A Conjecture of Matter:The Ticking Law of Time——A Mathematical Framework

This paper formalizes the theoretical framework of the Ticking Law of Time by establishing its complete mathematical formulation. The core proposition of the theory is that time is not an independently flowing background, but the total sequence of irreversible residues accumulated by material systems through closed rhythms. Based on the conceptual foundation of the theory, this paper defines all fundamental and derived variables, and establishes the complete mathematical structure governing the physical interval of a single tick, temporal residue accumulation, compression factor evolution, thermal-temporal coupling, information version updating, and structural transition criteria. Coupled feedback equations for gravitational potential, native period, temperature, and material complexity are presented, along with mathematical expressions for observable quantities including local Hubble parameter correction, redshift modification, and atomic clock drift. The complete evolutionary rules are presented in the form of a recurrence system. (Note on AI-Assisted Computation Certain mathematical derivations and physical 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.)