[shahar1]

Summary

Replaces the modified-Kahn body of TaskGroup.topological_sort (and the mirror in SerializedTaskGroup) with a projected sweep:

• Each child's per-task upstream_task_ids is projected onto sibling-level integer indices once up front (_project_child_deps).
• The sweep (_sweep_projection) then runs against the projection with a bytearray-backed emission flag - per-edge work happens once per sort instead of once per outer-loop pass.

Emission order is identical to the previous implementation. The existing order-sensitive tests (test_topological_sort1/2, test_topological_nested_groups, test_topological_group_dep) cover the contract.

Benchmark

Min of five runs, N=2000 children, ms per call. Source: https://gist.github.com/shahar1/9c61dc9f34f7e77cd29cfb9d67af7ceb

Shape	main	PR	speedup
chain (forward-declared)	1.39	0.75	1.84x
diamond (root → many → sink)	2.20	0.86	2.56x
independent (no deps)	0.65	0.35	1.84x
layered (4-layer full bipartite)	230.96	67.15	3.44x
nested (depth-3, walked across all groups)	17.78	4.77	3.73x
rev-chain (adversarial reverse insertion)	894.04	114.16	7.83x

The 7.8x on rev-chain comes from the projection precompute alone (one projection vs N projections); algorithmic complexity is unchanged and remains O(N²) on that shape until the follow-up PR.

The nested row times a recursive walk across all 39 nested groups (depth=3, ~222 tasks each); the root-only timing was dominated by setup overhead and was previously labelled ~noise in this table.

Test plan

• task-sdk/tests/task_sdk/definitions/test_taskgroup.py + test_dag.py — 145 passed (18 new shape-correctness cases)
• airflow-core/tests/unit/utils/test_task_group.py — 20 passed (1 new serialization round-trip case)
• airflow-core/tests/unit/serialization/ (task-group / topological filter) — 4 passed
• prek run mypy-task-sdk — passed
• prek run mypy-airflow-core — passed
• prek run --from-ref upstream/main --stage pre-commit — passed

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Was generative AI tooling used to co-author this PR?

• Yes — Claude Code (Opus 4.7)

Generated-by: Claude Code (Opus 4.7) following the guidelines