The Macroscale Quantum Wave Equation: Transitive Logical Derivation of Non-Associative Macro-State Evolution in Big Boot Gauge Theory (BBGT)

Abstract

{"Microscopic quantum dynamics is governed by the linear Schrodinger and Dirac equationsscaled by Planck’s constant (ℏ). However, continuous spacetime assumptions break downwhen attempting to describe macroscopic, topologically locked celestial systems without coordinate singularities. In this paper, we establish the standalone Macroscale QuantumWave Equation (the Darkon-Allotey Macro-Wave Equation) within Big Boot Gauge Theory (BBGT). By performing transitive logical inference over the non-associative octonionicalgebra OZIP, the Generative Zero identity (0×0 = e_−1=⇒0×0≡ 1), and the force-hierarchy action constant h_n= 2^nh_z, we derive the fundamental differential operator governing macrostate wavefunctions ΨM(X, t, τ ). We incorporate the Allotey resonance phase-shift operator δˆAlloteyand the non-orientable Mobius Graph Laplacian ∆Mobiusover the K11 complete graph. This equation proves that macroscopic systems exhibit quantized topological phase protection, exact energy dispersion relations, and singularity-free boundary dynamics."}