Temporal Ratio Theory: A Conversion-Based Model of the Arrow of Time

Temporal Ratio Theory proposes that the arrow of time arises not from the structure of time itself, but from an asymmetric conversion operator that acts at the present boundary. In this model, the future is represented as an exponentially expanding field of unresolved potential, while the past is represented as a contracting field of concluded structure. The present is treated as a finite-width collapse zone in which potential is converted into structure via a sign-reversing operator.

This preprint formalizes the domains, operators, and field equations governing this model. It derives an exponential temporal ratio function, provides structural symmetry statements, embeds the temporal model within spacetime coordinates, and establishes a clear testable prediction: a measurable discontinuity must exist between field magnitudes approaching the present from positive and negative temporal domains. This discontinuity constitutes the falsifiable signature of the theory.

The framework is mathematically self-contained, minimal, and intended as a foundation for subsequent work in relativistic extensions, field-theoretic formulations, and links to thermodynamic or quantum measurement asymmetries.