probe: per-query D/F choice (D-MHB-2) and algebraic recipe table × percentile profiles (D-ART-1)

[AdaWorldAPI]

Two probes. Both are self-contained examples in lance-graph-mask-risc; neither changes production code.

D-MHB-2: closes the two open items of D-MHB-1

mexhat_bucket_probe.rs gains three arms:

• Q, a per-query D/F choice made from the window's exact present-cell count;
• HD, an early exit over D rows;
• HQ, an early exit after a per-query choice.

Results:

• Q runs within 0.93–1.33× of whichever of D and F is faster, at every density. This removes the 2.5× worst case of either fixed path. Recommendation: ADOPT, together with R-MHB-1.
• HD and HQ: REJECT. At sparse density a D row is already cheap, so the bound bookkeeping costs more than the rows it skips.

Correctness: Q equals D for cuts 0, 100 and ∞, and HD/HQ decide exactly as H does. Disable run: a D row that drops one cell turns the check red.

D-ART-1: algebraic recipe table

algebraic_recipe_probe.rs has five parts:

• Linear canonicaliser. Rotations are exact u32 turns; a negative scale becomes a half turn; translations stay lazy.
• Static guarded recipe table, [shape][linear class][terminal].
• Independent materialising oracle, which applies the raw chain to each vertex.
• Affine transforms of CrossPowerSums summaries, exact in i128.
• Four arms for projected order statistics of m-fold families, the Wankel triangle being m = 3.

Key results:

• 36,000 random (concept, chain, terminal) cases equal the oracle.
  • Count and centred second moments need 0 transcendental calls, against 56–64 for the oracle.
  • Collision is refused, not approximated.
• Centred Σ|z − c|² of any regular family with m ≥ 3 is (m r²/2)·‖L‖_F² for every linear L. It is phase-free even under shear. The m ≥ 3 guard is load-bearing, because m = 2 is a dyad.
• The phase-conditioned percentile profile reduces to two permutations of m entries plus one cosine. Ranks change only at 1/(2m) turn.
  • The result is exact (2e-13), the table is 24 B–2 KB, and the cost is 42 ns flat in m; generate + select costs 5 µs at m = 256.
  • A bucketed LUT is faster (10 ns), but its bucket edges must sit on the tie points: 63 buckets instead of 64 raise the error from 1e-2 to 1.4.
• CrossPowerSums under affine chains. The summary path is bitwise equal to materialise-and-fold (i128) and 2.5–4× cheaper than materialising. A warm summary transform costs 14 ns, independent of row count.
• Refusals are measured:
  • two populations with identical moments but different maxima and collisions;
  • a group key that reads a transformed column.
• Lookup cost: a static array takes 1.2 ns and SipHash HashMap 27 ns. A fully colliding hasher still returns the right recipe.
• Six disable runs each turned red:
  • the isotropy guard;
  • the half-turn fold;
  • the 1-D rank reversal;
  • the half-sector split;
  • the population refusal;
  • the general ‖L‖_F².

Proposed follow-up, not in this PR: an affine-transform method on ndarray CrossPowerSums. The recipe table itself is PARKED: no arithmetic expression IR exists to host it, since Quack's IR is Boolean-only.

Board: entries/2026-10-08-mexhat-df-choice.md and entries/2026-10-08-algebraic-recipe-probe.md, plus STATUS_BOARD.md rows D-MHB-2 and D-ART-1.

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https://claude.ai/code/session_01EFw2WdKr1oxvaKCJC2ua2R

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Summary by CodeRabbit

• Documentation
  • Added reports documenting benchmark results, correctness checks, and recommendations for experimental query-selection and transformation approaches.
  • Updated the research index and status board with two new tracked entries.
• Testing
  • Added standalone probes with oracle comparisons and benchmark coverage. No production behavior changes are included.

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• crates/lance-graph-mask-risc/examples/algebraic_recipe_probe.rs

📝 Walkthrough

Walkthrough

The pull request adds two standalone example probes. One evaluates algebraic recipe planning, population summary transforms, and quantile methods. The other measures per-query D/F selection and early-exit variants. Board reports and the entries index record their scope and results.

