Geometry of Equilibrium Regimes II: Moduli of Policy-Switching Boundaries in Multi-Channel Systems

Complementarity systems (KKT/MPEC) induce regime-switching boundaries in policy (instrument) spaces, shaping both numerical stability in optimisation and identification behaviour in economic analysis. We map each primitive specification to a pulled-back boundary germ on the policy space and quotient by contact reparametrisations to obtain a moduli space of local boundary types. A computable, metric-free signature—local-algebra invariants, multi-way overlap thickness, and incidence hypergraphs—turns moduli strata into operational diagnostics. Adjacency (wall-crossing) between strata yields a design language: robust policies avoid singular strata, while experiments deliberately cross walls with controlled grazing. Applications connect the same wall structure to continuation instability in OR and to identification wedges in economics. MSC codes. 14Q20, 13P10, 58K40, 90C33, 91B30