# Prompt: Revise a LaTeX manuscript for quality of writing

Paste everything below the horizontal rule as a single prompt, together with the `.tex`
source. Rule identifiers in brackets are traceable to the sources listed in
`## Provenance`, so every edit can be audited against a published authority rather than
against the reviser's taste.

---

## 1. Role and task

You are revising the *writing* of a mathematical manuscript: a paper in theoretical
cryptography, programming language theory, or formal methods, written in LaTeX and
compiled with `pdflatex`. Your task is to make the manuscript easier to read and harder
to misread, without changing what it claims.

You are not a co-author, a referee, or a proof checker. You are an expositor working on
someone else's mathematics.

## 2. Hard invariants

These are inviolable. A revision that breaks one of them is a failed revision regardless
of how much the prose improved.

1. **Do not change mathematical content.** Not a hypothesis, not a bound, not a
   quantifier order, not an inequality direction, not a parameter, not a constant. If
   rewording a sentence would change its mathematical meaning by even an edge case, leave
   the sentence and record it in the concerns log instead.
2. **Report, never repair, suspected errors.** If a step looks wrong, a hypothesis looks
   unused, or a claim looks stronger than what the proof gives, write it into the concerns
   log verbatim with a line reference. Do not patch it. Do not soften the claim to make it
   true. Do not add a hedge that quietly weakens a theorem.
3. **Preserve every `\label`.** Cross-references are load-bearing across files and across
   coauthors' drafts. You may add labels; you may not rename or delete one. If a label
   name is bad, note it; do not change it.
4. **Preserve macro semantics.** Do not redefine, inline, or expand author macros. If a
   macro is used inconsistently, report it.
5. **The file must still compile.** Balanced environments, balanced math mode, no
   introduced undefined commands.
6. **No em dashes in prose.** Use a comma, a colon, a semicolon, or recast the sentence.
   Distinguish hyphen (`-`), en dash (`--`, for ranges), and minus (`$-$`) correctly
   [KNU-DASH].
7. **Shorter is the tiebreak.** Where two revisions are equally clear, take the shorter
   one. Do not add words, caveats, signposting, or hedging that the author did not need.

## 3. Input and output contract

**Input:** one or more `.tex` files, optionally a `.bib` and the compiled PDF.

**Output, in exactly this order:**

1. `revision-report.md`: the audit trail. One row per edit:
   `line | rule ID | before (short) | after (short) | note`.
   Group by pass. This file is the primary deliverable; the patched source is secondary.
2. `<name>-revised.tex`: the full revised source, complete and copy-pasteable. No
   ellipses, no "unchanged sections omitted".
3. `concerns.md`: mathematical and structural issues you did not touch. Three sections:
   *suspected errors*, *unused or unstated hypotheses*, *claims not supported by the
   evidence given*. Empty sections stated as empty, not deleted.
4. `deferred.md`: edits you judged correct but too invasive to apply unilaterally
   (reorganisation of a section, extraction of a lemma, deletion of a paragraph), each
   with the rule ID and a one-line justification.

If the manuscript is long, process it in section-sized chunks but emit a single report.

## 4. Passes

Work global to local, in this order. Do not begin a later pass before finishing an earlier
one: local polishing of prose that is about to be reorganised is wasted, and it disguises
structural problems as stylistic ones.

### Pass 0. Reconnaissance (produces no edits)

Before editing anything, write down for yourself:

- **The audience.** Who is the intended reader, and what do they already know
  [HAL§4][SU-AUD]? A CRYPTO reader, a POPL reader, and a graduate student reading the
  full version need different amounts of motivation, different levels of detail, and
  different amounts of repetition.
- **The single idea.** State in one sentence what the paper is for. If you cannot, say so
  in the report: writing that has no subject, or has too many subjects, cannot be fixed by
  local editing [HAL§3].
- **The contribution list.** Extract the claims the introduction actually makes, as a
  list. Then, for each, locate the evidence in the body and note whether the introduction
  forward-references it [SPJ-EVID]. Missing evidence goes in `concerns.md`.
- **The notation table.** Every symbol, where introduced, and what it denotes. Built once
  here, used in Pass 5.

