Codex — Fast Track Coverage Roadmap
Drafted 2026-05-17. Successor to the ad-hoc batch plans
(WAVE_3_PLAN.md, WAVE_4_PLAN.md). Defines the forward push from
the current ~14% audited / ~12% unit-touched state toward Fast Track
equivalence-completeness on all 93 books.
Read alongside:
docs/catalogs/FASTTRACK_BOOKLIST.md— canonical list of 93 books.docs/plans/FASTTRACK_EQUIVALENCE_PLAN.md— what "equivalence-covered" means.manifests/production/plan.json— live state of audits and units.
§1 Where we are (snapshot, 2026-05-17)
- Total Fast Track books: 93 (4 prereq + 21 §1 + 20 §2 + 48 §3).
- Books with a plan stub in
plans/fasttrack/: 14 (prereqs Lang + Apostol I/II; §1.04 Ahlfors, §1.05 Brown, §1.05a Brown-Higgins-Sivera, §1.17 Bott-Tu, §3.21 Hartshorne, §3.35 Lawson- Michelsohn; plus four substitute/adjacent: Arnold Math Methods, Cannas da Silva Symplectic, Forster Riemann Surfaces, Hatcher Algebraic Topology). - Books with shipped Codex units (source_audits in plan.json): 11.
- Total shipped units: 313 across 9 sections (00–08).
- Books not yet audited: 79 of 93.
Coverage rate by section (rough — counts shipped-units density vs FT expectation):
| Section | FT books | Plans drafted | Units shipped | State |
|---|---|---|---|---|
| 0 Prereqs | 4 | 3 (Arnold ODE missing) | 7 (precalc) + indirect | Light coverage |
| 1 Fundamental Mechanics/Geom | 21 | 5 (Ahlfors, Brown×2, Bott-Tu, +Arnold MM substitute) | ~150 (analysis, mod-geom, symplectic) | Concentrated; gaps in physics texts (Landau Mech / Classical Fields) |
| 2 Quantum & Stat Phys | 20 | 0 | ~22 (stat-mech section only, no QM/QFT) | Empty — single largest gap |
| 3 Modern Geom / Alg Top / Foundations | 48 | 6 (Hartshorne, Lawson-Michelsohn, Hatcher substitute, Cannas substitute, Donaldson + Forster Riemann Surfaces) | ~134 (algebraic geometry, rep theory, parts of modern geometry) | Patchy — strong on alg-geom/rep-theory, weak on Milnor track, K-theory, Serre track, Penrose-Rindler |
The single most consequential gap is Section 2 (Quantum & Stat Phys): 20 books, zero plan stubs, and the stat-mech units that exist are not anchored against any specific Section 2 text.
§2 Strategy: two tracks running in parallel
A book moves through these stages:
unaudited → plan-stub (P0/P1-lite) → punch-list units written (P3) → equivalence-covered (P4)
~1 day ~3 hr/unit, 10-30 units ~1 day verification
The cost asymmetry matters. A plan stub is 1 day. A full unit set for one book is 30–90 hours of focused production. Therefore:
- Track A (cheap, fast): drive every FT book to plan-stub state. 79 books × 1 day = 79 working days of audit work. This is the coverage map. Without plan stubs we are flying blind on what units are needed.
- Track B (expensive, slow): turn shipped plan stubs into shipped units, one book at a time. This is where the actual learning content lives.
The two tracks proceed in parallel, but Track A must lead Track B by at least 5–10 books so that production has visibility into what comes next.
§3 Wave 5 — next 10 audits (Track A)
Recommended ordering for the next 10 plan stubs to write. Criteria:
- Section 2 unblock (currently 0 plans for the whole quantum section).
- Free / author-hosted PDFs (no acquisition friction).
- Prereq position (unlock downstream Codex chapters).
