A Triadic Theory of Spacetime: Recalculation of Established General Relativistic Results for Verification

This paper applies the Triadic Theory of Spacetime framework to recalculate two experimentally confirmed cornerstones of General Relativity: the deflection of light in the Sun's gravitational field and gravitational redshift. This work is based on the Triadic Theory of Spacetime framework [1,2], which identifies eight essential properties of spacetime structure: absolute staticity, absolute rhythmicity, space-time inseparability, topological stability, locality, positional determinacy, scale invariance, and dynamic evolvability. To represent these properties in mathematically tractable form, the framework introduces the Double-Loop Structure as an idealized mathematical model. The recalculations presented in this paper draw directly upon Postulate 1 (Absolute Vacuum), Postulate 4 (Global Translation), Theorem 1 (Spatial Confinement), Theorem 2 (Time Definition), Operation 3 (Combination), and Operation 4 (Deformation). Without employing the Einstein field equations, both recalculations reproduce the established formulas exactly in the macroscopic limit. This paper provides a detailed reinterpretation of each term in the formulas: the gravitational constant $G$ is the macroscopic elastic modulus of the spacetime structure network, and redshift is the manifestation of differences in the rhythmic frequencies of distinct spacetime regions. This paper further identifies testable predictions under extreme conditions (rapidly rotating bodies, strong-field regions) where this theory may diverge from General Relativity. (Note on AI-Assisted Computation Certain mathematical derivations and calculations in this paper were performed by an AI tool (large language model) based on the theoretical framework and postulate system provided by the author. Specifically, the AI tool contributed to: formula derivation, equation solving, integral evaluation, series summation, and recalculation verification of established quantum mechanical results. All physical insights, core assumptions, logical premises, and the theoretical framework itself were independently developed by the author. The AI tool served solely as an auxiliary instrument for mathematical derivation and computational verification, comparable in role to symbolic computation software or numerical tools routinely employed by researchers. The author has reviewed every derived result for physical plausibility, consistency with known experimental data, and logical coherence, and assumes full responsibility for all conclusions. This statement is provided in the interest of academic transparency, while clearly distinguishing between the originality of ideas and the auxiliary role of computation.)