Trigonometric Reformulation, Tensorial Dynamics, and Topological Folding in Non-Dual Dimensional Habitation

We present an extended mathematical framework governing dimensional habitation (d) as a function of spiritual identification mass, specifically conscious Persona Mass (p) and unconscious Shadow Mass (s). First, we demonstrate the trigonometric reformulation of the Master Dimensional Equation via angular substitution x = tan2 θ, yielding bounded representations of non-linear soul dynamics. Second, we extend this formulation to higher-dimensional spaces using a 3D tensor M and state vectors Z, showing that geometric folding of n-space generates n additional cross-plane diagonals per added dimension. Third, we establish the connection between World Soul Emanation (k) and Epistrophé (¯h) through quantum wavepacket breathing dynamics, showing how extreme limits lead to macroscopic stonification or plasma dissipation. Finally, we resolve the differential boundary dynamics into linear and cubic polynomial regions, proving that total liquidation of identification (p; s) ! (0; 0) uniquely recovers the non-dual ground state d = 1 (Aham Prakāśa). Contact: [email protected]