# PH-NUM-001

**Name:** Quadrature convergence warning

**Severity:** warning

**Input modes:** adapter+dump

PH-NUM-001 is a **structural stub in v1.0**: on `MeshField` inputs it
emits `PASS` with a pass-through baseline integral as `raw_value` and
the reason string `"qorder convergence check is a stub until V1.1"`;
on any non-MeshField it emits `SKIPPED`. It does **not** compute a
convergence rate, **not** compare quadrature at orders $q$ vs $2q$,
and **not** measure any variational crime in v1.0.

The rule ships as a stub because `MeshField.integrate` does not expose
a `qorder` kwarg in v1.0, so the rule cannot perform the intended
q-vs-$2q$ comparison. The stub preserves the rule's registry slot,
the CLI surface, and the SARIF emission shape, so a future v1.1
implementation can plug in the real check without breaking any
public API.

The harness-level validation does exercise polynomial-exactness via
Gauss-Legendre quadrature on a scikit-fem unit-square P2 mesh: known
monomials of controlled degree are integrated against unit weight,
and the result is compared to closed-form analytical values. Three
regimes are measured — exact (degree ≤ intorder, error at float64
roundoff), under-integrated (degree > intorder with gap ≥ 3, error
≥ $10^{-6}$), and convergence (fix degree, sweep intorder, errors
drop ~12 orders of magnitude).

Per the v1.0 stability policy, the rule's verdict surface is stable;
only the implementation (the v1.1 q-vs-$2q$ check) will change in a
minor release.