| # | FT entry | Book | Author | Source | Why now |
|---|---|---|---|---|---|
| 1 | 2.02 | Quantum Theory, Groups and Representations | Peter Woit | FREE (Columbia) | Section 2 gateway. Bridges rep theory (3.11/3.13) to QM. PDF in reference/fasttrack-texts/02-quantum-stat/. |
| 2 | 2.03 | QFT Lecture Notes | Sourav Chatterjee | FREE (Stanford) | Cheapest path to a Section 2 QFT plan; short, self-contained. |
| 3 | 2.01 | Quantum Mechanics: Non-Relativistic Theory | Landau, Lifshitz | BUY | Anchors all of Section 2. Companion to 2.02. |
| 4 | 2.10 | Statistical Physics 1 | Landau, Lifshitz | BUY | Anchors the existing 08-stat-mech/ units retroactively. Highest leverage in §2 because we already have ~22 stat-mech units that need a book to map against. |
| 5 | 0.4 | Ordinary Differential Equations | Vladimir Arnold | BUY | Last missing prereq stub. Closes Section 0. |
| 6 | 1.02 | Mechanics | Landau, Lifshitz | BUY | Foundational Section 1 physics text; already in books_unaudited. |
| 7 | 1.03 | Classical Theory of Fields | Landau, Lifshitz | BUY | Bridges Section 1 → Section 2 via SR/EM/GR. |
| 8 | 3.38 | A Concise Course in Algebraic Topology | J. Peter May | FREE (UChicago) | Currently substituted by Hatcher; needs canonical plan since FT explicitly chooses May. |
| 9 | 3.40 | Simplicial Objects in Algebraic Topology | J. Peter May | FREE (UChicago) | Companion to 3.38; PDF already in reference/fasttrack-texts/03-modern-geometry/. |
| 10 | 3.42 | Complex Cobordism and Stable Homotopy Groups of Spheres | Doug Ravenel | FREE (Green Book) | Master-tier connective unit between Section 3 algebraic topology and higher-categorical material. |
Wave 5 deliverable: 10 new files under plans/fasttrack/. Updates to
manifests/production/plan.json audits_done (13 → 23) and
books_unaudited (48 → 38). Section 2 coverage goes from 0/20 to 4/20
plans.
§4 Wave 6 — next 10 audits after Wave 5
Sequenced to deepen Section 2 and unblock Section 3 gateways.
| # | FT entry | Book | Author | Source | Why |
|---|---|---|---|---|---|
| 1 | 2.04–2.09 | Generalized Functions Vols 1–6 | Gel'fand, Vilenkin | BUY | Treat as one combined audit; 6 books, one plan with per-volume sections. Foundational for distributions in QM/QFT. |
| 2 | 2.17 | The Quantum Theory of Fields Vol. 1 | Weinberg | BUY | Anchors QFT. Foundations only — Vol 2/3 are later waves. |
| 3 | 3.01 | Algebra | Serge Lang | BUY | Foundational §3 text; touches half the §3 chapters. |
| 4 | 3.03 | Morse Theory | John Milnor | BUY (archives free) | Anchors 03-modern-geometry/ Morse track; pairs with our existing units. |
| 5 | 3.08 | Characteristic Classes | Milnor, Stasheff | BUY | Currently unanchored despite Codex having 06-characteristic-classes/. |
| 6 | 3.10 | K Theory | Michael Atiyah | BUY | Codex has 08-k-theory/ (3 units); needs canonical book mapping. |
| 7 | 3.11 | Representation Theory: A First Course | Fulton, Harris | BUY | Anchors 07-representation-theory/ (26 units, currently unanchored). |
| 8 | 3.18 | Foundations of Differential Geometry Vol 1 | Kobayashi, Nomizu | BUY | Anchors 02-manifolds/, 03-lie/, 05-bundles/. |
| 9 | 3.20 | Geometry of Yang-Mills Fields | Michael Atiyah | BUY | Anchors 07-gauge-theory/. |
| 10 | 3.36 | Spinors and Space-Time Vol 1 | Penrose, Rindler | BUY | Companion to shipped Lawson-Michelsohn punch-list. |
Wave 6 deliverable: 10 new files (counting Gel'fand-Vilenkin as one
combined audit). audits_done (23 → 33). Section 2 → 11/20, Section 3 →
~14/48.
§5 Waves 7–10 — finish Track A (everything else, ~10 books per wave)
After Wave 6 the remaining ~50 books split roughly:
- Wave 7: §3 Serre track (3.12, 3.13, 3.14, 3.15), Hirzebruch (3.25, 3.26), Voisin (3.27), Helgason (3.17), Kobayashi-Nomizu Vol 2 (3.19).
- Wave 8: §3 moduli/geometry of curves (3.22, 3.30, 3.31, 3.32, 3.33), Penrose-Rindler Vol 2 (3.37), May-Ponto (3.39), Goerss-Jardine (3.41).
- Wave 9: §3 endgame (3.43 Deligne et al, 3.44 DeWitt, 3.45 Gérard, 3.47 Brylinski, 3.48 Besse) + §2 endgame (2.11 Souriau, 2.12 Baxter, 2.13/2.14 Itzykson-Drouffe, 2.20 Landau QED).
