Emergence of Nuclear Structure from Time-Scalar Field Theory

We derive the emergence of nuclear-like composite structure from Time-Scalar Field Theory (TSFT), in which time is promoted to a physical scalar field Θ (x, t) and matter arises from coherence-stable eigenmodes of the scalar-time operator. Building on the previously derived particle spectrum, closure condition, and interaction hierarchy, we show that confined multi-fermion bound states arise naturally from composite coherence locking without introducing new fundamental postulates. Starting from the scalar-time field, the coherence eigenvalue problem, and the closure condition 3n + 2q + h ≡0 (mod 6), we construct admissible three-fermion composite states and derive the conditions under which integer-charged spin-1 2 nucleon-like structures emerge. In particular, we show that the minimal closure-preserving confined composites built from admissible fractional-charge fermionic modes yield a positively charged proton-like state and a neutral neutron-like state as the first nontrivial nuclear-scale bound structures of the theory. We further show that mass-energy equivalence is recovered directly from scalar-time eigenfrequency structure, without invoking General Relativity, through the identification of rest mass as the intrinsic coherence frequency of a stable mode. This yields the relativistic rest-energy relation E= mc² as a consequence of scalar-time wave dynamics and provides the natural energetic framework for composite nuclear binding. The resulting formalism supplies a self-contained derivation of nucleon-like bound states, composite confinement, and the first layer of nuclear structure directly from scalar-time coherence dynamics. This extends TSFT from particle and interaction emergence into the nuclear domain and provides a structural bridge from temporal resonance to matter architecture.