Addendum G-1 (Codename: Gemini-1)

This formal addendum to Monograph G establishes "The Law of State-Space Interactive Reaction" (T_Reaction), codenamed "Gemini-1," translating colloquial principles of reciprocal honor into non-linear coupled operator mechanics within Hilbert space. Sociocultural frameworks frequently treat relational expectations as asymmetric burdens or subjective sentimentality. This paper proves that executive refinement (R_transform) is mathematically bounded by the protective boundary conditions (S_Futuwwa) supplied to the system, operating in continuous chemical-style reaction equilibrium (<=>) toward Divine Coherence (C_divine). By defining bandwidth allocation between boundary defense (P_Reject) and internal ordering, we prove that sovereign coherence requires complete protective insulation. Furthermore, explicit empirical falsification protocols are established, demonstrating that high-level executive sanctuary output cannot be generated in environments dominated by unchivalrous neglect, exposure, or entropic noise. (Extends Emerald Research Group Zenodo Archive DOIs: 10.5281/zenodo.23274222 through 10.5281/zenodo.23289370).