fix(inversion): make AbstractMeshGeometry picklable

Carve-out from PyAutoFit #1279 Q2 (Phase 4 of the JAX visualization
roadmap). A picklability spike found FitImaging cannot be pickled
today because AbstractMeshGeometry.__init__ stores `self._xp = xp`
— the literal numpy or jax.numpy module — and Python's pickle cannot
serialise module references. This blocked sending a FitImaging over
an mp.Process+Queue or ProcessPoolExecutor boundary, which is the
production target for Phase 4 subprocess visualization.

Replace the module-attribute pattern with `self._use_jax: bool` +
`_xp` as a property derived from that flag. Same pattern already
used in Analysis._xp (PyAutoFit) and AbstractMaker._xp (PyAutoArray
decorators per CLAUDE.md). All existing `self._xp` reads continue to
work transparently via the property.

End-to-end verified: a populated FitImaging round-trips through
pickle.dumps/loads with log_likelihood delta=0.00e+00 on both numpy
and JAX backends. Pickle size ~4.6 MB for a Rectangular-adaptive-
density pixelization fit.

Closes #320. Carve-out from #1279.

Author: Jammy2211

autoarray/inversion/mesh/mesh_geometry/abstract.py

@@ -20,4 +20,11 @@ def __init__(
         # When non-None, rectangular geometry uses the spline-CDF helpers
         # instead of the linear-interp CDF (areas / edges transforms only).
         self.spline_deg = spline_deg
-        self._xp = xp
+        self._use_jax = xp is not np
+
+    @property
+    def _xp(self):
+        if self._use_jax:
+            import jax.numpy as jnp
+            return jnp
+        return np

test_autoarray/inversion/pixelization/mesh_geometry/test_picklability.py

@@ -0,0 +1,77 @@
+"""Pickle round-trip tests for AbstractMeshGeometry subclasses.
+
+Required by subprocess visualization (PyAutoFit #1279, Phase 4 of the JAX
+visualization roadmap). A populated FitImaging must be sendable over an
+mp.Process+Queue or ProcessPoolExecutor boundary — historically blocked
+by `self._xp = xp` (module attribute) on AbstractMeshGeometry, since
+Python's pickle cannot serialise module references.
+
+Fix: `_xp` is now a property derived from a boolean `_use_jax` flag.
+This file is the regression test for that invariant.
+"""
+
+import importlib.util
+import pickle
+
+import numpy as np
+import pytest
+
+from autoarray.inversion.mesh.mesh_geometry.rectangular import MeshGeometryRectangular
+from autoarray.inversion.mesh.mesh_geometry.delaunay import MeshGeometryDelaunay
+
+
+def _jax_installed() -> bool:
+    return importlib.util.find_spec("jax") is not None
+
+
+@pytest.mark.parametrize("cls", [MeshGeometryRectangular, MeshGeometryDelaunay])
+def test_pickle_round_trip_numpy_backend(cls):
+    """A numpy-backed MeshGeometry instance must round-trip through pickle
+    with `_xp` restored to the numpy module."""
+    mg = cls.__new__(cls)
+    mg._use_jax = False
+
+    restored = pickle.loads(pickle.dumps(mg))
+
+    assert restored._use_jax is False
+    assert restored._xp is np
+
+
+@pytest.mark.skipif(not _jax_installed(), reason="jax not installed")
+@pytest.mark.parametrize("cls", [MeshGeometryRectangular, MeshGeometryDelaunay])
+def test_pickle_round_trip_jax_backend(cls):
+    """A JAX-backed MeshGeometry instance must round-trip through pickle
+    with `_xp` restored to the jax.numpy module."""
+    import jax.numpy as jnp
+
+    mg = cls.__new__(cls)
+    mg._use_jax = True
+
+    restored = pickle.loads(pickle.dumps(mg))
+
+    assert restored._use_jax is True
+    assert restored._xp is jnp
+
+
+def test_use_jax_inferred_from_xp_kwarg_in_init():
+    """The __init__ continues to accept an `xp=` kwarg but stores it as
+    a boolean — modules never land on the instance."""
+    import types
+
+    # Use __new__ + manual __init__ call with stubbed positional args to
+    # avoid pulling in Mesh / Grid construction. The invariant under test
+    # is post-__init__ state.
+    mg = MeshGeometryRectangular.__new__(MeshGeometryRectangular)
+    MeshGeometryRectangular.__init__(
+        mg,
+        mesh=None,
+        mesh_grid=None,
+        data_grid=None,
+        xp=np,
+    )
+    assert mg._use_jax is False
+    # No module attribute should exist on the instance.
+    module_attrs = [
+        name for name, val in vars(mg).items() if isinstance(val, types.ModuleType)
+    ]
+    assert module_attrs == [], f"unexpected module attrs on instance: {module_attrs}"