Measurement and the Born Rule from Temporal Sampling in the Scalar Temporal Field Ontology

This work provides an ontological and operational grounding of the Born rule within the Scalar Temporal Field Ontology (STFO), in which time is represented as a monotonic scalar field τ(x). Measurement is modeled as an irreversible process of environmentally-induced temporal stabilization of macroscopic records. Probabilities are defined as τ-sampling weights over stabilized record sectors under repeated trials. It is shown that the disjointness and objective identity of stabilized records compel the standard probability axioms on quantum events, including normalization, additivity over exclusive outcomes, and noncontextuality. Established Gleason- and Busch-type representation theorems then uniquely yield the trace rule p(P)=Tr(ρP), and hence the Born rule for pure states. The paper does not modify quantum mechanics or its empirical predictions. Instead, it supplies a physical justification for the probability axioms traditionally assumed in quantum theory by grounding them in temporal stabilization along τ. The Born rule is thereby reinterpreted as the unique τ-consistent sampling measure on stabilized quantum events rather than an independent postulate.