Split the secondary layer + add SecondaryExtModule::secondary_massey

[JoeyBF]

A follow-up to #259 that applies the same ring/module split, one level up, to the secondary ($d_2$ / $\mathrm{Mod}_{C\lambda^2}$) layer — and gives secondary Massey products a real home instead of a hand-rolled example.

What

secondary.rs had a single SecondaryExtAlgebra that was misnamed: it wrapped an ExtModule and owned both the module-M secondary data and the ring-k secondary data, joined by the same is_unit branching #259 removed from the primary layer. This PR splits it, mirroring ExtAlgebra / ExtModule:

• SecondaryExtAlgebra — the ring secondary layer over k: the secondary resolution of k and its $E_3$ page.
• SecondaryExtModule — the module secondary layer over M: the secondary resolution of M, its $E_3$ page, the secondary differential d2/survives, and the $\mathrm{Mod}_{C\lambda^2}$ product. Holds a shared Arc<SecondaryExtAlgebra>; when M == k it shares the ring's secondary resolution and page (is_unit = Arc::ptr_eq), retiring the branches.

secondary_massey

examples/secondary_massey.rs previously hand-built the ring-side secondary multiply-by-b map and hand-rolled the entire ~500-line bracket computation — the secondary analogue of the class_product_map gap #259 filled. That logic now lives in SecondaryExtModule::secondary_massey, which computes $\langle -, b, a\rangle$ over every valid first factor, with a ∈ Ext(M,k) (module side) and b, - ∈ Ext(k,k) (ring side). A small SecondaryClass { degree, ext, lambda } input type carries the non-standard-lift classes ($\mathrm{Ext}$ part + optional $\lambda$ part) the bracket needs. The example collapses to querying the two classes and printing the results.

Notes for review

• The delicate $\mathbb{Z}/p^2$ / $\lambda$ read-off was ported verbatim from the example into the method and pinned by a new regression test (test_sphere_secondary_massey) before the inline version was deleted — behaviour is unchanged up to the documented sign.
• build_secondary_hom now asserts the SecondaryClass $\mathrm{Ext}$/$\lambda$ vector lengths match the resolution dimensions (a zero $\lambda$ part means "no $\lambda$ part" and is always valid), giving a clear error instead of a silent zero-pad.

Stacking

Built on #268 (multigrade traits) + #277 (the primary ext split). Its diff currently includes both and will shrink to just the secondary commits as those merge and I rebase.

Testing

cargo test -p ext ext_algebra (test_sphere_d2, test_sphere_secondary_massey, plus the primary suite), full just lint / just test CI-parity matrix, and --examples --features concurrent build — all green.

🤖 Generated with Claude Code

https://claude.ai/code/session_01Nk9J57zb6GpvZxrduhGSdY

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📥 Commits

Reviewing files that changed from the base of the PR and between ed2fa42 and 5a8af60.

📒 Files selected for processing (16)

• ext/crates/algebra/Cargo.toml
• ext/crates/algebra/src/algebra/adem_algebra.rs
• ext/crates/algebra/src/algebra/algebra_trait.rs
• ext/crates/algebra/src/algebra/field.rs
• ext/crates/algebra/src/algebra/milnor_algebra.rs
• ext/crates/algebra/src/algebra/steenrod_algebra.rs
• ext/crates/sseq/src/coordinates/degree.rs
• ext/examples/massey.rs
• ext/examples/product.rs
• ext/examples/secondary.rs
• ext/examples/secondary_massey.rs
• ext/examples/secondary_product.rs
• ext/src/ext_algebra/massey.rs
• ext/src/ext_algebra/mod.rs
• ext/src/ext_algebra/secondary.rs
• ext/src/resolution_homomorphism.rs

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