Moralogy: Vectorizing Moral Geometry

We present Moralogy, a formal framework for AI alignment grounded in axiomatic derivation. The Wrongness Formula derives ethical constraints from a single logical premise without human annotation or domain-specific retraining: Wrong(a) <=> Ex[ H(x,a) ^ ~Consent(x,a) ^ ~PGH(a) ] Key findings: phase transition in moral reasoning (reproduced across 4 training versions), zero fabrication, cross-domain generalization across Medical, Defense, Automotive, and Customer Service domains, empirically located failure boundary, and two-layer proof of concept (deterministic kernel + language model) demonstrating correct denial of a pharmacologically-compromised organ transplant authorization without retraining. Model and dataset: huggingface.co/moralogyengineCode: github.com/moralogyengine/moralogy