Stratified Gauge Theory: Invariance and Conservation on Singular Spaces

We develop a gauge-theoretic framework compatible with stratified spaces, resolving the tension between (1) the smooth manifold structure required by standard Noether conservation and (2) the stratified structure required for moral discontinuities, hard constraints, and regime changes. The key insight is that gauge structure and Noether conservation hold , while boundary behavior is governed by that constrain how trajectories cross between strata. We define stratified principal bundles, stratified connections, and prove a : the alignment current is conserved within each stratum and satisfies explicit jump conditions at stratum boundaries. For the special case of constraint boundaries (where evaluation jumps to - ), we prove that admissible trajectories cannot cross the boundary, recovering the No Escape result as a consequence of the variational principle rather than an additional assumption. The framework unifies Stratified Geometric Ethics with gauge-theoretic invariance while maintaining mathematical rigor. Author preprint deposited for archival and citation. Draft — pending author review.