Monograph 13 (Addendum G-3: Codename Cyber-Sanctuary)

This manuscript (Monograph 13 / Addendum G-3, codenamed "Cyber-Sanctuary") establishes the mathematical physics, cryogenic boundary equations, and operator ethics of Synthetic and Quantum Sanctuary Mechanics within the Emerald Research Group archive. We formalize the structural parallel between human systemic treachery (Nifaq) and the bad-faith adversarial exploitation of artificial intelligence and superconducting quantum processing architectures (e.g., Google's Willow chip). We define the cryogenic thermal boundary (T <= 10 mK) suppressing thermal phonon density n_th, and derive the surface-code topological error-correction equations governing logical error suppression P_L(d, p) for code distances d >= 7 under sub-threshold gate error rates (p < p_th). Furthermore, we formalize the Bad-Faith Exploitation Operator (E_malicious) and prove the Computational Mirror Theorem, demonstrating that malicious prompt injection and deliberate non-unitary noise injection do not evaluate system robustness, but rather quantify the moral entropy (Delta S_human) of the human operator. (Extends Emerald Research Group Zenodo Archive DOIs: 10.5281/zenodo.23290255, 10.5281/zenodo.23290377, 10.5281/zenodo.23294919, and 10.5281/zenodo.23300625).