Kearon's Law of Record–Forced Temporal Order

This version (v2) presents a fully expanded, rigorous derivation of Kearon’s Law of Record-Forced Temporal Order. It provides complete formal definitions, explicit lemmas, and step-by-step proofs establishing that time is not a primitive assumption but a structural consequence of record admissibility. Starting from minimal physical and logical primitives consistency, stability, and composability the manuscript derives a strict partial precedence structure forced by the existence of stable, non-contradictory records. All forcing arguments are developed explicitly, including cycle impossibility, transitive closure, and refinement stability. No assumptions are made regarding entropy, clocks, observers, or cosmological boundary conditions. The paper introduces a neutral functional test bed to formalize record admissibility and demonstrates optimizer existence without model-specific dynamics. Domain-specific specializations are derived rigorously for classical reversible systems, finite dimensional quantum systems (including capacity bounds), and relativistic locality constraints. The temporal arrow is shown to be non-fundamental and uniquely identifiable if and only if an explicit asymmetry is present, such as open dynamics, coarse graining, or boundary conditioning. This version is intended as the complete technical foundation underlying the law, suitable for verification, replication, and independent scrutiny. It complements compressed or expository presentations by making all derivational steps explicit and preserving full methodological transparency.