| name | anmath-supplementary |
| description | Use when deciding what belongs in appendices versus the main text of a pure-mathematics manuscript for Annals of Mathematics — technical/auxiliary results, long computations, and machine-assisted computation. Math journals generally have no science-style "supplemental material"; everything essential stays in the main text. |
Appendices and Auxiliary Results (anmath-supplementary)
When to trigger
- A long, self-contained computation interrupts the main line of argument
- You have auxiliary lemmas that are needed but not conceptually central
- The proof depends on a machine computation that must be documented
- You are tempted to "move detail to supplement" the way science papers do — pause first
Important: pure-mathematics journals generally do not have a science-style
"supplemental material" section. Everything essential to the proof stays in the main
text and must be fully present and verifiable there. Appendices hold material that is
necessary but would break the flow if kept inline.
What belongs where
| Material | Placement |
|---|
| The Main Theorem and its proof's logical skeleton | Main text, always |
| The crux / new idea | Main text, in full |
| Key lemmas used by the main argument | Main text (state and prove) |
| Long but routine computation verifying an estimate | Appendix, referenced from main text |
| Standard background lemmas recalled for completeness | Appendix or Preliminaries |
| Technical case analysis that would swamp the main flow | Appendix, with the conclusion stated in main text |
| Machine computation (code, what was checked) | Appendix + archived code/data |
| Anything a referee must check to believe the theorem | Main text — never hide it |
Appendix discipline
- Each appendix is self-contained and clearly scoped ("Appendix A. Proof of the
estimate in Lemma 3.4"). State in the main text exactly what the appendix establishes.
- The main text must stand on its logic with appendices referenced, not required to be
read in parallel to follow the argument.
- Do not use an appendix to hide a gap: if a step is essential and hard, it stays
visible. Appendices are for length relief, not for sweeping difficulty out of sight.
When an appendix is not enough: the companion-paper option
If auxiliary material grows into a self-contained contribution — its own theorem and
proof, plausible independent use — a companion paper is the honest structure, not a
hundred-page appendix. The canonical precedent, verified in
resources/exemplars/library.md: Wiles's 1995 modularity paper ran alongside the
Taylor–Wiles companion in the same Annals issue, citing it for the input it needs.
The discipline carries over: state precisely what you import, and prove it fully where
it lives. A companion is a second refereed paper, never a place to park an unproved
step.
Appendix mechanics
- Use letter appendices (Appendix A, B, …) with results numbered A.1, A.2, so
main-text citations stay unambiguous.
- Each main-text use reads like an import: "By Proposition A.2 (proved in Appendix A),
estimate (4.7) holds with C = C(n)" — so the reader can defer the appendix and still
audit the logic.
- Order appendices by first citation from the main text, not by topic.
- A referee should be able to read all appendices last, in one pass; an appendix that
must be consulted mid-argument belongs in the main text.
Computer-assisted proofs
- If a result depends on machine computation, describe precisely what was computed, the
software and version, and the exact claim verified.
- Make the code and data available (archive, repository, or supplement permitted by the
journal) so a referee can reproduce or audit it.
- The human-readable argument must make clear how the computation closes the proof; the
computation is evidence within a proof, not a substitute for exposition.
Checklist
Anti-patterns
- Treating an appendix as a science-style "supplement" and shipping essentials there
- Pushing the hard step to an appendix to make the main text look clean
- A machine computation with no description of what was actually checked
- Unavailable / unreproducible code behind a computer-assisted claim
- Appendices the reader must consult continuously just to follow the main argument
- An appendix that restates main-text material instead of carrying new detail
Output format
【Stays in main text】Main Thm, crux, key lemmas: ...
【To appendix】App A: ...; App B: ...
【Reason each is appendix-not-main】length relief, not gap-hiding: ...
【Computer-assisted?】no / yes — software, version, what was checked, archive location
【Gap check】no essential step hidden / fix: ...
【Next step】anmath-writing-style
