Analysis of the Emergence of WQT Energy Orthogonal Allocation from Envelope Interface Nesting Structure

Starting from the Envelope Interface nesting structure and citing the velocity hierarchy formula of the Meridian Envelope Interface, this paper demonstrates that the energy orthogonal allocation formulas of World Quantum Theory (WQT) are not independent postulates, but rather necessary algebraic consequences of Envelope Interface geometry. The derivation consists of two core levels. At the first level, we cite the core formula C_u^2 = V_u^2 + D_u^2 + S_u^2 from the Meridian Envelope Interface paper [6], which originates from the natural cancellation of the scaling factor K^2 in (K C_u)^2 = K^2 (V_u^2 + D_u^2 + S_u^2), combined with the fundamental meridian identity |S_u| = |D_u|, yielding c^2 = v^2 + d^2. At the second level, we define the Envelope Static Space-Time Quantity U_m = (d/c) * U and the Envelope Dynamic Space-Time Quantity U_p = (v/c) * U, and through pure algebraic derivation prove that U^2 = U_m^2 + U_p^2. The Comparative Space-Time Quantity U = (c/d) * v * c^2 is a pure geometric quantity with dimensions m^3/s^3. To connect it to the physical energy E (unit: J), we introduce the mass-speed factor k = m/v (unit: kg·s/m), which is variable—it changes with the measured object in self-referential measurement. The physical energy is E = U * k. Through structural identification and the mass-speed factor, the WQT energy allocation formulas E_m = (d/c) * E and E_p = (v/c) * E, together with the relativistic energy-momentum relation E^2 = (m c^2)^2 + (p c)^2, are all necessary consequences of Envelope Interface geometry.