Light-Speed Critical Field Theory: From Entropy-Velocity Coupling to the Ultimate Unification of Cosmic Eigen-Oscillations

This paper presents the final refined version of the Light-Speed Critical Field Theory (LSCFT).We first list the original twelve axioms and show how they are logically condensed into three fundamental axioms: light speed as a dimensional critical wall, negative correlation between entropy production rate and velocity, and dimensional mixing. Based on noncommutative geometry and the spectral action principle, we construct the final field equation with the critical-wall Dirac operator DCW as the sole fundamental variable.The equation includes a power-law spectral cutoff (k = 3), entropy-variation coupling,topological term, boundary term, and a quadratic entropy term, with a total of five free parameters. The paper details the physical origin of each term and its low-energy correspondence with existing theories (general relativity, Standard Model). We honestly list the shortcomings of the theory and present the derivation of three core predictions (solar flare 1.73-year period, solar wind speed 1.20-year period, Earth inner core 6-year oscillation)from the field equation that have obtained observational support. Finally, based on the final refined field equation, we list 30 quantitative predictions that can be tested within 1–10 years using public data, each given a specific numerical value or functional form.