Axiomatic Universal Second Variation

This paper introduces AUSV, a representation-independent framework derived from the second Fréchet variation of a real-valued functional S on admissible states. It demonstrates that AUSV generates curvature as an organizational phenomenon from symmetric-skew incompatibility, yielding a universal classifier E for curvature classes and canonical invariants via intrinsic refinement. Geometric projections manifest curvature as metric deformation, while categorical ones appear as 2-morphism coherence obstructions; both are shadows of AUSV structure. Invariants emerge from E's organization, not representational constructs, establishing geometry and category theory as equivalent realizations of intrinsic AUSV.