Order Unified Field Theory (14FT). Three core geometric constants, including the classical circumference ratio , the stable projection ratio , and the dual propagation correction , are proven to be inevitable structural outcomes of 14‑dimensional discrete symmetric geometry rather than empirical or artificially fitted parameters. Under the three fundamental axioms of monad close packing, orthogonal gyroscopic cyclic motion, and global phase coupling, all numerical corrections in the proton–electron and neutron–electron mass ratios are strictly derived from orbital enumeration, symmetry constraint, and topological path counting. This work eliminates free parameters in particle mass formulas, realizes the full first‑principle algebraic closure of the baryon mass spectrum, and provides a new geometric paradigm for solving the fundamental mass origin problem in particle physics.