# 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).