Ampere Longitudinal Force as Transient Phase-Gradient Stress in a Coherence Field

This work presents a falsifiable theoretical framework for longitudinal forces observed in pulsed current systems, reformulating Ampere’s finite-segment kernel as a transient phase-gradient stress within a coherence-based field description. A closed-form geometry factor is derived for two finite, collinear current segments, and a controlled coarse-graining procedure is provided showing how the nonlocal Ampere interaction reduces to a local gradient-pressure term under scale separation. A full stress-tensor derivation is given, including explicit momentum conservation and boundary flux accounting during current ramps. Order-of-magnitude estimates demonstrate that the predicted phase-gradient force scales with dI/dt and can exceed static Maxwell-stress predictions during fast transients. A concrete experimental discrimination protocol is proposed based on timing separation between I^2-driven forces and dI/dt-driven impulses, with null tests and parameter scans specified. The manuscript is intended as a pre-registered, experimentally actionable proposal. If the predicted timing and ramp-rate scalings are not observed, the hypothesis is explicitly falsified.