Traversability as a Dynamically Regulated State

This note introduces the Projection Gate framework, which reframes wormhole traversability as a dynamically regulated operational state rather than a static geometric property. Instead of treating accessibility as determined solely by topology or sustained violations of classical energy conditions, traversability is modeled as arising from controlled evolution of geodesic congruences in a compact region near the throat. A dimensionless gate functional, �, is defined to quantify cumulative congruence focusing and to serve as an operational order parameter distinguishing sealed and open modes. Using a reduced dynamical model based on the Raychaudhuri equation coupled to an anisotropic control channel, the framework exhibits threshold behavior, transient activation, and intrinsic self-sealing dynamics. The Projection Gate formulation is classical in structure while remaining compatible with quantum traversable wormhole protocols, providing a geometric control interface through which holographic or semiclassical mechanisms may operate. More broadly, the results suggest that causal accessibility in spacetime is not an intrinsic property of geometry but a controllable feature of congruence dynamics.