The Spectral Principle A Closed Derivation of Fundamental Physics
Petar Dryanovski
Abstract
A mathematical framework is presented in which the fundamental constants and particle masses of the Standard Model emerge from a single positive trace-one operator. The theory contains no free parameters. The spectral Laplacian of the operator fixes the constants pi, the golden ratio, and an exponential contraction factor that governs the mass hierarchy. The automorphism group of the associated spectral groupoid yields the gauge group SU(3)×SU(2)×U(1) via anomaly cancellation. A universal mass formula reproduces the masses of all twelve massive Standard Model particles. Its exponents decompose into a rigid integer lattice with a hidden constraint whose seven violations define a spectral charge that cycles through the mass-ordered particle spectrum. The fine structure constant, Weinberg angle, CKM mixing angles, and cosmological parameters for dark energy, dark matter, and baryonic matter are computed from spectral invariants without fitting. The paper includes a complete mathematical foundation: kernel uniqueness, Whitney-stratified gradient flow on the simplex, exact separatrix solutions, normal form reduction, Lyapunov foliation geometry with exact Ricci curvature, Laplace-Beltrami spectrum and heat kernel on the binary attractor, Hamilton-Jacobi structure, a coordinate-invariant torsion diagnostic for non-gradient flow distortion, Freidlin-Wentzell escape rate corrections, and a unified variational principle. This work builds on a previous paper that established the uniqueness of the admissible interaction kernel. The derivations are self-contained, and the numerical agreement with experimental values is documented throughout. No claims of finality are made; the framework is offered as a consistent mathematical structure that reproduces known physics and may be tested against future measurements.