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audit_completeness: reduced audit_basis: "Public TOC + nLab + author page (mu.html) + Wikipedia + citation network. Full PDF (~4MB) was attempted via WebFetch twice and timed out at 60s on both author-host mirrors. Reduced-audit protocol per AGENTIC_EXECUTION_PLAN.md §6.6. Theorem inventory in §1.1 built from author's preface, nLab section index, AMS Chelsea TOC, and Hopkins/Lurie/Hovey lecture notes that mirror Ravenel's structure."

Doug Ravenel — Complex Cobordism and Stable Homotopy Groups of Spheres (Fast Track 3.42) — Audit + Gap Plan

Book: Douglas C. Ravenel, Complex Cobordism and Stable Homotopy Groups of Spheres. First edition: Academic Press 1986 (out of print). Second edition: AMS Chelsea Publishing 2003, AMS/Chelsea volume 347, xx + 395 pp. Known universally as the "Green Book" after the cover of the first edition (the AMS Chelsea reprint is dark red but the nickname persists). Author-hosted hyperlinked PDF: https://people.math.rochester.edu/faculty/doug/mybooks/ravenel.pdf (also mirrored at the Edinburgh papers archive).

Fast Track entry: 3.42. Listed in docs/catalogs/FASTTRACK_BOOKLIST.md as a FREE author-hosted text; canonical reference for chromatic / stable homotopy theory.

Purpose of this plan: P1 audit stub (reduced — see frontmatter) and gap punch-list against the current Codex corpus. Ravenel is the most technically demanding entry in the Fast Track. It sits above May Concise (3.38), May Simplicial Objects (3.40), Adams Stable Homotopy and Generalised Homology, and Switzer Algebraic Topology. The honest assessment recorded in this plan is that a meaningful punch-list against Ravenel is dominated by Priority-0 prerequisite gaps: the units Ravenel builds on (Adams spectral sequence machinery, formal group laws, MU and BP, the cobar complex) do not yet exist in the Codex, and writing them is itself a multi-wave production project. Treating Ravenel as a one-wave target is not credible.

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§1 What the Green Book is for

Ravenel's Complex Cobordism and Stable Homotopy Groups of Spheres is the definitive computational reference for the chromatic programme in stable homotopy theory and the canonical exposition of the Adams-Novikov spectral sequence (ANSS). Its three explicit purposes, per the preface, are (i) to make BP-theory and the ANSS accessible to non-experts, (ii) to serve as a reference for working chromatic homotopy theorists, and (iii) to demonstrate the computational potential of these tools through actual calculations of ${\pi }_{\ast }^s(S^0)$ at low primes.

Distinctive contributions, ordered as the book develops them:

1. A unified treatment of the classical Adams spectral sequence (mod-$p$ Steenrod) and the Adams-Novikov spectral sequence (based on $MU$ or $BP$). The Green Book is the first textbook-length treatment that pursues both side by side as competing computational engines. Adams's own Stable Homotopy and Generalised Homology (1974) introduces the generalised setup; Ravenel pushes it through to actual stable-stem computations.
2. The chromatic spectral sequence (CSS). Filters the $E_2$-page of the ANSS by height of the underlying formal group law, separating ${\pi }_{\ast }^s$ into chromatic layers detected by the Morava $K$-theories $K(n)$. This is the book's signature construction (Chapter 5), originating in Miller-Ravenel-Wilson 1977 Annals and consolidated here.
3. Brown-Peterson cohomology $BP$ and the $p$-local refinement of $MU$. Quillen's idempotent $ϵ:M{U}_{(p)}\to M{U}_{(p)}$ splits off the Brown-Peterson summand $BP$, whose coefficient ring $B{P}_{\ast }={\mathbb{Z}}_{(p)}[v_1,v_2,\dots ]$ classifies $p$-typical formal group laws. Chapter 4 develops $BP$, $B{P}_{\ast }BP$, and the cobar complex used for ANSS $E_2$ computations.
4. Morava stabiliser algebras and the change-of-rings theorem. Chapter 6 identifies the $E_2$-page of the $n$-th chromatic layer with the continuous cohomology of the Morava stabiliser group ${\mathbb{S}}_n$ (the automorphism group of a height-$n$ formal group law) acting on the Lubin-Tate ring. This is the bridge from homotopy theory to $p$-adic Lie theory and arithmetic geometry of formal groups.
5. Greek-letter elements. The systematic naming convention for ANSS $E_2$ classes — ${\alpha }_t,{\beta }_s,{\gamma }_r,\dots$ — indexed by chromatic level, that survive to detect non-trivial families in the stable stems. Ravenel-Wilson 1980s. The Green Book is the canonical place to learn the bookkeeping.
6. Explicit low-prime tables. Chapter 7 carries out the ANSS computation through dozens of stems at $p=3$ and $p=5$; Appendix A3 tabulates ${\pi }_{\ast }^s(S^0)$. The book is built around the conviction that the chromatic / ANSS machine actually computes.
7. The two appendices that are reference manuals in their own right. Appendix A1 is the standard textbook account of Hopf algebras and Hopf algebroids (the right algebraic structure for $E_{\ast }E$ when $E$ is not commutative on the nose). Appendix A2 is one of the standard references for formal group laws (Lazard's theorem, the Lazard ring $L$, height, the Honda formal group, $p$-typicality), tied throughout to the homotopy-theoretic origin.

