Finite Clock-Signal Records and Lorentz-Type Inertial Structure in the Finite Relational Closure Framework

This preprint develops a finite-record reconstruction of special-relativistic inertial structure within the Finite Relational Closure Framework (FRCF). Rather than taking exact spacetime points, continuum coordinates, or inertial frames as primitive, the manuscript begins from finite measurement records: clock readings, signal exchanges, coincidence registrations, synchronization procedures, and finite-resolution event classes. Events are represented as equivalence classes of records that are indistinguishable within an operative resolution, while coordinate assignments are treated as effective labels introduced within admissible inertial contexts. The central claim is modest: given finite clock-signal-event records, stable coincidence structure, and a distinguished signal class preserved across admissible contexts, Lorentz-type transformations and Minkowski interval structure provide a sufficient effective representation of the resulting refinement-stable relational regime. The manuscript reconstructs this structure through finite event classes, admissible coordinate assignments, signal-preserving transformations, and interval invariance. It also interprets standard relativistic effects, including time dilation, length contraction, relativity of simultaneity, twin-clock comparisons, and longitudinal Doppler shift, as finite record-comparison effects rather than as changes in the intrinsic content of isolated objects. The paper situates this reconstruction alongside operational and constructive approaches to special relativity, while emphasizing the distinct FRCF starting point: finite records, finite-resolution equivalence, admissible refinement, and stable regime selection. It does not attempt to replace standard special relativity, derive the empirical value of (c), or address gravitation. Its purpose is to show how special-relativistic inertial structure can be incorporated into FRCF as a stable effective regime of finite relational clock-signal records.