A Conjecture of Matter: Time Effect as an Extension of the Time-Dilation Force Theory — A Mathematical Framework

This paper presents the mathematical framework for "A Conjecture of Matter: Time Effect as an Extension of the Time-Dilation Force Theory" [1]. It establishes a rigorous mathematical architecture for the theory, including basic definitions, core postulates, and key theorems. This framework preserves the complete mathematical structure of the time-dilation force theory [2,3], while introducing two new postulates — that the time effect is the unified origin of forces and that the time effect is also the combined result of all forces — and providing mathematical formulations for them. A newly added Dual-Cycle Theorem provides a unified dynamical explanation for the perpetual intensification of the time effect, cosmic expansion, and entropy increase. (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.)