Emergent Quantum Structure from Finite Measurement and Relational Constraints

This manuscript examines selected quantum-theoretic structures within the Finite Relational Closure Framework (FRCF). Starting from finite measurement contexts, admissible relational assignments, and measurement-induced equivalence classes, it develops a structural account of interference, complex-amplitude representation, probability, distinguishability, entanglement-like correlations, Bell-type contextual structure, no-signaling, apparent collapse, and the squared-modulus rule. The central proposal is that interference arises when relationally distinct assignments remain indistinguishable under a finite measurement and must be aggregated before observable intensities are assigned. Under the assumptions stated in the manuscript, this motivates a minimal two-component contribution structure, representable by complex amplitudes. Probabilities are obtained by normalizing intensities over finite outcome classes, while partial distinguishability suppresses interference through overlap of finite measurement records. The same measurement-based structure is extended to composite systems, where non-factorizable aggregation over joint admissible assignments provides a structural account of entanglement-like correlations. Apparent wave function collapse is interpreted as conditioning on a recorded finite outcome, corresponding to restriction of the admissible relational domain rather than physical reduction of an underlying state. The manuscript is intended as a finite-measurement and relational-constraint account of selected quantum-like structures, not as a complete reconstruction of quantum theory.