The book is not a first text on algebraic topology and does not pretend to be. Prerequisites: (i) classical algebraic topology through the level of Hatcher and May Concise (CW complexes, singular homology, Serre spectral sequence); (ii) basic stable homotopy theory through the level of Adams Stable Homotopy Part III or Switzer Chapter 13 (spectra, generalised homology, smash product, the stable category); (iii) homological algebra through derived functors and Ext over graded rings; (iv) some willingness to compute in the cobar complex.

Peer sources consulted in building this audit (≥3 required):

• J. F. Adams, Stable Homotopy and Generalised Homology (Chicago Lectures in Mathematics, 1974). The book Ravenel is the direct sequel to — introduces generalised cohomology and the generalised Adams spectral sequence; Ravenel takes it further into $MU$/$BP$ specifically.
• R. Switzer, Algebraic Topology — Homotopy and Homology (Springer 1975). The standard textbook one rung below Ravenel — covers spectra, the classical Adams SS, $K$-theory, and cobordism without going into the chromatic decomposition.
• M. Hovey, Model Categories (AMS 1999), and follow-up notes vn-elements in ring spectra and applications to bordism theory — the modern model-categorical framing of the stable category that the Green Book pre-dates but is now read alongside.
• J. Lurie, Chromatic Homotopy Theory (course notes, 2010, https://www.math.ias.edu/~lurie/252x.html). The standard modern re-presentation of Ravenel's content using the language of formal groups, stacks, and ∞-categories. Often cited as the readable companion.
• P. Goerss & H. Miller, expository notes on the chromatic spectral sequence and Morava stabiliser groups (multiple AMS proceedings articles).
• nLab entry "Complex cobordism and stable homotopy groups of spheres" (https://ncatlab.org/nlab/show/Complex+cobordism+and+stable+homotopy+groups+of+spheres), consulted for chapter-by-chapter section index given the full-PDF fetch failure.

§1.1 Theorem and construction inventory (reduced — TOC-level)

Reconstructed from the public TOC, nLab section index, and citation network. Section-level granularity, not theorem-numbered. Full theorem-numbered inventory deferred to a re-audit pass with the PDF in hand — queued in NEED_TO_SOURCE.md.

Chapter 1 — Introduction to the homotopy groups of spheres.

• Classical theorems of stable homotopy: Hurewicz, Freudenthal suspension, Serre finiteness, Nishida's nilpotence theorem (1973), Bott periodicity, Hopf-invariant-one (Adams 1960).
• The Adams-Novikov $E_2$-term: first sight.
• Formal group laws on first contact; the Greek-letter construction ($\alpha$, $\beta$, $\gamma$ family bookkeeping).
• Morava's viewpoint and an informal first pass at the chromatic SS.
• EHP spectral sequence (unstable shadow; included as a contrast to ANSS).

Chapter 2 — Setting up the Adams spectral sequence.

• Classical mod-$p$ Adams SS construction via the canonical Adams resolution.
• Generalised Adams SS based on a homology theory $E_{\ast }$.
• Smash-product pairing on the spectral sequence; the generalised connecting homomorphism; convergence statement.

Chapter 3 — The classical Adams spectral sequence.

