From Substance to Relation: Logical Faults of the Mass Concept and Its Reconstruction in Time Field Theory

This paper systematically dissects three deep logical faults underlying the traditional concept of mass in physics: the circular argumentation of mass calibration that presupposes gravitational coupling and the equivalence principle; the metaphysical presupposition of mass invariance without operational support; and the axiomatic dependence of the equivalence between gravitational and inertial mass that cannot be proven from first principles. We argue that these faults are not missing technical details, but inevitable products of the ontological commitment in the field-source dualist paradigm, where mass is presupposed as an intrinsic property independent of metric benchmarks. Based on the periodic metric monism of Time Field Theory (TFT), this paper proposes a thoroughly reconstructed concept of mass: mass is not a substantial property, but the relational strength between the gradient and the local value of the periodic metric field, formally expressed as \kappa\rho = (\nabla\gamma)^2/\gamma. This definition is strictly derived endogenously from the core axiom of flux conservation and fully anchored in operational definitions. Mass, gravity and inertia are no longer independent properties whose equivalence needs to be proven, but apparent values of the same metric grammar under different operational scenarios. The new conception of mass demotes the equivalence principle from an unquestionable axiom to a derivable logical theorem, and naturally resolves the puzzle of the "universal coincidence" in Eötvös-type experiments. We further present conceptual confirmations for puzzles such as dark matter and black hole singularities, and propose rigid falsifiable observational criteria, including a strong-field equivalence principle deviation test that directly examines the relational nature of mass. Full quantitative derivations of the three major phenomenological effects are presented in companion papers of the TFT series.