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Codex — Wave 4 Plan

Wave 4. Production of the deep prerequisites that Wave 3 units (and a handful of Wave 2 mid-tier units) declared pending_prereqs: true against. After Wave 4, every shipped unit's prerequisites should resolve to other shipped units — the curriculum DAG becomes traversable from leaf to apex with zero residual pending_prereqs: true.

Read OVERVIEW.md, docs/plans/WAVE_3_PLAN.md (Wave 3 Phase 3.1 + 3.2 are complete), docs/pilot-lessons.md (consolidated production lessons through Phase 3.2), docs/specs/QUALITY_RUBRIC.md (the validator gate).

1. Wave 4 scope

8 units still have pending_prereqs: true as of 2026-04-28 after Wave 3 Phase 3.2 closed:

Unit Pending on
01.01.03 Vector space 00.02.05 function, 01.01.01 field
01.02.01 Group 00.02.05 function
03.01.04 Tensor algebra 03.01.01 tensor product
03.01.05 Quotient algebra 03.01.02 associative algebra, 03.01.03 ideal
03.04.06 De Rham cohomology 03.04.04 exterior derivative, 03.04.05 Stokes' theorem
03.05.05 Double cover 03.12.02 covering space
03.08.04 Classifying space 03.12.01 homotopy / homotopy group
03.08.06 Stable homotopy 03.12.01 homotopy, 03.12.03 suspension, 03.12.04 spectrum

Plus one additional gap surfaced by Wave 1 / Wave 2 prereq lists but not yet in any unit's pending list:

  • 03.06.03 Stiefel-Whitney classes — referenced by Spin structure (which currently has pending_prereqs: false because the validator didn't catch this; could be tightened to true if rigour is desired, but Stiefel-Whitney is foundational to characteristic-class theory and worth producing as a Wave 4 unit either way).

Wave 4 production target: 10 units organised into two non-colliding strands.

2. Strand A — algebra / foundations (5 units, independent)

For the gpt-codex parallel session. See docs/batches/WAVE_4_GPT_BATCH.md (paste-ready scaffold).

Order Unit ID Title Path Anchor
1 00.02.05 Function content/00-precalc/02-set-and-function/00.02.05-function.md Halmos Naive Set Theory §8; Lang Algebra §0
2 01.01.01 Field content/01-foundations/01-linear-algebra/01.01.01-field.md Lang Algebra §III; Dummit-Foote §7
3 03.01.01 Tensor product content/03-modern-geometry/01-tensor-algebra/03.01.01-tensor-product.md Lang Algebra §XVI; Atiyah-Macdonald §2
4 03.01.02 Associative algebra content/03-modern-geometry/01-tensor-algebra/03.01.02-associative-algebra.md Lang Algebra §III; Bourbaki Algebra I Ch. III
5 03.01.03 Ideal in an algebra content/03-modern-geometry/01-tensor-algebra/03.01.03-ideal.md Lang Algebra §III §6; Atiyah-Macdonald §1

Unblocks (after this strand ships): 01.01.03 Vector space, 01.02.01 Group, 03.01.04 Tensor algebra, 03.01.05 Quotient algebra — i.e., 4 of the 8 pending units close.

3. Strand B — topology / differential geometry (5 units, independent)

For the claude session (taken concurrent with Strand A).

Order Unit ID Title Path Anchor
1 03.12.01 Homotopy and homotopy group content/03-modern-geometry/12-homotopy/03.12.01-homotopy.md Hatcher Algebraic Topology §1.1; May Concise Course Ch. 1
2 03.12.02 Covering space content/03-modern-geometry/12-homotopy/03.12.02-covering-space.md Hatcher §1.3; Bredon §III.3; May Ch. 3
3 03.04.04 Exterior derivative content/03-modern-geometry/04-differential-forms/03.04.04-exterior-derivative.md Spivak Vol. I §7; Bott-Tu §I.1
4 03.04.05 Stokes' theorem content/03-modern-geometry/04-differential-forms/03.04.05-stokes-theorem.md Spivak Vol. I §11; Bott-Tu §I.3; Lee §16
5 03.06.03 Stiefel-Whitney classes content/03-modern-geometry/06-characteristic-classes/03.06.03-stiefel-whitney.md Milnor-Stasheff §4–§8; Bott-Tu §23

Unblocks (after this strand ships): 03.04.06 De Rham cohomology, 03.05.05 Double cover, 03.08.04 Classifying space (partial — also needs Strand A), 03.08.06 Stable homotopy (partial — also needs suspension/spectra). After both strands close, at minimum 6 of 8 pending units close, with stable homotopy still needing the (deferred) suspension + spectrum units.