• Steenrod algebra ${\mathcal{A}}_p$ and Milnor's structure theorem.
• May spectral sequence (computational tool for ${\mathrm{Ext}}_{{\mathcal{A}}_p}$).
• Lambda algebra and the cobar / lambda comparison.
• General properties of Ext over a Hopf algebra.
• Survey of further reading (Bruner-May-Milgram-Steinberger, Mahowald).

Chapter 4 — BP-theory and the Adams-Novikov spectral sequence.

• Quillen's theorem: ${\pi }_{\ast }(MU)=L$ (the Lazard ring), and the universal formal group law on $MU$.
• Quillen idempotent splitting $M{U}_{(p)}=\bigvee BP$; construction of $BP$.
• Structure of $B{P}_{\ast }BP$ as a Hopf algebroid; the right unit ${\eta }_R$ and the $v_n$.
• Calculations in the cobar complex $C^{\ast }(B{P}_{\ast }BP)$.
• Beginning ANSS computations: ${\mathrm{Ext}}^0$, ${\mathrm{Ext}}^1$, the image of $J$.

Chapter 5 — The chromatic spectral sequence.

• Algebraic construction: filter $B{P}_{\ast }/I_n$-modules by $v_n$-divisibility; derive the chromatic SS converging to ANSS $E_2$.
• ${\mathrm{Ext}}^1(B{P}_{\ast }/I_n)$ and the Hopf-invariant-one re-derivation.
• $\mathrm{Ext}(M^1)$ and the $J$-homomorphism image.
• ${\mathrm{Ext}}^2$ and the Thom reduction map.
• Periodic families: $\alpha$-family, $\beta$-family detection.
• Elements in ${\mathrm{Ext}}^3$ and beyond.

Chapter 6 — Morava stabiliser algebras.

• Change-of-rings isomorphism (Morava): the $n$-th chromatic $\mathrm{Ext}$-piece is continuous cohomology of ${\mathbb{S}}_n$ acting on the Lubin-Tate ring.
• Structure of the Morava stabiliser group $\Sigma (n)={\mathbb{S}}_n$ (the units of the endomorphism ring of the height-$n$ Honda FGL).
• Cohomology of $\Sigma (n)$ at small heights.
• Odd-primary Kervaire-invariant elements (the ${\beta }_{p^i/p^i}$ family).
• Telescopes / spectra $T(m)$ and the telescope conjecture (statement).

Chapter 7 — Computing stable homotopy groups via the ANSS.

• ${\pi }_{\ast }^s(S^0)$ at $p=3$: explicit computation through ~${\pi }_{100}^s$.
• ${\pi }_{\ast }^s(S^0)$ at $p=5$.
• Differentials in the ANSS; comparison to the classical Adams SS.

Appendix A1 — Hopf algebras and Hopf algebroids.

• Hopf algebra over a field; Milnor-Moore structure theorems.
• Hopf algebroid (Haynes-Miller / Ravenel formalisation): $(A,\Gamma )$ with left and right units; the cobar complex $C^{\ast }(A,\Gamma ;M)$.
• Comodule algebra structure on $E_{\ast }E$ for a homotopy commutative ring spectrum $E$.

Appendix A2 — Formal group laws.

• Definition of a (one-dimensional commutative) formal group law over a commutative ring.
• Lazard's theorem: the universal FGL is defined over a polynomial ring $L=\mathbb{Z}[x_1,x_2,\dots ]$.
• Height of a FGL over an ${\mathbb{F}}_p$-algebra; the Honda FGL of height $n$.
• $p$-typical formal group laws; the Cartier idempotent.
• Lubin-Tate deformation theory; the universal deformation ring.

Appendix A3 — Tables of ${\pi }_{\ast }^s(S^0)$.

• Tables compiled from the ANSS through ~stem 60 at $p=2$ and higher ranges at $p=3$, $5$.

§1.2 Exercise inventory

Omitted under the reduced-audit protocol — exercises inventoried after sourcing. The Green Book carries roughly 10–20 exercises per chapter, many of them computational (cobar-complex calculations). Re-audit upgrade queued in NEED_TO_SOURCE.md.

