Rivet Configuration Selection and the Emergence of Particle Families in Time–Scalar Field Theory

We present a fully self-contained particle-selection framework within Time–Scalar Field Theory (TSFT) in which stable matter states emerge as coherence-admissible rivet configurations of an underlying scalar-time spectral geometry. Rather than assigning known particles retrospectively, the paper defines a unified rivet operator whose admissible eigenstates are selected jointly by spectral closure, holonomy sectorization, coherence stability, and bundle-compatible transport. The construction is designed to unify several previously separated TSFT developments into one formal predictive model: temporal eigenmode mass emergence, Floquet–holonomy sectorization, Dirac-compatible spin structure, rivet persistence, and charged-lepton generation selection. Within this framework, particle candidates are not inserted by hand. They arise as the discrete surviving subset of all mathematically possible coherence configurations. We first define the minimal rivet state vector and the associated TSFT rivet operator. We then derive admissibility laws for stable particle states, including spectral closure, bounded decoherence leakage, holonomy compatibility, and bundle-level coherence preservation. These conditions yield a finite low-lying catalog of candidate matter states. We organize these candidates into lepton-like, quark-like, neutral, and unstable branches, compare them with known particle properties, and identify which states correlate strongly with observed particles, which remain tentative, and which constitute genuine TSFT predictions or exclusions. The central claim is that matter is not an arbitrary collection of inputs, but the discrete coherence-stable subset of scalar-time spectral possibilities. In this sense, particle families, mass hierarchy, and charge structure become emergent consequences of temporal coherence selection rather than independent empirical postulates.