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Stable Continuum-Valued Observables from Finite Refinement Measurements: The RCS Framework and Its Physical Spectrum

This preprint develops a refinement–compatibility–stability (RCS) framework in which finite process occurrences generate rational calibration readouts indexed by a directed refinement system, and studies when such readouts determine a stable continuum value. Main results. Every s...

Stable Continuum-Valued Observables from Finite Refinement Measurements: The RCS Framework and Its Physical Spectrum

This preprint develops a refinement–compatibility–stability (RCS) framework in which finite process occurrences generate rational calibration readouts indexed by a directed refinement system, and studies when such readouts determine a stable continuum value. Throughout, a continu...

Observation–Feedback Closure I (v1.5.0): A Self-Consistent Relational Reconstruction from Directed Processes and Internal Occurrence Arithmetic to Functional Dimensionality and Conditional Geometric, Temporal, and Topological Extensions

This preprint is version v1.5.0 of Observation–Feedback Closure I. It presents a foundational reconstruction and logical restructuring of the OF Closure framework rather than a merely additive extension of v1.4.0. The principal purpose of this version is to repair three foundatio...