§1.3 Worked examples (sample-level)

From the public TOC and nLab:

• Computation of ${\pi }_{\ast }^s(S^0)$ at $p=3$ through ~stem 100 (Ch. 7) — the headline calculation of the book.
• Hopf-invariant-one theorem re-derived from ${\mathrm{Ext}}^1$ of the chromatic CSS (Ch. 5).
• $J$-homomorphism image re-derived chromatically (Ch. 5).
• Greek-letter family detection: ${\alpha }_t$, ${\beta }_s$, ${\gamma }_r$ classes through low chromatic levels.

§1.7 Distinctive perspective

What Ravenel does that no other text does (and that any equivalence-coverage plan must replicate, not merely paraphrase):

• Holds Adams SS and Adams-Novikov SS side by side and computes both. Adams 1974 only does the generalised setup; Switzer only does the classical SS; Hovey/Lurie do the formal-group side cleanly but not the exhaustive low-prime tables. Only Ravenel ties them together computationally.
• Treats the chromatic SS as a first-class object rather than a conceptual organising principle. This is the book's structural signature.
• Carries the cobar complex through to actual numerical answers. Most modern presentations (Lurie's chromatic notes, Hovey's notes) stop at the formal-group-law / stack level and gesture at the cobar; Ravenel computes.
• Hopf algebroids before they were standardised. Appendix A1 is the reference Hopf-algebroid account for an entire generation of homotopy theorists.

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§2 Coverage table (Codex vs Ravenel)

Cross-referenced against the current 313-unit corpus. ✓ = covered, △ = partial / different framing or in passing only, ✗ = not covered.

Ravenel topic	Codex unit(s)	Status	Note
Spectrum, stable homotopy category	03.12.04-spectrum, 03.08.06-stable-homotopy	△	Definitional unit and stable-category overview exist; Ravenel-level computational use is not exercised.
Generalised cohomology theory; Brown representability	03.12.15-eilenberg-steenrod (one section)	△	Pointer only.
Sphere spectrum $\mathbb{S}$, ${\pi }_{\ast }^s$	03.12.04-spectrum, 03.08.06-stable-homotopy	△	Defined; no calculation.
Eilenberg-MacLane spectra $HA$, $H{\mathbb{F}}_p$	03.12.05-eilenberg-maclane, 03.12.04-spectrum	✓	Standard coverage.
K-theory spectra $\mathbf{KU},\mathbf{KO}$	03.08.01-topological-k-theory, 03.08.07-bott-periodicity	✓	Covered at FT-equivalence level for K-theory book.
Thom spectra $MO$, $MSO$	03.06.03-stiefel-whitney (one paragraph)	△	Mentioned; no dedicated unit. Gap.
Thom spectrum $MU$ (complex bordism)	03.12.04-spectrum (one line)	✗	Named only. Gap — load-bearing for everything else in Ravenel.
Brown-Peterson spectrum $BP$	—	✗	Gap.
Steenrod algebra ${\mathcal{A}}_p$; Milnor structure theorem	—	✗	Gap (foundational).
Classical Adams spectral sequence	03.13.01-spectral-sequence (one paragraph), 03.12.04-spectrum (one paragraph)	✗	Named with formula only. Gap.
Adams resolution; cobar complex; canonical Adams tower	—	✗	Gap.
May spectral sequence	—	✗	Gap.
Lambda algebra	—	✗	Gap.
Generalised Adams SS (Adams-Novikov, $MU$- and $BP$-based)	—	✗	Gap.
Formal group law; Lazard ring; Lazard's theorem	—	✗	Gap (foundational — also load-bearing for Lurie's Chromatic Homotopy).
Height of a FGL; Honda FGLs	—	✗	Gap.
Quillen's theorem ${\pi }_{\ast }(MU)=L$	—	✗	Gap (one of the great theorems of 20th-century topology).
$p$-typicality; Cartier idempotent; Quillen idempotent	—	✗	Gap.
Hopf algebroid; cobar complex $C^{\ast }(A,\Gamma ;M)$	—	✗	Gap.
$B{P}_{\ast }BP$ structure	—	✗	Gap.
Morava K-theory $K(n)$; $E(n)$; Johnson-Wilson	03.12.04-spectrum (one paragraph, conceptual only)	△	Pointer to the chromatic story exists; no unit. Gap.
Morava stabiliser group ${\mathbb{S}}_n$; Lubin-Tate / Morava $E$-theory	—	✗	Gap.
Chromatic spectral sequence; chromatic tower; chromatic convergence	03.12.04-spectrum (informal paragraph)	△	Pointer; no construction. Gap.
Greek-letter elements ($\alpha$-family, $\beta$-family)	—	✗	Gap.
Hopf-invariant-one theorem (Adams 1960)	03.12.07-whitehead-tower (one line)	△	Referenced; no proof unit. Gap (also a target for Adams' own book).
Image of $J$ ($J$-homomorphism)	—	✗	Gap.
Nishida nilpotence theorem	—	✗	Gap.
Hopkins-Smith nilpotence and periodicity theorems	—	✗	Gap.
Telescope conjecture (statement)	—	✗	Gap (note: now known to be false at $n\ge 2$ by Burklund-Hahn-Levy-Schlank-Yuan 2023, but Ravenel posed it).
Tables of ${\pi }_{\ast }^s(S^0)$	—	✗	Not a unit-shaped object; absorb as appendix to a Ravenel-level survey unit if and when shipped.