- Wave 10: §1 residual (1.06 Ahlfors-Sario, 1.08/1.09 Mackenzie ×2, 1.10/1.14/1.15 Sternberg ×3, 1.11 Arnold-Dubrovin Symplectic, 1.12 Arnold Hydrodynamics, 1.13 Whitney, 1.18 Shifrin, 1.19 Griffiths-Morgan, 1.20 D. Arnold FEEC).
Total Track A budget: 79 audits ÷ 10 per wave = 8 waves at ~1 working
week per wave = ~2 working months sustained, or ~4 months at half-pace.
End state: 93/93 plan stubs in plans/fasttrack/, full picture of what
production must produce.
§6 Track B — production scheduling
Once Track A is N books ahead, production proceeds book-by-book according to the priority-1 punch-lists in each plan stub. The natural production order (driven by prereq DAG, not by FT numbering) is:
- Brown 1.05 priority-1 (7 units, ~21 hr). Unblocks Brown 1.05a NAT
and most of
03.12-homotopy/. - Brown 1.05a priority-1 (5 units, ~17 hr). Higher-dim algebraic topology. Depends on (1).
- Bott-Tu priority-1 (punch-list count 0 — already shipped). Skip.
- Hartshorne priority-1 (12 units). Codex already has 37 alg-geom units; Hartshorne audit identified specific gaps.
- Apostol Vol I + Vol II priority-1 (18+13 units). Anchors §0 prereqs.
- Lang Basic Math priority-1 (22 units). Anchors §0.1.
- Wave 5 audits' priority-1 sets (Woit, Chatterjee, Landau ×3, Arnold ODE, May ×2, Ravenel) — Track B unlocks once their stubs ship.
Sustained pace. With one operator weaving + one production agent shipping ~2 units per day, Track B clears ~50 units per week. The full ~1500 units needed for FT equivalence (≈ 16 units per book × 93 books, minus overlap) clears in ~30 weeks of sustained work, or ~14–18 months at realistic 50% capacity.
§7 Milestones and acceptance
- M1 (end of Wave 5): Section 2 has 4 plan stubs; total stubs 24/93 (26%).
- M2 (end of Wave 6): Total stubs 34/93 (37%). Every Codex section (07, 08 especially) has an anchoring §2 or §3 book audited.
- M3 (end of Wave 10): All 93 books plan-stubbed. This is the coverage-map milestone — from here, every unit Codex produces can be justified by exactly which FT punch-list line it closes.
- M4 (Track B at 50%): Half of the priority-1 punch-list units across the corpus shipped. Estimated mid-2027 at sustained pace.
- M5 (equivalence-complete): All books at ≥95% theorem-layer coverage
per
FASTTRACK_EQUIVALENCE_PLAN.md§3.4. Estimated late-2027 to mid-2028.
§8 Risks and mitigations
| Risk | Mitigation |
|---|---|
| Track A audits drift away from FT canonical books and become substitute-text studies (as happened with Cannas, Forster, Hatcher). | Each plan stub must declare its FT entry # in the title line. The 4 existing substitute-text plans should be renamed to mark them as deepenings, and a canonical plan for the FT-listed book should still be written. |
| Section 2 punch-lists are massive (physics texts have hundreds of named results). | Treat each Section 2 book as a multi-wave production target. Don't try to ship a Landau-Lifshitz priority-1 set in one batch. |
| Sourcing friction on BUY-only books (most of §1/§2 physics texts, all of §3 endgame). | Wave 5 deliberately prioritizes FREE texts. Resolve BUY sourcing in parallel — library access, used-book acquisition — so it doesn't block Wave 6+ audits. |
| Plan-stub format drift across batches. | All plan stubs follow the brown-topology-and-groupoids.md template (§1 What the book is for / §2 Coverage table / §3 Punch-list / §4 Implementation / §5 What this plan does NOT cover / §6 Acceptance criteria). The Brown-Higgins-Sivera plan added 2026-05-17 is the most recent reference template. |
§9 Next concrete action
Pick a Wave 5 book and ship its plan stub:
- Lowest friction: §2.03 Chatterjee QFT — free PDF already in
reference/fasttrack-texts/02-quantum-stat/, short text, opens Section 2. - Highest leverage: §2.10 Landau Stat Phys 1 — retroactively anchors the existing 22 stat-mech units, instantly closes coverage on one whole Codex section.
Recommendation: ship Chatterjee first (lowest cost to validate the Wave 5 cadence), then Landau Stat Phys 1 second (highest leverage once cadence is proven).