# Case Study 02 — PhysicsNeMo MGN

CS02 validates physics-lint against NVIDIA's PhysicsNeMo MeshGraphNet (MGN)
checkpoint for 2D cylinder vortex shedding. The substrate is incompressible
Navier-Stokes on a mesh; the rule methodology exercised is PH-CON-001 (mass conservation),
with PH-CON-002 and PH-CON-003 correctly emitting `SKIP` via the
`open-driven-dissipative` substrate-class dispatch (D0-22 + D0-23 v9 — KE is
neither strictly dissipative nor strictly conservative on a cylinder-wake
flow that imports KE from inflow and dissipates in the wake).

**Headline result.** PH-CON-001 fires across 5 in-band trajectories sampled
from the 23 in-band members (Strouhal in [0.16, 0.21]) of the Phase-2
pre-fire audit. The median MGN/GT mass-conservation gap is `-0.36%` of GT,
range `[-1.07%, +0.41%]`; every per-trajectory gap sits inside the ~5.8%
harness-FE-on-P1 discretization floor. The canonical trajectory-44 pair
lands at 5.857% (GT) / 5.881% (MGN). All 7 D0-24 verdicts PASS.

**What the result demonstrates and does NOT demonstrate.** PASS verdicts
for PH-CON-001 mean MGN is within the GT / harness-FE-on-P1 floor envelope
on that trajectory; they are **NOT** a claim of physical incompressibility
to 5%. PH-CON-001 at this discretization bounds MGN's deviation from
GT-equivalence rather than from physical incompressibility — distinguishing
the two would require a tighter discretization (deferred to v1.x; see
"What physics-lint did NOT catch §1" below for the floor-bounds-resolution
distinction). The result is a small-N statistical characterization across
the in-band subset, not a full-distribution claim or a CI-gate-threshold
derivation.

**Scope qualifier — PH-BC-001 no-slip is structurally inapplicable.**
[D0-27][D0-27-cs02-link]: the CS02 inference protocol masks
boundary nodes during rollout (`v_diff_masked = torch.where(mask2,
pred_i_velo, zeros)`), freezing wall-node velocities at their step-0
ground-truth value of zero. A no-slip check on this rollout computes
`||v_wall|| ~ 0` and PASSes by construction, detecting nothing about the
surrogate. P2.2 retired the planned mesh wall-node BC capability-build
on this finding. PH-SYM-001/002/003/004 are scoped particle-side only per
spec §1.2 and are not exercised on the mesh side.

**PH-CON-001 routing — harness, not public rule.** PH-CON-001 as shipped
in physics-lint v1.0 returns `SKIPPED` on `pde != "heat"`. CS02 routes
PH-CON-001 through the mesh harness as **structural-identity reapplication**:
the mass-conservation identity (∫ρ over the domain, ∇·v on incompressible
NS) is reapplied by the harness, validated against the analytical mass-
conservation fixture. This is NOT "rule ran without modification" — it is
the class-level pattern for V1 rules with input-domain restrictions, and
the load-bearing methodology claim of CS02. The shipped CLI and Action do
not yet ingest the mesh substrate either (`loader.py` rejects
`field.type = "mesh"`); CLI/Action loader integration for mesh — and for
particle — is planned for v1.2.0 (see `docs/backlog/v1.2.md`).

The detailed validation harness, the per-trajectory table, the cross-stack
table integrating with rung-4a/4b, and the full "what physics-lint did NOT
catch" enumeration are below.

[D0-27-cs02-link]: https://github.com/tyy0811/physics-lint/blob/master/external_validation/_rollout_anchors/methodology/DECISIONS.md