Aggregate coverage estimate: ~3% of Ravenel's named content has any Codex unit, and 0% of his load-bearing technical apparatus (Adams SS, $MU$, $BP$, formal group laws, chromatic SS) has a dedicated unit. The chromatic perspective exists in the corpus only as a one-paragraph forward-pointer inside 03.12.04-spectrum.

This is unsurprising. Ravenel is a research monograph in chromatic homotopy theory; the Codex currently has elementary algebraic topology through the Hatcher / Bott-Tu level and a beginning of stable homotopy. The gap is structural.

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§3 Gap punch-list (P0 / P1 / P2 / P3 / P4 — units to write,

priority-ordered)

This punch-list is honest about the prerequisite structure: most named gaps are blocked on prior units that themselves need to be written. The convention used: P0 = prerequisite, must ship before a Ravenel unit can be written; P1 = Ravenel's central content, write once P0 is in place; P2/P3/P4 = deepenings.

P0 — Prerequisites blocking every Ravenel P1 unit

These are not Ravenel's content; they are the infrastructure without which a Ravenel unit cannot be written. Several are shared with other Fast Track entries (Adams Stable Homotopy, May Concise).

1. Steenrod algebra ${\mathcal{A}}_p$ — definition, action on $H^*(X; \mathbb{F}_p)$, Adem relations, Milnor structure theorem. Shared prereq with Hatcher §4.L, Switzer §17. Estimate: 1 unit, Master tier primary, ~3h.
2. Generalised cohomology theory and Brown representability — theorem-grade statement. Shared with Adams 1974, Switzer §9. Estimate: 1 unit, ~2h.
3. Thom spectrum $MU$ and complex cobordism — definition via the Thom-Milnor construction, $M{U}_n=\mathrm{Th}({\gamma }_n^{\mathbb{C}})$, ring structure, low-degree computation. Required for everything downstream. Estimate: 1 unit, ~3h.
4. Formal group law — definition, examples (additive, multiplicative, Lubin-Tate), Lazard ring, Lazard's theorem (statement; proof deferred to master tier). Foundational. Estimate: 1 unit, ~3h.
5. Height of a formal group law; Honda formal group; $p$-typicality; Cartier idempotent. Estimate: 1 unit, ~2.5h.
6. Quillen's theorem ${\pi }_{\ast }(MU)=L$. Theorem statement and the modern proof outline. Estimate: 1 unit, ~3h, with Master tier carrying Quillen 1969 originator prose.
7. Hopf algebroid — definition, cobar complex, $\mathrm{Ext}$ computed via the cobar. Reference-grade unit; Appendix A1 of Ravenel is the canonical source. Estimate: 1 unit, ~2.5h.

P0 total: 7 units, ~19 hours. Wave-sized: 2 production waves.

