Metric-Aware Non-Normal Response Certification for Rotating and Vortex-Type Projected Dynamics

This preprint develops a metric-aware certification framework for projected non-normal response operators arising in rotating and vortex-type reduced dynamics. The central object is the metric-realized operator, used to separate coordinate artifacts from physically meaningful singular-value, pseudospectral, and transient-response diagnostics. The manuscript includes a toy eigenvalue-mirage calibration benchmark, a rotating-frame response benchmark with closed-form validation, a regularized vortex-core benchmark with adaptive pseudospectral refinement, and a manufactured dense-lattice stress test treated only as diagnostic evidence. The work distinguishes theorem-level certificates from diagnostic numerical evidence and includes source and reproducibility packages.