Sigma-Preservation as Objective Ethics Morality as the Conservation Law of Reciprocal Recognition

Moral theories often fail at the same point: they lack a non-negotiable invariant that distinguishes repair from extraction when power, appetite, consensus, or aggregate welfare gives extraction a socially acceptable name. This paper proposes such an invariant. In Recognition Science, reciprocal comparison carries the canonical cost J(x) = ½(x + x⁻¹) − 1, x > 0, the unique reciprocal cost under the Recognition Composition Law and the stated regularity and calibration assumptions. At the agent scale, directed recognition bonds carry positive multipliers. Their log-space imbalance defines a skew variable σ. Moral admissibility is ledger closure at σ = 0; objective ethics is the minimization of total recognition cost subject to that closure condition. A balanced extraction pair has exact cost C_ext(σ) = J(eᵠ) + J(e⁻ᵠ) = 2(cosh σ − 1). This cost is zero only at σ = 0, strictly positive away from zero, strictly convex, and has restoring force toward balance. The same convex structure yields cost-lowering equilibration: replacing unequal skews by their mean strictly reduces pair and ensemble cost while preserving total skew. The space of admissible moral moves is generated completely and minimally by two golden-ratio-locked primitives, accurate posting and bounded mercy, from which the classical virtue vocabulary is recovered. Temptation appears as the gap between a concave, saturating local reward and the convex, compounding cost over the same skew. For bounded agents with finite reserve and finite renewable budget, sustained extraction above budget destroys viability in finite time. Under positive coupling, neighbor imbalance enters one's own forward cost, yielding other-regarding normativity without adding an altruism axiom. The final practical "ought" is conditional on one thin premise of practical reason: a deliberator is committed to continued agency. Given that premise, non-extraction is rationally required for any agent that intends to remain an agent. The framework produces testable predictions for dyads, institutions, AI systems, and social networks through sigma-estimation protocols.