Changes

Algebraic Recipe Probe

Layer / File(s)	Summary
Recipe planning and evaluation crates/lance-graph-mask-risc/examples/algebraic_recipe_probe.rs	The probe defines recipe inputs and terminals, canonicalizes transformation chains, and evaluates guarded recipes against a reference evaluator. Checks cover recipe guards, collision handling, and randomized comparisons.
Population summary transforms crates/lance-graph-mask-risc/examples/algebraic_recipe_probe.rs	The probe adds integer affine transformations for second-moment summaries and masked array folding. It compares summary and row-transform paths and checks when grouped folds can pass through a transform.
Quantile methods and probe results crates/lance-graph-mask-risc/examples/algebraic_recipe_probe.rs, .claude/board/entries/2026-10-08-algebraic-recipe-probe.md, .claude/board/STATUS_BOARD.md, .claude/board/entries/README.md	The probe compares projected order-statistic methods and recipe lookup implementations, including a negative-scale rank reversal check. The report and board record the probe scope, measurements, results, and status.

Mexhat D/F Selection Probe

Layer / File(s)	Summary
D/F selection and early-exit arms crates/lance-graph-mask-risc/examples/mexhat_bucket_probe.rs	Arm Q counts present cells in the query window and selects D or F using a cutoff. The H-based variants apply early exit while evaluating D rows, F rows, or a query-level D/F choice.
Agreement checks and crossover measurements crates/lance-graph-mask-risc/examples/mexhat_bucket_probe.rs, .claude/board/entries/2026-10-08-mexhat-df-choice.md, .claude/board/STATUS_BOARD.md, .claude/board/entries/README.md	The probe checks Q against D and the early-exit variants against H. It benchmarks the arms and sweeps Q cutoffs and grid densities. The report, board, and index record results and status.

Priority: ⬇️ Low

Estimated code review effort: 4 (Complex) | ~45 minutes

Change: Other

Suggested reviewers: claude

Merge Risk: 🔵 Low · up to 3d55b

The change adds only probe examples and documentation. The algebraic probe overstates the precision of its oracle agreement. It reports a relative 1e-9 bound while the check is effectively absolute 1e-3. Correcting the check or the label would make the recorded evidence accurate. Merge risk is otherwise low.

🚥 Pre-merge checks | ✅ 4 | ❌ 1

❌ Failed checks (1 warning)

Check name	Status	Explanation	Resolution
Docstring Coverage	⚠️ Warning	Docstring coverage is 35.62% which is insufficient. The required threshold is 80.00%. Docstring coverage is scoped to functions touched by this diff. Analyzed 73 functions across 2 files. (4 skipped: …	Write docstrings for the functions missing them to satisfy the coverage threshold.

✅ Passed checks (4 passed)

Check name	Status	Explanation
Description Check	✅ Passed	Check skipped - CodeRabbit’s high-level summary is enabled.
Title check	✅ Passed	The title accurately identifies the two main probe changes: per-query D/F selection and the algebraic recipe table with percentile profiles. It is specific and concise enough for the changeset.
Linked Issues check	✅ Passed	Check skipped because no linked issues were found for this pull request.
Out of Scope Changes check	✅ Passed	Check skipped because no linked issues were found for this pull request.

Full details: Docstring Coverage

Explanation

Docstring coverage is 35.62% which is insufficient. The required threshold is 80.00%. Docstring coverage is scoped to functions touched by this diff. Analyzed 73 functions across 2 files. (4 skipped: 4 unsupported.)

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• 🪄 Fix CodeRabbit comments on this PR

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@crates/lance-graph-mask-risc/examples/algebraic_recipe_probe.rs:
- Around line 712-713: Update close to compare against a tolerance relative to
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📒 Files selected for processing (6)

• .claude/board/STATUS_BOARD.md
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• .claude/board/entries/2026-10-08-mexhat-df-choice.md
• .claude/board/entries/README.md
• crates/lance-graph-mask-risc/examples/algebraic_recipe_probe.rs
• crates/lance-graph-mask-risc/examples/mexhat_bucket_probe.rs

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