Rotated free slip on a FLAT wall does not reproduce the equivalent component Dirichlet condition (2e-3, and not a convergence artefact)

[lmoresi]

On a flat, axis-aligned wall add_rotated_freeslip_bc(0.0, "Top") and
add_dirichlet_bc((None, 0.0), "Top") are the same discrete constraint: the
measure-weighted node normal is exactly (0,1), so striking the rotated normal
row is striking u_y. The two solves do not agree.

Minimal reproduction

Unit box, StructuredQuadBox(elementRes=(32,32)), uniform viscosity 1,
bodyforce = (0, cos(pi x) sin(pi z)), free slip on all four walls (Left,
Right, Bottom by component Dirichlet), petsc_use_pressure_nullspace = True,
tolerance = 1e-9. Reference is a monolithic LU solve of the component-Dirichlet
problem. The two top corner nodes are EXCLUDED from every norm (they are the
known recovery corner, #608).

run	‖u − u_ref‖ / ‖u_ref‖
component Dirichlet, default solver	8.9e-09
component Dirichlet, pc_type=lu	0 (the reference)
rotated free slip, default solver	2.0e-03
rotated free slip, _rotated_use_lu = True	2.1e-03

The last row is the point: with an exact linear solve on both sides the answers
still differ by 2e-3, so this is the discrete problem, not convergence.

What it is not

• Not the corner. Dropping a ball of radius 1/32, 2/32, 4/32, 8/32 around each
  top corner takes the ratio of velocity errors from 1.49 to 1.19; a 20% excess
  survives dropping a quarter of the domain.
• Not the tolerance. tolerance = 1e-9 and 1e-12 give bit-identical
  answers on the rotated path (3.313e-03 both, SolCx eta_B=10).
• Not the pressure gauge. The rotated path builds the constant-pressure null
  vector; its pressure comes back with a non-zero mean (−0.224 where the
  Dirichlet run gives 1e-12), but a constant pressure has no gradient and cannot
  move the velocity.
• Not the viscosity contrast — and this is the odd part. Same comparison
  against contrast: uniform 3.2e-03, eta_B=10 2.7e-03, eta_B=1e6 9.3e-08.
  The two agree on the hard problem and disagree on the easy one.

Why it matters

It is the reason a SolCx velocity error reads 1.7e-03 with a component-Dirichlet
lid and 3.3e-03 with a rotated one, which reads as the rotated constraint being
half as accurate on a geometry where it should be identical. On curved boundaries
there is no component condition to compare against, so this comparison is only
available on a box — which is where it should be guarded.

Found while measuring boundary-condition treatments for UWTN 2026-016;
reproduction in that note's examples/solcx.py.

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