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Cycle 4 — Cross-Domain Style-Parity Plan

Drafted 2026-05-19. First Opus 4.7 cycle since Cycle 3 (2026-05-18). Working orientation for Tyler.

Premise: Math is ~75% of shipped units and is the de facto style standard (7-section template + multi-section Master + Lean formalization + ~7000 wpu). Physics is close to parity in 12-quantum / 09-classical-mech / 13-gr-cosmology (83–89% Lean, 6000+ wpu), but bio and chem are shipping at 50–60% depth with near-zero Lean coverage (bio 0–12%, chem 8–40%). Cycle 4 closes that gap.

This plan supersedes pending_approvals.md items M–T as stale (already absorbed into subsequent silent cycles — 376 units shipped, 58 books audited, books_unaudited: []) and replaces them with the real current question: how do we get bio/chem/under-served physics to the math-style standard, without stopping math frontier progress?

§1 State of play (verified 2026-05-19)

Domain Chapters Units shipped Share Lean coverage Words/unit
Math (00–07) 9 489 75% ~100% ~7000
Physics 12-quantum 1 15 2% 87% 6100
Physics 09-classical-mech 1 12 2% 83% 6400
Physics 13-gr-cosmology 1 9 1.4% 89% comparable
Physics 11-stat-mech-physics 1 9 1.4% 44% –
Physics 10-em-sr 1 10 1.5% 0% 7400
Chem 14-genchem-pchem 1 10 1.5% 40% 3500
Chem 15-orgchem 1 12 1.8% 8% –
Chem 16-inorgchem 1 8 1.2% 12% –
Bio 17-mol-cell-bio 1 17 2.6% 6% –
Bio 18-organismal-bio 1 8 1.2% 12% –
Bio 19-eco-evo-bio 1 12 1.8% 0% 4000

Master-section depth: a representative bio unit Master section is 737 words; a math-style physics unit Master is 2032 words (~2.75×). Bio/chem collapse their Master to a single named sub-section, not 3+.

1.1 Structural cleanup items found this session (corrected 2026-05-19)

These are NOT duplicate-content issues — they're naming/numbering bugs. Detail:

  • 09-quantum-theory/ (2 units) vs 09-classical-mech/ (12 units): shared Chapter-9 number, distinct content. 09-quantum-theory holds Woit/rep-theory-style QM (free particle as E(3) rep, complex structures + squeezed states); 09-classical-mech holds Hamiltonian/Lagrangian. Both are legitimate; both can't be Chapter 9. Recommendation: rename 09-quantum-theory/ → 03-modern-geometry/15-quantum-rep-theory/ (math-track home, matches the existing math/physics-track split) and renumber the 2 units to 03.15.0x. Frees Chapter 9 for classical mech alone.
  • 11-thermodynamics/ (1 unit) vs 11-stat-mech-physics/ (9 units): shared Chapter-11 number, distinct content. The orphan unit is 11.04.02-souriau-gibbs-state.md (symplectic-side stat mech). Recommendation: move to 05-symplectic/ as 05.XX.YY-souriau-gibbs-state.md, delete empty 11-thermodynamics/ directory.
  • True duplicate inside 12-quantum/: 12.02.01-hilbert-space-formalism.md (9454w, 02-formalism/) and 12.02.01-hilbert-spaces-kets-and-bras.md (3974w, 02-hilbert-formalism/) cover the same topic at different depths. Recommendation: keep the 9454w version as canonical, archive the 3974w version, redirect cross-links.
  • ID collision inside 12-quantum/: 12.03.01-schrodinger-heisenberg-pictures.md (03-time-evolution/) and 12.03.01-bosonic-fock-space-and-second-quantisation.md (03-fock-spaces/) share ID 12.03.01 but cover different topics. Recommendation: renumber Bosonic Fock to 12.13.01 (new Fock-spaces chapter); keep Schrödinger/Heisenberg as 12.03.01. Re-update prereq pointers in 4–5 dependent units.
  • pending_approvals.md items M–T (Cycle-3 surfaced items) appear stale — silent cycles since 2026-05-18 shipped ~55 units and 36 audits without logging back to pending_approvals.md or orchestrator_status.md. Items should be marked OBSOLETE / absorbed into silent cycles rather than left active.

