Matter-Core Solutions in the Scalar Temporal Field Ontology

We construct localized matter-core solutions within the Scalar Temporal Field Ontology (STFO), in which time is modeled as a dynamical scalar field τ(x^μ).Using a spherically symmetric ansatz, we derive the effective energy functional governing static configurations, including gradient, elastic, and self-interaction contributions.We show that finite-energy cores arise from a balance between temporal gradient compression and elastic resistance terms, yielding stabilized configurations without singularities.This work establishes a concrete mechanism for matter as localized temporal structure and forms the foundation for subsequent analysis of bound modes and atomic-scale phenomena within STFO.