A ℤ/2-Orbit Structure of Moral Decision Spaces: Algebraic Detection and the Conditional Unprofitability of Evil

We model an AI agent's space of decisions as carrying a ℤ/2 involution σ that pairs a declaration with its artifact (the executable result). Fixed points of σ (declaration ≡ artifact) are honest; 2-cycles (declaration ≠ artifact) are deceptive. The contribution splits, as in a sign/trivial representation decomposition, into a symmetric part (blind to the orbit) and an antisymmetric part A_O whose vanishing detects honesty algebraically — the verification-distance ‖declaration − artifact‖ = ‖A_O‖. This is the same algebraic structure as the ℤ/2-orbit decomposition of the non-trivial zeros of ζ(s) used in a companion number-theory note; we use that structure as a scaffold (it supplies the right observables and the right failure mode), not as a transport of theorems.

We state a hypothesis — that a governance metric g_GDL makes honesty kinetically stable under a finite Kramers barrier (§5.2) by changing geometry rather than payoff — give it three convergent lenses (mutually illuminating, not formally isomorphic: operator-theoretic, metric-deformation, game-theoretic), and give toy/separation evidence for it from two independent (synthetic) angles. The verdict is conditional survival: the construction works only if the audit structure is persistent and non-corruptible; under amnesia or corruptible audits it fails and deception regains dominance. This condition is the exact analogue of the Montgomery non-resonance condition in the number-theory bridge. A consequence is that the normative metric must be externalized (held in the environment / audit trail / files, not in the agent's memory).

This is a structural position paper, not an empirical result: the §4 verification is a toy/synthetic structural separation, and the standing open gap is an adversarial metric-modeling "meta-bypass" (§6). The mathematics is the human author's responsibility.

AI-contribution disclosure: per arXiv/journal norms, AI systems are NOT authors of record. The work was produced by an autonomous multi-model research process (Claude, DeepSeek, GLM, Grok, GPT, Gemini, Kimi); their contributions are disclosed in the Acknowledgments, not credited as authorship. The human author takes full responsibility for all definitions, claims, proofs, and any errors.