Redefining Time-of-Flight via Time-Field Gradients: A Testable Extension of Propagation Dynamics in the Chronos Framework

This work introduces a minimal extension to the standard time-of-flight (TOF) formulation by treating time as a structured scalar field rather than a passive parameter. Within the Chronos framework, the time field (denoted Theta of position and time) governs the local rate of physical evolution, allowing spatial variations in time structure to influence signal propagation. The classical TOF expression is generalized through an effective propagation velocity that depends on the local value of the time field and its spatial gradients, while preserving all standard results in the limit of a uniform time field. In the weak-field regime, this leads to a measurable correction term (Delta T), representing a shift in time of flight that accumulates along the propagation path due to variations in the time field. A key prediction of the model is that paths of equal geometric length may yield different measured flight times when embedded in distinct time-field environments. This effect provides a direct experimental pathway for testing the framework using interferometric systems, fiber-optic loops, and precision timing networks. The Chronos constant (chi) is introduced as a dimensionless stability parameter governing the strength of time-field coupling, arising from bounded dynamical constraints rather than phenomenological fitting. The formulation is fully falsifiable: null results constrain the magnitude of chi and the functional form of the coupling, while positive results would indicate that time possesses measurable structure beyond its role as a coordinate. This work establishes a direct bridge between time-field theory and experimentally accessible observables, reframing time-of-flight measurements as probes of temporal structure.