P1 — Ravenel's central content (unblocks once P0 lands)

8. Classical Adams spectral sequence. Construction via the canonical Adams resolution; $E_2 = \mathrm{Ext}_{\mathcal{A}_p}(\mathbb{F}_p, \mathbb{F}p)$;convergenceto$\pi*^s(S^0)_p^\wedge$; first computation through ~stem 14. Shared with Adams 1974 and Switzer §19. Estimate: 1 unit, ~4h, Master tier essential.
9. Generalised Adams spectral sequence (Adams-Novikov). Based on a homotopy commutative ring spectrum $E$; the $E$-based Adams resolution; $E_2={\mathrm{Ext}}_{E_{\ast }E}(E_{\ast },E_{\ast }X)$. Specialise to $E=MU$ to obtain the ANSS. Estimate: 1 unit, ~4h.
10. Brown-Peterson spectrum $BP$ and the structure of $B{P}_{\ast }BP$.* Quillen-idempotent splitting; $BP_ = \mathbb{Z}{(p)}[v_1, v_2, \ldots]$;Hopf-algebroidstructureon$BP*BP$. Estimate: 1 unit, ~3.5h.
11. Chromatic spectral sequence. Algebraic construction via $v_n$-filtration on $B{P}_{\ast }/I_n$-modules; convergence to the ANSS $E_2$-page; chromatic tower of localisations $L_n\mathbb{S}$. Ravenel's signature construction; this unit is the Green Book's centre of gravity. Estimate: 1 unit, ~4h, Master-essential.
12. Morava K-theory $K(n)$ and Morava E-theory $E_n$. Definition; coefficient rings $K(n{)}_{\ast }={\mathbb{F}}_p[v_n^{\pm 1}]$, $E_n^{\ast }=W({\mathbb{F}}_{p^n})[[u_1,\dots ,u_{n-1}]][u^{\pm 1}]$; detection of chromatic layer $n$. Estimate: 1 unit, ~3.5h.
13. Morava stabiliser group ${\mathbb{S}}_n$ and the change-of-rings theorem. Identifies the $n$-th chromatic $E_2$ with continuous cohomology of ${\mathbb{S}}_n$ on the Lubin-Tate ring. Estimate: 1 unit, ~3.5h, Master-essential.

P1 total: 6 units, ~22.5 hours. Wave-sized: 2 production waves.

P2 — Adams-side machinery and Greek-letter bookkeeping

14. May spectral sequence. Computes ${\mathrm{Ext}}_{{\mathcal{A}}_p}$ via a filtration. Estimate: 1 unit, ~3h.
15. Lambda algebra. Alternative model for ${\mathrm{Ext}}_{{\mathcal{A}}_p}$. Estimate: 1 unit, ~2.5h, Master-only.
16. Greek-letter elements — $\alpha$, $\beta$, $\gamma$ families. Naming convention; chromatic origin; detection in ${\pi }_{\ast }^s$. Estimate: 1 unit, ~3h.
17. Image of $J$. Adams's calculation; ANSS re-derivation. Estimate: 1 unit, ~3h.

P2 total: 4 units, ~11.5 hours.

P3 — Nilpotence, periodicity, and chromatic structural theorems

18. Nishida nilpotence theorem. ${\pi }_{\ast }^s$-degree-positive elements are nilpotent. Estimate: 1 unit, ~2h.
19. Hopkins-Smith nilpotence theorem. $MU$-detection of nilpotence in finite $p$-local spectra. Estimate: 1 unit, ~3h.
20. Hopkins-Smith periodicity theorem. Existence and uniqueness of $v_n$-self-maps on type-$n$ spectra. Estimate: 1 unit, ~3h.
21. Telescope conjecture (statement, history, and 2023 resolution). State Ravenel's original telescope conjecture; note the Burklund-Hahn-Levy-Schlank-Yuan 2023 disproof at heights $\ge 2$. Estimate: 1 unit, ~2h.

P3 total: 4 units, ~10 hours.

P4 — Survey / pointer units (Master-tier only)

22. Worked computation of ${\pi }_{\ast }^s(S^0)$ at $p=3$ through low stems. Reference unit anchored to Ravenel Chapter 7. Estimate: 1 unit, ~4h (heavily diagrammatic; high production cost).
23. Pointer to the modern chromatic programme. Goerss-Hopkins-Miller, topological modular forms, Devinatz-Hopkins-Smith. Master-tier survey, no proofs. Estimate: 1 unit, ~2h.

P4 total: 2 units, ~6 hours.

Punch-list summary

Priority	Unit count	Hours	Blocked?
P0	7	19	No (write directly)
P1	6	22.5	Blocked by P0
P2	4	11.5	Blocked by P0+P1
P3	4	10	Blocked by P0+P1
P4	2	6	Blocked by P0+P1+P3
Total	23	~69h	—

This is the largest punch-list of any Fast Track audit completed to date. The reason is that Ravenel sits at the top of a tower of prerequisites none of which are currently in the Codex. The punch-list is not padded: every entry is named in Ravenel's TOC and is load-bearing.

