PH-RES-002

Name: FD-vs-AD residual cross-check discrepancy

Severity: warning

Input modes: adapter

PH-RES-002 compares the AD-computed Laplacian against a 4th-order central FD Laplacian. The emitted quantity is the maximum interior relative discrepancy on a smooth method-of-manufactured-solutions (MMS) fixture. Under refinement on a smooth field, the discrepancy shrinks at \(O(h^4)\) (the FD truncation rate); the AD path is machine-precision exact, so the FD term dominates. The rule fires when the measured slope departs from the expected \(O(h^4)\) band, signalling either an MMS-fixture error or an AD-path bug in the surrogate. The rule emits SKIPPED on dump-mode fields (no callable model is available for AD).