Add hash-free seqno index tables to the Milnor algebra

[JoeyBF]

Splits the GPU-agnostic seqno index out of the Nassau GPU work (#264) so it can land on its own. Second of three; follows the benchmark split (#269).

What

A flat, arc-swapped hash-free index for the Milnor basis: an O(number of p-part entries) rank computed from a precomputed g table, with no hash lookup.

• SeqnoTables + compute_seqno_tables (idempotent, concurrency-safe via ArcSwapOption::rcu) + seqno, applicable at p = 2 with a trivial profile and stable ordering.
• benches/seqno.rs: an A/B of the table index against the basis hashmap (needs the criterion harness from Migrate the algebra benchmark suite to criterion #269).

Notes

This is general infrastructure, independent of the GPU backend — it's the uploadable/on-device index primitive and an independently benchmarkable alternative to the basis hashmap. The CPU basis index deliberately still uses the hashmap (the tables lose to it on the CPU), and compute_basis does not build them; this is documented at try_basis_element_to_index.

Test plan

• cargo test -p algebra — seqno_matches_enumeration_order passes
• cargo bench --no-run -p algebra — the seqno bench compiles
• just lint (nightly fmt + clippy, -D warnings)

🤖 Generated with Claude Code

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Generated by Claude Code

Summary by CodeRabbit

• New Features

  • Added faster sequence-number lookups for supported Milnor algebra cases.
  • Added on-demand table generation for sequence-number calculations.

• Performance

  • Improved basis index calculation by enabling hash-free lookup paths.
  • Added benchmarks comparing sequence-number and hashmap-based lookups.

• Bug Fixes

  • Added validation that sequence-number results match basis enumeration order.

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Review details

⚙️ Run configuration

Configuration used: Organization UI

Review profile: ASSERTIVE

Plan: Pro

Run ID: bc53080d-8868-4e3d-a157-28cfc1cfd9e3

📥 Commits

Reviewing files that changed from the base of the PR and between e41c769 and 5c4f429.

📒 Files selected for processing (1)

• ext/crates/algebra/src/algebra/milnor_algebra.rs

📝 Walkthrough

Walkthrough

The algebra crate adds cached, hash-free sequence-number ranking for applicable Milnor algebras, validates it against enumeration order, and introduces a Criterion benchmark comparing it with hashmap-based lookup.

Changes

Sequence-number lookup

Layer / File(s)	Summary
Sequence-number table storage and eligibility ext/crates/algebra/src/algebra/milnor_algebra.rs	MilnorAlgebra stores optional ArcSwap-backed tables, initializes them, documents lookup behavior, and defines applicability conditions.
Table construction and ranking ext/crates/algebra/src/algebra/milnor_algebra.rs	Tables are computed and atomically extended, seqno ranks basis elements from p_part, and a unit test compares results with enumeration order.
Lookup benchmark integration ext/crates/algebra/Cargo.toml, ext/crates/algebra/benches/seqno.rs	A Criterion benchmark target compares hashmap and table lookups across configured degrees.

|

Estimated code review effort: 3 (Moderate) | ~25 minutes

Sequence Diagram(s)

sequenceDiagram
  participant Benchmark
  participant MilnorAlgebra
  participant SeqnoTables
  Benchmark->>MilnorAlgebra: compute_basis()
  Benchmark->>MilnorAlgebra: compute_seqno_tables(max_degree)
  MilnorAlgebra->>SeqnoTables: publish cached table
  Benchmark->>MilnorAlgebra: basis_element_to_index(element)
  Benchmark->>MilnorAlgebra: seqno(element.p_part)
  MilnorAlgebra-->>Benchmark: return lookup index

Loading

Possibly related PRs

• SpectralSequences/sseq#269: Adds related Criterion benchmark infrastructure and bench-target wiring.

Poem

I’m a rabbit with ranks in a table so neat,
Hashes hop aside for a lookup fleet.
The degrees all sparkle, the benchmarks run,
While seqno counts softly beneath the sun.
Squeak—cached indices, a burrow well done!

🚥 Pre-merge checks | ✅ 5

✅ Passed checks (5 passed)

Check name	Status	Explanation
Description Check	✅ Passed	Check skipped - CodeRabbit’s high-level summary is enabled.
Title check	✅ Passed	The title clearly summarizes the main change: adding hash-free seqno index tables to the Milnor algebra.
Docstring Coverage	✅ Passed	No functions found in the changed files to evaluate docstring coverage. Skipping docstring coverage check.
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.

✨ Finishing Touches

🧪 Generate unit tests (beta)

• Create PR with unit tests

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Actionable comments posted: 2

🤖 Prompt for all review comments with AI agents

Verify each finding against current code. Fix only still-valid issues, skip the
rest with a brief reason, keep changes minimal, and validate.

Inline comments:
In `@ext/crates/algebra/src/algebra/milnor_algebra.rs`:
- Around line 1941-1958: The test seqno_matches_enumeration_order only validates
a single compute_seqno_tables call. Extend coverage by invoking
compute_seqno_tables again with a larger max_degree and rechecking seqno
correctness, and add concurrent callers if practical to exercise the monotonic,
non-shrinking publication behavior documented for compute_seqno_tables.
- Around line 1006-1026: Update seqno to add a debug_assert before indexing t.g,
validating that cur_d is within the loaded table’s max_degree (and preserving
the existing table-not-built diagnostic). Ensure the assertion identifies the
requested degree and table capacity so stale or partially built seqno tables
fail with a clear diagnostic rather than a raw Vec bounds panic.

🪄 Autofix (Beta)

Fix all unresolved CodeRabbit comments on this PR:

• Push a commit to this branch (recommended)
• Create a new PR with the fixes

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ℹ️ Review info

⚙️ Run configuration

Configuration used: Organization UI

Review profile: ASSERTIVE

Plan: Pro

Run ID: 61e89921-4801-4d53-b8e0-c3229727be50

📥 Commits

Reviewing files that changed from the base of the PR and between 4867b30 and e41c769.

📒 Files selected for processing (3)

• ext/crates/algebra/Cargo.toml
• ext/crates/algebra/benches/seqno.rs
• ext/crates/algebra/src/algebra/milnor_algebra.rs