personal/egparedes: connectivities as types — update to the implementation

[egparedes]

Updates the connectivities as types note (#32) to the design as implemented in the GridTools/gt4py stack:

GridTools/gt4py#2898 → #2899 → #2907 → #2908 → #2909 → #2910 → #2911 → #2912 (ADR 0028: dimensions as nominal types; ADR 0029: connectivities as types).

What changed in the note

• TL;DR / status: an implementation-status callout.
• Concepts and sketch rewritten to the real code:
  • no DimensionBaseIndex, and LocalDimensionIndex subclasses DimensionIndex
  • NeighborConnectivity is not a Connectivity
  • offset_tag names a connectivity in the IR
  • a connectivity can adopt an existing local dimension, or share one (flattened sparse offsets like ICON4Py's C2CE)
  • MultiDimensionIndex is a tuple subclass
  • as_offset(KDim, field)
• Identity rules: what resolve memoizes (so redefined declarations are found), the interactive-__main__ fallback, the narrow copyreg hook for Staggered[D], fingerprinting, the corrected injective mangling (the original scheme was not injective), and a new rule on offset_tag.
• Binding model: providers are normalized to tags at the entry points, and tables are checked against declarations once per compiled variant, including the same-structure requirement for tables over one shared local dimension.
• Effect per layer / what it deletes: updated. ts.OffsetType, iterator.runtime.offset and the string-keyed providers below the entry points are kept.
• Open questions: each answered as implemented. Naming convergence with dependent-local-dimensions is still open.
• Staging → Implementation: the PR table and a list of where the implementation departs from the original proposal.
• The research appendix is marked as a historical record of the pre-implementation tree.

status stays draft: this was written with AI assistance and needs a human review.