On the Emergence of Proper Time from Ordinal Registration Processes: A Non-Circular Approach

This work proposes a minimal non-circular framework for the emergence of proper time grounded on ordinal registration processes. A distinction is introduced between a pre-geometric ontological ordering, modeled as a partially ordered set, and operational proper time defined as a local rate of irreversible physical registration. The formalism avoids assuming time as a primitive parameter and instead derives temporal structure from structural response dynamics. In the weak-field limit, the model recovers relativistic time dilation through a response function associated with the metric component g₀₀, providing consistency with general relativity. The approach engages with foundational issues in quantum gravity and the problem of time, offering a structurally minimal alternative to parameterized or relational formulations.