Codex — Fast Track Equivalence Plan

A scaffold-of-scaffolds. Specifies how Codex achieves equivalent information transfer with every book on the Fast Track booklist — not just topic overlap, but full pedagogical equivalence: a Codex reader should be able to do everything a Fast Track reader could do without ever opening the book.

This document does not produce curriculum content directly. It produces the system by which curriculum content for each Fast Track book is planned, scaffolded, and verified — so that the work can be tackled agentically across the 72-book corpus.

Read alongside docs/catalogs/FASTTRACK_BOOKLIST.md, docs/plans/CURRICULUM_V0_5_PLAN.md, docs/plans/V05_SUPPORTING_UNITS_PLAN.md, docs/specs/QUALITY_RUBRIC.md, docs/specs/UNIT_SPEC.md.

---

1. Mission statement

For every book B on the Fast Track, produce a subset C(B) of Codex units such that a learner who completes C(B) — at the appropriate tier — has equivalent operational ability to a learner who completed B itself: they can state and prove the book's theorems, solve the book's exercises, recognize the book's notation, apply the book's tools to new problems, and possess the conceptual map the author intended to convey.

The metric is not "what fraction of B's topics appear in Codex." That metric is too coarse. The metric is: can a Codex reader pick up where a B reader leaves off, inside B's native subject and adjacent ones, without surprises?

If the answer is yes, B is equivalence-covered. The Fast Track is equivalence-complete when all 72 books are equivalence-covered.

---

2. The layered equivalence model

A book transfers information at seven distinct layers. Equivalence requires capturing all seven. Most "online curriculum" projects only cover layers 1 and 6 (the named theorems and a softened intuition); they fail on the rest. Codex must cover all seven explicitly.

#	Layer	What the book transfers	How Codex captures it	Equivalence test
1	Theorem layer	Every named theorem, proposition, lemma, definition	Each ≥1 Codex unit at Intermediate or Master tier	Reader can state and prove every theorem in the book's TOC
2	Exercise layer	Each numbered exercise, with the difficulty and the role it plays in later proofs	Codex unit's ## Exercises [Intermediate+] block + inline answers	Reader can solve every exercise in the book using only Codex content
3	Worked-example layer	Concrete computations the author works through	Codex ## Worked example [Beginner] or inline computations in Intermediate	Reader can reproduce every concrete computation the book performs
4	Notation layer	The author's notation conventions, often distinctive	Per-book notation crosswalk in notation/<book>.md; mentions in unit Master sections	Reader can read any subsequent paper that uses the book's notation
5	Sequencing layer	What the author builds in chapter k and uses in chapter k+n	Codex DAG (manifests/deps.json) reflects the book's prerequisite chain	Reader can traverse the same prerequisite path Codex provides
6	Intuition layer	Prose-level insights that justify why the math is the right math, not just correct math	Codex ## Intuition [Beginner] and Master ## Historical & philosophical context sections	Reader can explain why a definition takes the form it does, not just what it is
7	Application layer	The book's worked applications, examples beyond the core theory	Codex Master ## Connections sections and dedicated application units	Reader can apply the theory to the same problems the book applies it to

Equivalence is reached when all seven layers are demonstrably captured, per book, per chapter.

---

3. The per-book plan template

Every book B gets exactly one planning document at plans/fasttrack/<book-slug>.md, structured as follows. The template is rigid so coverage can be tracked uniformly.

# <Book-slug> — Fast Track Equivalence Plan

**Book:** <Author>, *<Title>* (<Year>)
**Fast Track entry:** <booklist#>
**Pages:** <count> · **Chapters:** <count> · **Exercises:** <count>
**Subject:** <primary subject area>
**Strand assignment:** <one of A/B/C/D/E/F/...>
**Plan status:** <draft|audited|gap-analysed|production|verified|equivalence-covered>

---

## §1. Book audit

### 1.1 Table of contents
[Chapter and section breakdown — every section listed]

### 1.2 Theorem inventory
[Every named theorem/proposition/lemma/definition with chapter location]

### 1.3 Exercise inventory
[Every exercise with chapter location, difficulty estimate, role:
 "load-bearing" (used in later proofs), "applied" (concrete computation),
 "extension" (open-ended exploration)]

### 1.4 Worked-example inventory
[Every worked example with chapter location and what it illustrates]

### 1.5 Notation conventions
[Distinctive notation, reading conventions, sign conventions]

### 1.6 Sequencing graph
[Chapter dependency arrows — "Ch 4 uses Ch 2 §3 and Ch 3"]

### 1.7 Author's distinctive perspective
[What this book offers that peer texts don't — what makes Fast Track include it]

---

## §2. Codex coverage diff

### 2.1 Theorem coverage
[Table: book theorem → Codex unit (or "GAP")]

### 2.2 Exercise coverage
[Table: book exercise → Codex exercise location (or "GAP")]

### 2.3 Worked-example coverage
[Table: book example → Codex location (or "GAP")]

### 2.4 Notation coverage
[Crosswalk: book notation → Codex notation]

### 2.5 Sequencing coverage
[Codex DAG paths matching book's chapter dependencies]

### 2.6 Intuition coverage
[Per chapter: is the book's framing captured in some Codex Beginner/Master section?]

### 2.7 Application coverage
[Per book application: is it covered in a Codex Connections or applied unit?]

### 2.8 Coverage scorecard
| Layer | Captured | Total | % | Status |
|---|---|---|---|---|
| Theorems | xx | yy | nn% | ✓/△/✗ |
| Exercises | xx | yy | nn% | ✓/△/✗ |
| ... |

---

## §3. Production plan

### 3.1 New units to produce
[List of new Codex unit IDs, titles, parent strand, prerequisites, originator/anchor]

### 3.2 Existing units to deepen
[For each existing unit: what theorems, exercises, examples to add]

### 3.3 Exercise packs
[For exercises that don't fit cleanly into existing units' exercise sections,
 produce per-chapter exercise-collection units]

### 3.4 Notation crosswalk file
[Path to `notation/<book>.md` with the conventions captured]

### 3.5 DAG edges to add
[New `prerequisites` arrows in deps.json reflecting book sequencing]

### 3.6 Agent decomposition
[Production split among parallel agents — typically 2–6 agents per book]

---

## §4. Equivalence verification

### 4.1 Book-as-input self-check
[A test: present the book's TOC to an evaluator agent;
 ask "is everything there in Codex?"; require yes per layer]

### 4.2 Exercise reproducibility check
[Sample 10% of book exercises; verify a reader using only Codex
 can solve them]

### 4.3 Notation comprehension check
[Sample passages of the book; verify Codex reader can parse the notation]

### 4.4 Equivalence sign-off
[Plan transitions to status `equivalence-covered` when 4.1, 4.2, 4.3 all pass]

This template is a contract. Every book gets one. Coverage is tracked uniformly across all 72 books.

---

4. Agent orchestration — how each per-book plan is produced

Each book takes 5 distinct agent passes, in dependency order. Within a pass, agents on different books run in parallel; across passes, work is serial per book.

Pass 1 — Audit agent (one per book, parallel-safe)

Input: Book identity (author, title, year, ISBN, Fast Track entry). Tools: WebSearch, WebFetch (for TOCs, reviews, syllabus pages, MathOverflow discussions, Wikipedia, Goodreads of academic books, university course pages that use the book). Task: Produce §1 of the per-book plan: TOC, theorem inventory, exercise inventory, worked-example inventory, notation, sequencing, distinctive perspective. Output: plans/fasttrack/<book-slug>.md with §1 filled in; status audited.

Agent prompt template:

You are auditing the book