LFIS–06: Boundary Dynamics — Curvature Flow, Edge Stability, and Transition Behavior

LFIS–06 derives the boundary-compatibility and transition-kinematics laws that follow from the finite representability structure established in LFIS–05. The volume packages the two-mode capacity condition into a boundary function Φ = ρ² − LFC², distinguishing interior representability, saturation boundary, and failed two-mode continuation. The central result is the constrained compatibility law DΦ = 0 for variations that remain on the saturation surface, together with the level-set boundary-motion law governing advancing and receding capacity boundaries. LFIS–06 clarifies that saturation is not representability failure: positive-projection loading is blocked at the boundary, while negative-projection relief or discharge can remain admissible. Transition behaviour is stated in angular form, with LFR retained only as an interior chart. LFIS–06 supplies the local boundary-kinematics infrastructure used by later volumes on drift-sink structure, photon propagation, measurement limits, horizon behaviour, and full three-mode representability.