4. Strand collision avoidance

The two strands operate on disjoint chapter directories:

  • Strand A: content/00-precalc/02-set-and-function/, content/01-foundations/01-linear-algebra/01.01.01-*, content/03-modern-geometry/01-tensor-algebra/
  • Strand B: content/03-modern-geometry/12-homotopy/, content/03-modern-geometry/04-differential-forms/03.04.04-*, content/03-modern-geometry/04-differential-forms/03.04.05-*, content/03-modern-geometry/06-characteristic-classes/03.06.03-*

Shared files both strands edit:

  • docs/catalogs/CONCEPT_CATALOG.md — append-only; new entries added in different sections
  • manifests/deps.json — append-only; both strands add to shipped set
  • docs/pilot-lessons.md — append-only

Risk of last-write-wins on shared files is acceptable — historically (Wave 2, Wave 3 Phase 3.2) this hasn't caused issues because each session adds new content rather than modifying shared lines.

If a conflict surfaces, prefer manual reconciliation: take the union of additions from both sessions, validate, ship.

5. Phase structure

Wave 4 ships in one phase — both strands run concurrently, total ~10 units. After both report back, run a flag-flip cleanup pass on the 8 originally-pending units, then ship Wave 4.

6. Wave 5 scope (sketch)

After Wave 4, the remaining gaps are:

  • Stable homotopy (03.08.06) needs 03.12.03 suspension functor and 03.12.04 spectrum / stable category. These are deeper than typical curriculum entries and could be deferred indefinitely if we accept stable homotopy with a partial pending-prereqs flag, or produced in Wave 5 as part of a "homotopy theory completion" batch.
  • Possible apex expansion: per OVERVIEW.md, additional apex strands beyond spin geometry (algebraic geometry, symplectic geometry, representation theory, statistical mechanics) would be the natural Wave 5 / v0.5 work. This is lateral expansion rather than depth, and constitutes the transition from v0.x to v1 of the curriculum.

Wave 5 candidate units (4–6 units, optional):

  • 03.12.03 Suspension (homotopy-theoretic)
  • 03.12.04 Spectrum / stable homotopy category
  • 03.12.05 Eilenberg-MacLane space (foundation for ordinary cohomology in homotopy theory)
  • 03.05.06 Reduction of structure group (alternative formulation of spin / oriented bundles, useful)

Wave 5 is optional in the sense that the curriculum DAG is already substantially complete after Wave 4. Its primary purpose is closing the last pending_prereqs: true flags rather than introducing new content.

7. Success criteria (Wave 4)

Wave 4 succeeds if:

  • All 10 Wave 4 units ship at 27/27 rubric.
  • After Wave 4 ships, validate_all.py is green at unit count ≥ 63 (53 currently shipped + 10 Wave 4).
  • At least 6 of 8 previously-pending_prereqs: true units flip to false (the 2 holdouts being stable homotopy and possibly classifying space, both blocking on suspension/spectrum which is deferred to Wave 5 if at all).
  • pnpm build clean at ≥ 68 pages rendered.
  • LM editorial review pass on the 10 new units catches no flagrant Master-prose violations (rubric §M).

Wave 4 fails if:

  • Production introduces curriculum-bloat units that don't appear in any other unit's prerequisites: list.
  • The DAG remains untraversable from leaf to apex after Wave 4 closes — i.e., more than 2 units still have pending_prereqs: true.

8. Exit conditions

After Wave 4:

  • If Wave 5 is scoped: produce 4–6 stretch units to close the last 2 pending flags and bring the DAG to total closure.
  • If Wave 5 is deferred: declare v0.x scope complete with a documented "stable homotopy / classifying space pending on Wave 5" footnote. Move on to v0.5 lateral expansion (additional apex strands) or v1 launch readiness (rendering, exercise interactivity, RAG, reviewer attestation).

The transition out of Wave 4 is the natural inflection from "depth completion" to "lateral / production readiness" work.

Wave 4 plan drafted 2026-04-28 during Phase 3.2 cleanup. Two-strand parallel production.