We derive the emergence of fundamental interaction sectors from Time-Scalar Field Theory (TSFT), where time is promoted to a physical scalar field Θ(x, t). Beginning from coherencestable particle eigenmodes previously derived within TSFT, we demonstrate that three distinct interaction regimes arise naturally from temporal-frame deformation dynamics. These regimes correspond to (i) propagating curvature interactions, (ii) conversion interactions between eigenmodes, and (iii) composite coherence locking interactions. We show that these interaction classes emerge from the dynamical status of temporal deformation fields andadmit a gauge-compatible formulation without externally imposed gauge postulates. We further derive selection rules, conservation laws, and mediator structures governing these interaction sectors. From these results, we demonstrate the emergence of composite matter states, integer-charged bound structures, and residual composite interactions that naturallyproduce multi-core bound configurations. This framework provides a unified derivation of interaction hierarchies, composite matter formation, and emergent nuclear-like structure directly from scalar-time dynamics.
Jordan Gabriel Farrell (Thu,) studied this question.