A Finite-Dimensional Coherent-Sector Extension of Quantum Dynamics and a Two-Stage Interference Diagnostic

We introduce a finite-dimensional coherent-sector (CS) framework in which ordinary quantum degrees of freedom are supplemented by affiliation and retained-record labels. The construction explores whether measurement-like branching can be modeled phenomenologically as dynamics on an enlarged state space, rather than imposed only through an external state-update rule. In the strict limiting version of the minimal model studied here, coherent exchange terms act within a common CS, while inter-CS couplings are represented by record-producing channels. We formulate the framework for a two-degree, two-level system. The one-CS model reproduces ordinary coherent exchange, whereas the two-CS model leads to affiliation-changing dynamics governed by finite-dimensional Markov channels. In the first-record approximation, probability is transferred from an initial no-record class into branch classes. In the ongoing-affiliation model, the coarse-grained affiliation probabilities obey a closed master equation. The strict limiting model also predicts a direct Stage-1 signature: an initially mixed-affiliation pair need not exhibit immediate coherent Rabi exchange, because coherent exchange begins only after affiliation-changing transitions produce same-CS branches. We then formulate a two-stage affiliation-memory diagnostic in which, after a Stage-1 inter-CS interaction, the ordinary pre-probe state is prepared, verified, or post-selected before a Stage-2 coherence probe. Standard quantum mechanics predicts the Stage-2 coherent response to depend only on this ordinary pre-probe state, whereas the CS model predicts an additional dependence through the pre-probe conditioned CS-affiliation distribution generated during Stage 1. The construction is developed as a minimal finite-dimensional framework for deriving experimentally testable, model-conditional consequences of CS-affiliation dynamics. This manuscript is a preprint and has not undergone peer review.