Recursive Clocks and Operational Time Asymmetry: An Abstract Framework

We develop an operational framework for time measurement based solely on observable event sequences and their causal transport, without assuming any specific physical theory. By defining clocks as event-producing processes and introducing recursive temporal stretching under composition of transport contexts, we show that time asymmetry arises generically from the structure of transport itself. The hierarchy of transport contexts exhibits exponential scaling, quantifying the emergent asymmetry. We prove that this asymmetry is locally hidden due to collapse of transport equivalence classes, but necessarily becomes observablewhen increasing separation enforces path fixity. Crucially, the asymmetry is epistemic (arising from information loss in operational measurement) rather than ontic (requiring modification of fundamental dynamics), making it compatible with time-reversal-invariant underlying laws. The framework requires no assumptions about spacetime geometry, matter content, or dynamical irreversibility, establishing a minimal foundation for understanding temporal asymmetry as an inference effect rooted in operational structure rather than fundamental physics.