perf(gfql): dense two-hop count round 3 — elide second bincount via gather-sum identity - #1851
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…gather-sum identity sum_b indeg(b)*outdeg(b) = sum_e indeg(src(e)): the out-degree bincount and aligned product-sum collapse into one gather-sum of in-degrees at each edge's source. One O(E) bincount remains on every backend (cupy also drops a kernel launch). No new guards, no new state. Spy pins moved to the one-bincount shape; new degree-product oracle pin covers raw and shifted lanes on duplicate-heavy random graphs. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01MF7uRZLKZaD6Q9FGWSmyXi
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Same owner rule as #1846: claims live in pins (one-bincount spy shapes, degree-product oracle, budget-boundary both-sides), not comment prose. Comment/docstring-only change. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01MF7uRZLKZaD6Q9FGWSmyXi
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Stacked on #1847 (round 2). ONE algebraic change to the proof-gated dense-domain kernel, values identical by construction:
Elision of the second degree table:
sum_b indeg(b)*outdeg(b) = sum_e indeg(src(e))— each middle node contributes its in-degree once per out-edge — so the out-degree bincount and the aligned product-sum collapse into a single gather-sum of in-degrees at each edge's source. Exactly one O(E) bincount remains, on every backend (on cupy this also drops a kernel launch). No new guards, no new state, no concurrency.The host-threading variant measured alongside this was split out to draft #1852 pending the owner's call on library-owned thread pools; this PR is the thread-free core.
Testing: T6 mechanism-spy pins moved to the one-bincount shape (shift-elision, scratch-buffer, mixed-dtype, both budget-boundary sides); new degree-product oracle pin on duplicate-heavy random graphs covering both the raw and shifted lanes. mypy clean; no new casts.
Measured effects and verdicts live with the receipted lanes in pyg-bench (r3 candidate lanes in progress) and the docs board.
🤖 Generated with Claude Code
https://claude.ai/code/session_01MF7uRZLKZaD6Q9FGWSmyXi