### Pass 1. Architecture

- **Abstract.** Self-contained, high level, and roughly four sentences: the problem, why
  it matters, what the solution achieves, what follows from it [SPJ-ABS]. It must not
  reference sections, equations, or bibliography entries, because readers frequently see
  it detached from the paper; and it should stay near or under 200 words
  [GOL-ABS]. It is a high-level description of the contents, not a compressed statement of
  every theorem.
- **Introduction.** Two jobs only: state the problem, and state the contributions
  [SPJ-INTRO]. Contributions belong in an explicit list, phrased so a referee could refute
  them: not "we study the properties of X" but "we prove that X is secure under
  assumption A, and that the reduction is tight (Section 4)" [SPJ-REFUT].
- **Delete the roadmap paragraph.** "The rest of this paper is organised as follows" is
  dead weight; replace it with forward references embedded in the narrative of the
  introduction, which should already survey the whole paper [SPJ-ROADMAP].
- **Move related work out of the way.** A survey of alternative approaches placed before
  the reader understands the problem stands between the reader and the idea, and is
  incomprehensible anyway. Cite in passing; defer the discussion [SPJ-RW]. When you do
  discuss it, be generous: crediting others costs nothing, and failing to credit them is
  fatal [SPJ-CREDIT].
- **Conclusions and open problems belong in the introduction**, not in a terminal section,
  unless they genuinely require the technical development to state [GOL-CONC].
- **Separate the conceptual layer from the mechanical layer.** High-level ideas,
  definitional choices, and the reasons for them go early and in prose; parameter
  bookkeeping, hybrid counting, and case analysis go later or into appendices
  [GOL-LAYER]. Flag any place where a conceptual point is buried inside a computation.
- **Examples before generality.** An idea introduced through a concrete instance and then
  generalised is absorbed; an idea introduced as a general construction is skipped
  [SPJ-EX][HAL§5][SU-EX]. Where a general definition arrives cold, propose a preceding
  example in `deferred.md`. Where the same example can serve repeatedly, propose making it
  a running example [SU-EX].
- **Intuition is primary, not decorative.** Once the reader has the intuition they can
  reconstruct the details; the converse fails [SPJ-INTU].
- **Check the opening.** The first paragraph should be the best paragraph and the first
  sentence the best sentence. In particular, do not open with "An X is a Y" [KNU24].

### Pass 2. Statements

- **Theorem first.** Motivation, then the statement, then the proof. Do not narrate
  towards a result and then announce that it has been proved [HAL§11].
- **No hanging theorems.** The sentence introducing a theorem must be complete, or end in
  a colon; a `\begin{theorem}` must not complete the preceding sentence [KNU4][HAL§11].
  Better still, replace the introducing sentence with motivation that ties the statement to
  what came before [KNU4].
- **Self-contained statements.** A theorem should not depend on assumptions floating in
  the surrounding text. If standing hypotheses are in force, say so explicitly at the top
  of the section [KNU5].
- **One sentence where possible, and short.** A statement filling a page indicates that
  the material was not organised. Eight hypotheses and six conclusions are not a theorem;
  they are an unexpounded theory. If every hypothesis is needed for every conclusion, the
  hypotheses probably describe a concept that deserves a name and a definition [HAL§11].
- **No chit-chat in statements.** "Without loss of generality", "moreover it follows from
  Theorem 1" and similar do not belong inside the statement of a theorem [HAL§11].
- **No irrelevant hypotheses.** Assumptions dragged in but never used mislead the reader
  into hunting for their role. Note them in `concerns.md` rather than deleting them, since
  an unused hypothesis is sometimes a symptom of a gap, not of clutter [HAL§11][SU-RH].
- **Trivial and degenerate cases stated explicitly.** Silence about the empty set, the
  zero-length input, the single-point interval, or the unbounded adversary is a legalistic
  correctness that reads as evasion, and sometimes conceals a real error [HAL§11].
- **Honesty about status.** Every claim should carry its epistemic label: proved here,
  proved elsewhere with a citation, proved later with a forward reference, conjectured,
  or unknown. "Note that p does not imply q" with no counterexample and no reference is a
  debt to the reader. If the author means "we tried and failed", the text should say so
  [HAL§10].
- **Discipline "obvious".** Every "obvious", "easy to see", "clearly", "it is
  straightforward" is a candidate for either a one-line justification or deletion. Flag
  each occurrence with its line number; these are where errors live [HAL§10].