§2 The math-style contract (revised 2026-05-19 after Tyler's clarification)

Key reframe: Math-style doesn't mean "Lean everywhere." For bio/chem/physics-applied chapters, the standard is prose-first depth that conveys systems, with formal math/Lean used only where it adds explanatory force (e.g., a population-genetics ODE is natural; a Lean category-theory abstraction of an enzyme is not). The validator already supports this: lean_status: none + a declared lean_mathlib_gap rationale passes 27/27 cleanly.

A "math-style" unit, regardless of domain, has:

  1. 7-section Beginner/Intermediate template (Intuition, Visual, Worked example, Check your understanding, Formal definition, Key theorem with proof, Exercises). All domains already do this. ✓
  2. Lean formalization section — required for math, optional for bio/chem/applied-physics. When omitted, unit declares lean_status: none and names a lean_mathlib_gap (why this content doesn't formalize natively). When included for bio/chem, it must formalize a substantive claim (Hardy-Weinberg invariance as a probability lemma, Fisher's fundamental theorem as a real-valued bound), not a forced categorical wrapper.
  3. Master tier with ≥ 3 named H2 sub-sections, each substantively developed. Each sub-section is a distinct advanced angle: a deeper mechanism, a connection to an adjacent system, an alternative formulation, an edge case where the textbook story breaks. Bio/chem currently collapse Master to one sub-section — this is the primary fix.
  4. 6000–10000 words. Bio at 4000 and chem at 3500 is half-depth. The added 3000+ words go into Master prose, not necessarily into formalization.
  5. 27/27 validator pass via python3 scripts/validate_unit.py <path>. Same gate as math.

A "style-parity upgrade" of an existing unit = adding (3)–(4) to a unit that already has the 7-section template; Lean status (2) decided per unit, not forced. A "style-parity new production" = ship a new unit that hits all five from the start.

Operative principle (Tyler 2026-05-19): bio/chem/applied-physics should be "grounded mostly in word information to convey systems, then also have math if needed." Math/theoretical-physics is the inverse: math is the medium and prose surrounds it. Both pass 27/27; both are "math style" in the validator's sense, but they look different on the page.

§3 Three-track operating model

Run all three in parallel each cycle. Budget the agents accordingly.

Track A — Math T1 frontier (skim, don't stop)

Keep 1–2 units per cycle from the T1-only skipped_units.md queue head (KR-theory, Bosonic Fock, φ⁴, characteristic-classes cluster). Opus-tier is the only producer capable of these; if we don't ship them, they accumulate forever. But cap at 1–2/cycle so bandwidth goes to closing the cross-domain gap.

Track B — Bio/chem deepening (existing units → Lean + Master expansion)

The 67 already-shipped bio+chem units pass the 7-section template but lack Lean + multi-section Master. Deepening is faster than new production (the Beginner/Intermediate halves stay; we add ~3000 words of Master + 200-line Lean section). Target: 2–3 deepenings per cycle. Each deepening must re-validate 27/27.

Track C — Bio/chem/physics new production at math-style depth

For chapters with under-coverage (e.g., 11-stat-mech-physics has only 9 units; 18-organismal-bio has only 8 across 7 sub-chapters), ship new units at full math-style depth from the first draft — never let a 3500-word stub bypass the contract. Target: 2–3 new per cycle.

3.1 Cycle budget (6 units, per Tyler's earlier answer)

  • 2 × Track A (math T1 frontier from queue head)
  • 2 × Track B (bio/chem deepening of high-leverage existing units)
  • 2 × Track C (bio/chem new at math-style depth)

§4 Concrete Cycle-4 dispatch slate

Track A — Math T1 frontier (2)

Unit Title Where it lives Notes
A1 03.08.12 KR-theory (K-theory with reality) content/03-modern-geometry/08-k-theory/
A2 08.10.03 φ⁴ theory and the Dyson series content/08-stat-mech/10-qft/ (NEW sub-chapter — opens stat-side QFT entry strand; prereq: existing 12.03.01 bosonic Fock

(Both T1-only; both have producible mathematical content with proofs and Lean targets.)

Track B — Bio/chem deepening (2)

Pick units that maximize cross-domain leverage (already cited by many other units; deepening lifts everything downstream). Per §2 revised: Lean is optional for these; focus is prose depth and Master multi-sectioning.

