Periodic Self-Consistency as the Ontological Foundation of Mathematical-Physical Isomorphism: A Solution to Wigner's Puzzle of the Unreasonable Effectiveness of Mathematics Based on Time Field Theory

Proposed by Eugene Wigner in 1960, the thesis of "the unreasonable effectiveness of mathematics in the natural sciences" points to the deep root of the striking correspondence between physical reality and mathematical forms, and remains a core unsolved problem in the philosophy of physics and mathematics. Existing explanatory approaches mostly remain at the epistemological or pragmatic level and fail to reveal the ontological necessity of the isomorphism between the two.
Based on the core axiomatic system of Time Field Theory (TFT), this paper proposes an ontological solution: the physical world and the mathematical system are not two independent, accidentally matching structures, but natural manifestations of the same "periodic self-consistent metric logic" at the real level and the formal level respectively. This paper demonstrates that the minimum metric unit of the physical world is the local periodic oscillation satisfying the perfect circle postulate, and the minimum logical unit of the mathematical system is the abstract unit element obeying conservation rules. The two share exactly the same meta-constraint: nothing can be created out of nothing, nothing can vanish into nothing, and only equivalent connections are permitted. Physical laws are the inevitable outcome of the self-consistent distribution of periodic benchmarks, and mathematical theorems are the necessary corollary of equivalent operations on unit elements. Their isomorphism is guaranteed by a shared ontological root, and is by no means an accidental miracle.
This work serves as the general treatise on the philosophy of mathematics and physics of the TFT metretike system. It is the philosophical extension of TFT Series No.30 (General Outline of Metretike), and the philosophical summary of Series No.34 (Endogenous Derivation of Riemannian Geometry) and Series No.35 (Three Equivalent Mathematical Forms of the Core Constraint).