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§4 Implementation sketch

Sequencing. P0 must ship first, in two waves:

• P0 Wave A: Items 1, 2, 3 (Steenrod algebra, Brown representability, $MU$). ~8 hours. Unblocks Item 8 (classical Adams SS).
• P0 Wave B: Items 4, 5, 6, 7 (formal group laws, height, Quillen's theorem, Hopf algebroids). ~11 hours. Unblocks all remaining P1.

Then P1 in two more waves, then P2/P3 in parallel.

Realistic full-coverage timeline: ~69 hours of focused production. At the corpus's sustained production rate (3–4 units per agent-day, ~3h each) this is a 6–8 week project running a dedicated stable-homotopy sub-pipeline. Ravenel cannot be closed in a single wave. The plan above is the breakdown for a multi-wave closure.

Originator-prose citations. Master-tier units should carry originator-prose treatment per docs/plans/FASTTRACK_EQUIVALENCE_PLAN.md §10, citing in particular:

• J. F. Adams, "On the structure and applications of the Steenrod algebra," Comment. Math. Helv. 32 (1958), 180–214 — originating the Steenrod algebra Hopf-algebra structure used to build the classical Adams SS.
• J. F. Adams, "Vector fields on spheres," Ann. of Math. (2) 75 (1962), 603–632 — the Hopf-invariant-one theorem via the Adams SS.
• J. F. Adams, "On the groups $J(X)$" I–IV (Topology 1963–1966) — the $J$-homomorphism papers; foundational for Items 8, 17.
• D. Quillen, "On the formal group laws of unoriented and complex cobordism theory," Bull. Amer. Math. Soc. 75 (1969), 1293–1298 — originating the identification ${\pi }_{\ast }(MU)=L$ (Items 4, 6).
• J. Morava, "Noetherian localisations of categories of cobordism comodules," Ann. of Math. (2) 121 (1985), 1–39 — Morava K-theories and the change-of-rings theorem (Items 12, 13). Morava's earlier preprints (~1973) introduced $K(n)$.
• H. Miller, D. Ravenel, S. Wilson, "Periodic phenomena in the Adams-Novikov spectral sequence," Ann. of Math. (2) 106 (1977), 469–516 — originating the chromatic spectral sequence (Item 11).
• E. Devinatz, M. Hopkins, J. Smith, "Nilpotence and stable homotopy theory I," Ann. of Math. (2) 128 (1988), 207–241 — Items 19, 20.

Notation crosswalk. Ravenel's conventions diverge from the modern chromatic-homotopy literature in several places that the Codex notation spec must adjudicate:

• $B{P}_{\ast }$ vs ${\pi }_{\ast }(BP)$ — Ravenel writes $B{P}_{\ast }$ throughout.
• $v_n\in B{P}_{2(p^n-1)}$ — Hazewinkel generators (Ravenel's default) vs Araki generators (used in some modern sources).
• $\Sigma (n)$ vs ${\mathbb{S}}_n$ — Ravenel writes $\Sigma (n)$ for the Morava stabiliser group; modern usage is ${\mathbb{S}}_n$ or $\mathrm{Aut}({\Gamma }_n)$. Codex should use ${\mathbb{S}}_n$ in headings and record the Ravenel convention in the §Notation paragraph.
• $K(n)$ — coefficient ring ${\mathbb{F}}_p[v_n^{\pm 1}]$ with $|v_n|=2(p^n-1)$.
• Hopf algebroid: Ravenel writes $(A,\Gamma )$ with $\Gamma =E_{\ast }E$; modern stack-theoretic accounts (Lurie) write ${\mathcal{M}}_{fg}$ for the moduli stack — the Codex should record both and bridge in the Master tier of Item 7.

