Scalar Temporal Field Ontology: Emergent Gravity, Mass, and Inertia from Temporal Structure

This work develops the Scalar Temporal Field Ontology (STFO), in which time is modeled as a dynamical scalar field τ(x^μ). We demonstrate that in the weak-field regime, spatial gradients of τ reproduce:- inverse-square gravitational attraction,- universal free fall,- gravitational time dilation,- redshift, and- light deflection at leading order. We further show that localized high-gradient configurations of the temporal field exhibit elastic resistance to compression, suggesting a mechanism for non-singular compact structures. These configurations carry finite energy, providing a natural definition of mass as stored temporal energy. Within this framework, inertial and gravitational mass arise from the same underlying quantity, establishing their equivalence as a structural consequence of the theory. Limitations are explicitly discussed, including the absence of a full post-Newtonian derivation and exact localized solutions. This work is intended as a foundational classical framework for further development and testing.