离散KAM加密理论:从存在论公理到35个物理常数的谱系导出

The Standard Model of particle physics contains 19 free parameters, and the ΛCDM cosmological model introduces another six empirical constants. The underlying origin of these fundamental physical constants is a longstanding unsolved core problem in theoretical physics. Conventional theoretical frameworks can only fit constant values against experimental data, and cannot uniformly derive all constants from first principles without introducing adjustable free parameters. This paper constructs the Discrete KAM Encryption Theory, which takes two ontological primitive postulates and three fundamental axioms as all constraints, and completely derives a full spectrum consisting of 35 fundamental constants for particle physics and cosmology.

The theoretical system establishes two parallel ultimate primitive postulates: the absolute void standing for the absolute external boundary of the system, and the primordial original operation that cannot be further decomposed. On this basis, three axioms are formulated: symmetric completeness, minimal separability and rigid uniqueness. We strictly prove that the binary set {0,1} is the only minimal basis satisfying all constraints, and the underlying symmetric structure is generated by the dihedral group D12. We adopt encryption factor 2 to construct hierarchical discrete lattice sequences, and define measurement functions and topological curvature functions to describe geometric features of discrete spaces. Using the Melnikov function, we solve the critical encryption level for the transition from discrete structures to continuous space, whose value equals four minus pi divided by twenty-four. A unified global spectral correction factor named eta L2 is also derived in this work.

We define the encrypted KAM operator, and decompose its spectrum into five non-overlapping sub-spectra at the critical encryption level, corresponding to geometric invariants, lepton masses, quark masses, gauge mixing matrix elements and cosmological parameters respectively. All 35 physical constants correspond to eigenvalues under different irreducible representations of the operator, with no manually adjustable parameters throughout the whole derivation. Complete derivations of the axiom system, proofs of core theorems and fully reproducible Python numerical codes are provided in the paper. Key physical quantities calculated theoretically, including the reciprocal of the fine-structure constant, mass ratios of leptons and quarks, CKM matrix elements, CP-violating phase and density fractions of various cosmic components, all deviate from existing particle physics and cosmological experimental observations within one standard deviation.

Based on this theory, four experimentally testable predictions are put forward: the sum of neutrino masses is approximately 0.157 electron volts; no supersymmetric new particles exist; protons are absolutely stable; no new gauge bosons beyond the U(1)×SU(2)×SU(3) gauge group can be found. Instead of denying or replacing the Standard Model and ΛCDM cosmological model, this theory provides an underlying discrete symmetric geometric interpretation for all fundamental physical constants from an ontological axiomatic perspective, and builds an analytical framework unifying discrete symmetry theory, KAM perturbation theory, spectral graph theory, particle physics and cosmology.