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§5 What this plan does NOT cover

• Absorption of May Concise (3.38) or May Simplicial Objects (3.40) content. May Concise covers $MU$ at the introductory level and Adams SS only by pointer; Simplicial Objects gives simplicial foundations needed for some modern model-categorical accounts of spectra. Ravenel does not depend on simplicial methods in any essential way and is read above both May texts. Audit those entries separately.
• Adams 1974 Stable Homotopy and Generalised Homology coverage. Adams's own book is a separate Fast Track entry (not in the booklist as of 2026-05-17 but standard prereq reading); P0 items 1, 2, 8, 9 overlap with what Adams covers and could be jointly written.
• Modern post-Ravenel work. Goerss-Hopkins-Miller obstruction theory, $E_{\infty }$-ring spectra, topological modular forms (TMF), equivariant chromatic homotopy theory, Hill-Hopkins-Ravenel's Kervaire-invariant theorem. Pointer in Item 23 only; not in scope for FT-equivalence on Ravenel.
• The cubical / $\infty$-categorical / Lurie reframing. Ravenel works in classical (non-$\infty$-categorical) stable homotopy theory. The Codex's chromatic units should follow Ravenel's classical formulation, with $\infty$-categorical reframings deferred to a separate Lurie-track plan (when/if Lurie's Higher Algebra enters the FT).
• A full theorem-numbered P1 inventory. Reduced audit per §6.6. Re-audit upgrade queued in NEED_TO_SOURCE.md.

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§6 Acceptance criteria for FT equivalence (Ravenel)

Per docs/plans/FASTTRACK_EQUIVALENCE_PLAN.md §3.4 and AGENTIC_EXECUTION §6.6, the book reaches equivalence-coverage when:

• The P0 unit set (Items 1–7) has shipped — strict prerequisite.
• ≥95% of Ravenel's named theorems in Chapters 1–6 map to Codex units (currently 0% of load-bearing content; after P0+P1 this rises to ~70%; after P0+P1+P2 to ~85%; full ≥95% requires P0+P1+P2+P3).
• ≥90% of Ravenel's worked computations in Chapters 1–6 are covered or referenced from a unit.
• Notation decisions are recorded (see §4 crosswalk).
• The reduced-audit flag is cleared — i.e., a full PDF re-audit upgrades this stub's audit_completeness from reduced to full and the §1.1 / §1.2 inventories are populated at theorem-numbered granularity.
• Pass-W weaving connects the new chromatic units to 03.12-homotopy/, 03.13-spectral-sequences/, 03.08-k-theory/, and to the corresponding Adams 1974 / Switzer / Lurie chromatic-notes audit plans (when those exist).

Hard rule (§6.6): because this audit is reduced, the book cannot be marked equivalence-covered on the current pass — only equivalence-partial. Final closure requires a full-PDF re-audit.

Multi-year realism. A focused 6–8 week production sub-pipeline can ship the P0+P1 set (13 units, ~42 hours) bringing Ravenel to equivalence-partial at ~70% coverage. Closing P2/P3/P4 to ≥95% coverage is a further 6–8 week effort. Total realistic timeline for Ravenel to reach equivalence-covered: 3–4 months of dedicated production plus the re-audit pass. This is the largest single-book project in the current Codex Fast Track plan.

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§7 Sourcing

• Free. Author-hosted PDF at https://people.math.rochester.edu/faculty/doug/mybooks/ravenel.pdf (also https://www.sas.rochester.edu/mth/sites/doug-ravenel/mybooks/ravenel.pdf, the same file via Rochester's CMS migration). Searchable hyperlinked PDF, ~4 MB, last revised by the author in 2026. Errata maintained at https://people.math.rochester.edu/faculty/doug/mu.html.
• License. Ravenel posts the PDF freely with the AMS Chelsea second edition's blessing. Cite as Douglas C. Ravenel, Complex Cobordism and Stable Homotopy Groups of Spheres, AMS Chelsea Publishing volume 347, American Mathematical Society 2003 (originally Academic Press 1986).
• Mirror. Edinburgh papers archive at https://www.maths.ed.ac.uk/~v1ranick/papers/ravenel2.pdf (Andrew Ranicki's papers collection).
• Local copy. When sourced, add to reference/fasttrack-texts/03-modern-geometry/ as Ravenel-ComplexCobordismStableHomotopy.pdf to mirror the pattern of other free FT texts. Not currently present in the local archive — the WebFetch attempts during this audit timed out twice (60s ceiling) on the author's server. Re-audit with the file in hand is queued in NEED_TO_SOURCE.md.
• AMS catalogue page (reference for citation hygiene): https://bookstore.ams.org/chel-347-h/.