refactor[next]: identify a connectivity by its local dimension, not by its tag

[havogt]

Stacked on GridTools#2730 (refactor[next]: carry the connectivity name in OffsetType``). Opened here in the fork so the diff is only the incremental commit; base is offset_type_name, GridTools#2730's own branch, into which `main` has been merged (`e9f588886`). Not for upstream review as-is — GridTools#2730 lands first.

Why

A FieldOffset's tag, its declared local dimension, the connectivity's own local dimension and the offset-provider key all have to be the same string. This is not a FieldOffset constraint — a sparse field argument with no FieldOffset anywhere fails identically:

Local = Dimension("Local", kind=DimensionKind.LOCAL)

@field_operator
def fo(s: gtx.Field[gtx.Dims[Vertex, Local], gtx.float64]) -> ...:
    return neighbor_sum(s, axis=Local)

fo(s, out=out, offset_provider={"V2E": conn})
# KeyError: "Offset 'Local' not found in offset provider."   embedded AND gtfn

Eleven sites hold a local Dimension, need its ConnectivityType (max_neighbors, skip_value), and recover it by using dim.value as an offset-provider key. embedded/nd_array_field.py says so in a comment (# assumes offset and local dimension have same name, since GridTools#1441); unroll_reduce acquired it in GridTools#2267 when it stopped reading the OffsetLiteral off the IR and started reading arg.type.offset_type.value.

GridTools#2730 fixes the leg where the source-level identifier became the tag. This fixes the leg where the local dimension becomes the tag.

What

• common.get_offset_by_neighbor_dim — find the element whose neighbor_dim is the given dimension; raise naming the tags if ambiguous.
• embedded._List and SparseListIterator carry the Dimension rather than a tag, so _List.__gt_type__ needs no lookup at all.
• dace reads conn_type.neighbor_dim where it previously rebuilt a Dimension from the tag.
• transform_utils._check_offset_declarations, called from past_to_gtir beside _deduce_grid_type, checks each FieldOffset's source/target against the connectivity supplied for it. Required, not extra scope: the lookup change removes the accidental KeyError that used to catch a declaration disagreeing with its connectivity, and gtfn would otherwise run such a program silently.

itir_to_gtfn_ir already emitted both C++ tag structs when the names differed (GridTools#1789, db5325bf0); nothing else was prepared.

Notes for review

• Four of the eleven sites were not findable by grepping get_offset( — they reach the provider via a raw dict index, a SparseTag, or a fabricated Dimension. The new tests found them.
• test_unroll_reduce.py needed updating, and how is itself evidence: dummy_connectivity_type built every connectivity with neighbor dim dummy_neighbor while registering it under "Dim"/"Dim2". The dimension the ListType carried and the dimension the connectivity carried were already inconsistent in the fixtures and nothing noticed, because only the key was ever read.
• New failure mode: two connectivities sharing a local dimension now raise instead of silently resolving to whichever is named like it. icon4py has 15 local dims, each belonging to exactly one offset — no ambiguity there.
• Embedded field-operator calls do not go through past_to_gtir, so the declaration check does not fire there; the pre-existing "Field can not be reduced as it doesn't have dimension" error stands. Both paths fail, only the wording differs.
• Could be split into two commits (lookup / declaration check) if preferred.

Tests

New tests/next_tests/integration_tests/feature_tests/ffront_tests/test_offset_naming.py — 36 passing across embedded / roundtrip / gtfn / dace × simple_mesh / skip_value_mesh.

mypy src/ clean (361 files), ruff check, ruff format --check, tach check clean. unit_tests 2135 passed; multi_feature_tests 532 passed; reductions + external_local_field + import_from_mod + scan + offset_naming 517 passed.

https://claude.ai/code/session_01Mg1pdvaBDqG1meMcWjvWH7