We present a theoretical framework explaining why the Plasma Resonant Constant κ = π × φ × α ≈ 0.037094 governs magnetic activity cycles in precisely those astrophysical systems satisfying three independent physical conditions. Through systematic boundary testing across stellar spectral types, accretion disk systems, and extreme-field objects, we demonstrate that each constant independently encodes one validity condition: π encodes spherical cavity geometry, φ encodes sustained cyclic dynamo behavior, and α encodes weak electromagnetic leakage at the plasma-vacuum interface. A first-principles derivation from ideal MHD equations, spherical harmonic projection, and cavity-QED boundary coupling reproduces κ without free parameters. Quantitative correlations confirm all three conditions (r = 0.596 for cycle stability; r = 0.678 for field strength). The formula is self-describing in the precise sense that violating any single condition while preserving the other two eliminates the resonance. This is Paper 4 in a series; see DOI: 10.5281/zenodo.18879100 and DOI: 10.5281/zenodo.18905897 for the observational foundation.