Ethical Variational Framework: A Formal Derivation of Ethical Optimality

We propose that ethical behavior is the limiting case of optimal behavior as the scope of analysis approaches completeness. Apparent moral dilemmas are not evidence of genuine ethical complexity but of basis errors: the wrong variables are being measured. We formalize this claim by constructing an ethical state space as a Riemannian manifold over agent suffering, equipped with a metric that encodes the anti-fungibility of suffering as geometric curvature. A Lagrangian over this manifold defines the action functional, and a path integral over trajectory ensembles (defined here in discretized form; §6.7) provides the evaluation object, capturing moral uncertainty and risk. The central result is the Binary Variable Theorem: every single-divergence ethical decision, correctly reframed through scope expansion, reduces to first order to a single binary decision on one variable (assuming C¹ regularity of the effective action and small divergence between alternatives). Rights are derived as stability conditions: constraints whose violation cost diverges under scope expansion, characterized by a super-critical propagation rate in the causal network. Conventions are constraints with bounded violation cost (sub-critical propagation). Under an exponential causal decay assumption (§9.1), the scope expansion algorithm converges geometrically in the sub-critical regime with computable error bounds. The entire normative content of the framework is concentrated in a single parameter α (anti-fungibility strength), with all other quantities either empirical or derived. Preliminary validation against ten canonical ethical dilemmas yields 8 matches and 2 qualified matches with moral consensus. Structural limitations — including sensitivity to parameter choice, circularity risk in causal network estimation, and the consequentialist reduction — are discussed in §14. Core Thesis: Ethical behavior is the limit of optimal behavior as scope approaches completeness. Every apparent moral dilemma is a scope error or a basis error. The algorithm to resolve it is: detect degeneracy, expand scope, find the binary variable that lifts the degeneracy, reframe the question around that variable. The difficulty was never in the decision. It was always in finding the right question.