Vector Continuity and Direction Memory

Vector Continuity and Direction Memory establishes the geometric laws governing admissible trajectories in near-critical systems. The paper proves that control paths must satisfy vector continuity—prohibiting abrupt directional reversals—and must preserve direction memory across transitions to avoid implicit oscillation, amplification, and spectral ascent. Direction memory acts as a stabilizing invariant that constrains allowable motion through operator space, ensuring that perturbations remain basin-aligned and non-destabilizing. The result is a complete characterization of geometric path admissibility within the Einsteinian Stack.