Axiodynamics Addendum BRC-1 — Vectorial Axiological Distance: Directional Asymmetry and Fc⊗Fi Grounding

The scalar axiological distance introduced in Kleden (2025) provides a symmetric metric for quantifying ideological divergence between political agents in multidimensional axiological space. While adequate for population-level structural analyses, the symmetry property - inherited from the pseudo-metric formalism - is a pragmatic simplification: agents with distinct affective configurations experience the same structural gap through phenomenologically different orientations. This document formalizes the transition from scalar to its vectorial generalization in four steps: (1) breaking symmetry through explicit dyadic Fc/Fi differentiation; (2) introducing a dyadic orientation operator anchored in the Fc ⊗ Fi orthogonal plane; (3) re-anchoring as a derived scalar from ; and (4) providing the complete formal definition with properties. This transition constitutes a protective-belt extension in the Lakatosian sense: all previously published results using remain valid as norm-equivalent approximations. Applications to the U.S. political distance cases from Kleden (2025) demonstrate that the scalar model's empirical bias parameter admits a structural interpretation as a Fc/Fi directional proxy, generating a falsifiable empirical prediction.