This research paper establishes a deterministic mathematical framework for the study of systemic initialization in macroscopic bio-magnetic fields. By employing Vectorial Harmonic Induction (VHI), we model the ambient N-body gravito-magnetic vectors at the point of system activation to derive a persistent geometric state termed the Initial Systemic Phase-Lock (S_0). The framework utilizes harmonic scaling constants (\kappa_E and \kappa_C) to maintain volumetric conservation within a Z^3 state-space. Furthermore, the paper introduces the Binary Phase-Lock Hypothesis (BPLH), utilizing tensor products to predict the interaction between independent initialized entities under external vector perturbations. This work provides a rigorous basis for future retrospective data analysis in systemic persistence and phase-locked resilience