Drive section neighbor-finding from xgcm topology metadata

[hdrake]

What & why

Section-finding currently hard-codes how to deal with a few grid topologies via a topology= string ("latlon"/"cartesian"/"MOM-tripolar"), and the whole transport/tracer pipeline assumes a single logically-rectangular (Y, X) tile. This PR makes neighbor-finding read from the xgcm.Grid the caller already supplies — its boundary and face_connections metadata — so periodicity and inter-tile connectivity "just work," and extends section-finding and transports to multi-tile grids (lat-lon-cap, cubed-sphere).

Changes

Single-tile (no behavior change). Neighbors follow from each axis' boundary ("periodic" → wrap, else clip), read via the public axis.boundary property (drops private ._boundary). The topology= argument and the hard-coded north-fold formula are gone. Existing tests pass unchanged.

Multi-tile geometry (face_connections). gridutils.build_neighbor_maps builds index-valued arrays, pads them once with xgcm, and reads the halos to get each corner's neighbors with axis-rotation/reversal already applied — reusing xgcm's tested padding rather than reimplementing topology. A reciprocity check raises rather than return the silently-wrong neighbors xgcm's padding produces (hash-seed-dependently) for the hardest reversed topologies. Section state carries a face index; grid_section returns it for multi-tile grids.

Transports / tracers across seams. Each section edge's normal velocity is read in a single face's frame (source-first dual-anchor), so no velocity is rotated across a seam. The per-edge sign is computed geometrically — "does the stored velocity point to the left of the section's direction of travel?" — so it stays consistent across rotated faces without relying on a single global orientation factor. convergent_transport/extract_tracer select the contributing face pointwise.

Verification

• All existing single-tile tests pass unchanged (the geographic sign reproduces them to machine precision).
• Split-grid equivalence (a 2-face grid is a flat grid cut in half; transport must match the uncut grid) for symmetric and non-symmetric axis-preserving seams, exact to rtol 1e-12.
• Streamfunction-difference test for a genuinely rotated 2-face grid: transport across the rotated seam = psi(P2) - psi(P1) — a known, non-zero, rotation-independent answer needing no model data.
• 24 tests pass, deterministic across PYTHONHASHSEED. New tests in sectionate/tests/test_section_multitile.py.

Known limitations (guarded, not silent)

• The tripolar/bipolar fold (a face self-connection) raises NotImplementedError; xgcm doesn't support it either (xgcm#194).
• On the most complex grids (full cubed-sphere, lat-lon-cap arctic cap), xgcm's own padding is unreliable, so the reciprocity check can refuse the section path itself — an upstream issue, surfaced as a clear error rather than wrong output.

🤖 Generated with Claude Code

[hdrake]

Reopening against MOM6-community/sectionate instead.