Unit Title Current state Deepening brief
B1 19.03.01 Natural selection — directional/stabilizing/disruptive 3880w, no Lean, 737w Master
B2 14.04.01 Hydrogen atom quantum chemistry 3899w, has Lean (40% chapter coverage) — but Master is single section

Track C — Bio/chem new at math-style depth (2)

Unit Title Section/chapter Why this one
C1 19.02.01-extension or new ID 19.02.05 Wright-Fisher model and the diffusion approximation 19-eco-evo-bio/02-pop-genetics
C2 17.07.02 Receptor-tyrosine-kinase signaling — MAPK cascade 17-mol-cell-bio/07-signaling

Both Track C units open with full Lean + multi-section Master from line 1, not retro-fitted.

§5 Dispatch protocol

Per AGENTIC_EXECUTION_PLAN.md §11 (still authoritative): 6 agents in a single parallel-dispatch message from the top-level Claude Code session. Each gets the unit-specific brief plus the §2 math-style contract as a hard constraint.

Self-validation loop required: each agent runs python3 scripts/validate_unit.py <path> before reporting done. Parent re-validates after return (don't trust agent self-reports — see Cycle 2 retro).

Pass W dispatched after all 6 return clean.

5.1 Style-parity contract appended to every Cycle-4 dispatch brief

Hard requirements (failure = re-dispatch, not partial accept):

  1. 7-section Beginner/Intermediate template present (Intuition → Visual → Worked example → Check your understanding → Formal definition → Key theorem with proof → Exercises).
  2. For math / theoretical-physics units: Lean formalization section with non-sorry code compiling against current Mathlib. For bio / chem / applied-physics units: Lean optional — if omitted, frontmatter declares lean_status: none plus a lean_mathlib_gap rationale; if included, must formalize a substantive claim (probability lemma, ODE existence, invariance principle), not a forced abstraction.
  3. Master tier with ≥ 3 named H2 sub-sections, each substantively developed. For bio/chem this is the most important contract item — single-sub-section Master is the current style gap. Each sub-section should be a distinct advanced angle: mechanism, alternative formulation, edge case, cross-system connection.
  4. Word count ≥ 6000 for new production; ≥ 8000 for deepening. Increase goes into Master prose (and Lean if applicable), not into Beginner-tier padding.
  5. validate_unit.py returns 27/27.
  6. Concept catalog entry added if needed (overriding any "don't edit catalog" instruction — validator gate beats dispatch instruction, per Cycle-1 retro).
  7. Bio/chem/applied-physics units prefer prose-first explanation of systems; equations and Lean appear where they add explanatory force, not as decoration.

§6 What this cycle does NOT do

  • Doesn't open new chapters. The structural cleanup (§1.1) is a separate pass.
  • Doesn't run new audits. All 58 books audited.
  • Doesn't re-frame pending_approvals.md items B–T (most are obsolete; will mark in a single sweep, not item-by-item).
  • Doesn't touch the Lean compile pipeline. Lean sections per §2 must compile against current Mathlib — agents responsible for confirming.

§7 What success looks like

After Cycle 4 ships:

  • Math T1 backlog: 110 → 108 units remaining.
  • Bio Master-sub-section depth: 1 → 3+ in B1 (proof that prose-first deepening hits the contract).
  • Chem 14-genchem-pchem hydrogen: Master single-section → 4 sub-sections.
  • 2 new bio/chem units shipped at full 6000+ word depth from line 1.
  • Cycle-5 plan can scale Track B/C aggressively because the contract is proven workable.

If any of those don't land, the contract is too aggressive for bio/chem and we re-calibrate before Cycle 5 — that's the honest signal we want from this cycle.

§8 Open questions for Tyler

  1. Structural cleanup (§1.1): do it inline as part of Cycle 4 (low risk; renames + git moves), or defer to a dedicated cleanup cycle?
  2. Bio Lean content: Lean-formalize population-genetics math (PMF, expectations, allele-frequency dynamics) inside bio units, or relegate all Lean to a 19.0-formalization/ chapter that bio units cross-link to? (Recommendation: in-unit Lean. The math is part of the biology.)
  3. Track A unit A2 (φ⁴) location: open 08-stat-mech/10-qft/ (new sub-chapter, opens stat-side QFT) vs put it in 12-quantum/03-fock-spaces/ (alongside the bosonic-Fock unit already there)? (Recommendation: stat-side. φ⁴ is partition-function-centric, not operator-centric.)
  4. Cycle 4 deepening pattern as standard: should every future bio/chem dispatch require the math-style contract (§2/§5.1), or keep "stub then deepen" allowed for chapters that need fast scaffolding? (Recommendation: standard from Cycle 5 onward; Cycle 4 is the proof.)