Analysis of the Envelope Interface's Perception of the Distance to the Meridian Touching Wave Packet

This paper defines three Touching Wave Packet Adjustment Velocities — tangential adjustment velocity V_m, central adjustment velocity S_m, and radial adjustment velocity D_m — that describe the difference between the parent Envelope Interface and the Meridian Touching Wave Packet in velocity space. Each adjustment velocity is collinear with a specific parent Envelope Interface direction: V_m with V_0, S_m with D_0, and D_m with S_0. Using the constraint that the Touching Wave Packet resultant velocity equals C_u = D_0 = S_0, we derive the distance formula L = √(V_m² + S_m² + D_m²). This distance represents the Envelope Interface's perception of the Touching Wave Packet — not a spatial distance, but a velocity space distance. The Envelope Interface "senses" the Touching Wave Packet by computing the difference between its own velocity structure and the Touching Wave Packet's velocity structure. We further derive the law of cosines form L² = C_0² + C_u² − 2(V_0V_u + S_0S_u + S_0D_u). Keywords: Envelope Interface, Touching Wave Packet, adjustment velocity, distance perception, velocity space, World Quantum Theory