diff --git a/docs/developer/subsystems/analytic-solutions.md b/docs/developer/subsystems/analytic-solutions.md
index 1cff3d8e..8ec412ff 100644
--- a/docs/developer/subsystems/analytic-solutions.md
+++ b/docs/developer/subsystems/analytic-solutions.md
@@ -990,7 +990,7 @@ are under `.self_gravity`. Velocity is unchanged by that postprocessing.
 
 ### Validation
 
-`tests/test_1029_analytic_zhong2008.py` checks every parenthesized analytical
+`tests/test_1030_analytic_zhong2008.py` checks every parenthesized analytical
 entry in Zhong et al. (2008) Tables 2 and 3: three load depths, four harmonic
 degrees, isoviscous and `10^4`-lid cases, and eight response quantities per
 case. The 192 comparisons agree within the precision printed in the paper. The
diff --git a/src/underworld3/analytic/kramer.py b/src/underworld3/analytic/kramer.py
index 13330513..b57942b6 100644
--- a/src/underworld3/analytic/kramer.py
+++ b/src/underworld3/analytic/kramer.py
@@ -266,16 +266,16 @@ def apply_boundary_conditions(self, solver):
         to use" section of ``docs/developer/subsystems/rotated-freeslip.md``.
         """
 
+        # The pressure nullspace belongs to the DOMAIN, not to the wall type.
+        # Both cases here are an enclosed annulus — velocity prescribed
+        # everywhere on both arcs, or wall-normal flow zero on both — so in
+        # either the pressure is determined only up to a constant and the
+        # nullspace has to be removed. It used to be set after an early
+        # `return` that the zero-slip branch took, so that case ran a singular
+        # saddle and could return a quiet, wrong answer (#577).
         if self.boundary == "zero":
-            # TODO(BUG): issue #577 — the zero-slip case leaves the pressure
-            # nullspace in place, where every other enclosed case in the suite
-            # removes it. An annulus with both arcs held at zero velocity is
-            # enclosed, so its pressure is determined only up to a constant and
-            # a direct solve on the singular saddle can return a quiet, wrong
-            # answer. Preserved here because this refactor is
-            # behaviour-preserving by contract; fix it under its own test.
             prescribed_velocity(solver, self.boundaries, (0.0, 0.0))
-            return
+        else:
+            free_slip(solver, self.boundaries)
 
-        free_slip(solver, self.boundaries)
         solver.petsc_use_pressure_nullspace = True
diff --git a/src/underworld3/meshing/cartesian.py b/src/underworld3/meshing/cartesian.py
index 3e4d3ca2..1dab453b 100644
--- a/src/underworld3/meshing/cartesian.py
+++ b/src/underworld3/meshing/cartesian.py
@@ -1427,7 +1427,16 @@ class boundary_normals_3D(Enum):
         if uw.mpi.rank == 0:
             os.makedirs(mesh_file_dir(), exist_ok=True)
 
-        uw_filename = f"{mesh_file_dir()}/uw_structuredQuadBox_minC{minCoords}_maxC{maxCoords}.msh"
+        # `elementRes` is part of the name because it is part of the mesh.
+        # Without it every StructuredQuadBox on the same box — 16x16, 32x32,
+        # a resolution sweep — writes and reads ONE path, so two processes at
+        # different resolutions race on it and one reads the other's mesh
+        # (#618). The annulus already carries its cell size for this reason:
+        # `uw_annulus_ro1.0_ri0.5_csize0.05.msh`.
+        uw_filename = (
+            f"{mesh_file_dir()}/uw_structuredQuadBox_minC{minCoords}"
+            f"_maxC{maxCoords}_res{tuple(elementRes)}.msh"
+        )
     else:
         uw_filename = filename
 
diff --git a/tests/test_1029_analytic_zhong2008.py b/tests/test_1030_analytic_zhong2008.py
similarity index 99%
rename from tests/test_1029_analytic_zhong2008.py
rename to tests/test_1030_analytic_zhong2008.py
index 859f2b8a..131b2d3d 100644
--- a/tests/test_1029_analytic_zhong2008.py
+++ b/tests/test_1030_analytic_zhong2008.py
@@ -5,7 +5,7 @@
 published propagator row so a sign, stress scaling, layer-order, or self-gravity
 regression cannot hide behind agreement with one selected case.
 
-Run: pixi run python -m pytest tests/test_1029_analytic_zhong2008.py -v
+Run: pixi run python -m pytest tests/test_1030_analytic_zhong2008.py -v
 """
 
 import numpy as np