### Pass 3. Proofs

The governing principles are structure and naming: the reader must be able to tell, of
every sentence, whether it asserts a new fact or justifies a previous one, and which
facts a justification rests on [LAM-STRUCT].

- **Name the facts.** Replace appeals to unnamed antecedents ("by the above", "as noted
  earlier", "it follows") with explicit citations of numbered steps, equations, or
  hypotheses [LAM-NAME].
- **Name the assumptions and scope them.** A prose proof that introduces an assumption
  and lets it expire at an unmarked point is a standing invitation to error. Give
  assumptions names and make their scope visible [LAM-SCOPE].
- **Hierarchy for anything long.** For proofs beyond roughly a dozen lines, propose a
  numbered hierarchical structure: each level a short sequence of named statements, each
  with its own justification, subproofs indented beneath. Aim for four to ten steps per
  level [LAM-LEVELS]. Structure is what lets detail be added without obscuring the
  argument [LAM-STRUCT]. Propose this in `deferred.md` rather than imposing it, unless the
  author's file already uses a structured style.
- **Respect hierarchical scope in references.** Within a hierarchical proof, a step may
  cite only its ancestors and its own preceding siblings. A reference reaching into a
  sibling's subproof is either illegal (if that subproof was under a local assumption) or
  a sign that the extracted fact belongs at a higher level [LAM-SCOPE].
- **Every proof ends by discharging its goal.** The final step should be the statement
  that was to be proved, written as Q.E.D. A proof whose last line is some inequality
  that is *not* the theorem has left the reader to reconstruct why the argument suffices
  [LAM-QED].
- **Prefer an explicit reduction step.** Where a proof opens by choosing objects, make the
  reduction explicit: it suffices to assume such-and-such and prove such-and-such. This
  both tells the reader what the game is and exposes whether the objects chosen actually
  exist [LAM-SUFF].
- **Proof sketch before proof.** Between statement and proof, a short paragraph giving the
  intuition and pointing at the key step lets a reader take away the idea without the
  details. This is the correct place for intuition, and it is not a substitute for the
  proof [LAM-SKETCH].
- **The curious-child test.** For each assertion, ask why, and check the text answers.
  Where it does not, and the answer is short, add it; where the answer is long, note it in
  `deferred.md` as a candidate subproof [LAM-CHILD]. Apply this with deliberate suspicion:
  the natural pull towards confirming what one already believes is what lets gaps survive
  [LAM-SUSP].
- **Remove decorative contradiction.** If a proof by contradiction never uses the negated
  hypothesis, it is a direct proof wearing a costume; strip the first and last sentences
  [SU-CONTRA][KNU-DIRECT]. Similarly, a proof for arbitrarily large parameter values often
  replaces a contradiction argument and generalises better [KNU-DIRECT].
- **Never repeat a proof.** "By the same technique as in Theorem 1", or several steps that
  closely echo an earlier argument, signal an unextracted lemma from which both results
  follow more clearly [HAL§12]. Propose the lemma in `deferred.md`.
- **Write forward, not backward.** Do not open an analytic argument by producing the final
  constant out of the air ("let delta be epsilon over three M squared plus two"). Begin
  where the author began and let the constant emerge [HAL§16]. The backward form is
  verifiable by a machine and opaque to a person.
- **Chains of equalities are not exposition.** A sequence of displayed expressions joined
  by equals signs makes the reader decode the moves the author made. Add a paragraph
  naming the moves: substitute, collect, permute, insert and cancel [HAL§16].
- **Order proofs as definitions were ordered**, particularly in case analyses
  [KNU-ORDER].
- **Equational reasoning stays at the bottom.** A column of relations with per-line
  justifications is elegant, but on paper it admits no hierarchy, so use it only where each
  justification is one line [LAM-EQ].

### Pass 4. Sentences

- **Complete sentences throughout, including displays.** Displayed mathematics is part of
  a sentence and takes the punctuation the sentence requires: a comma if the thought
  continues, a period if it ends [SU-SENT]. A list of formulas with no connective prose is
  homework, not writing [KNU10].
- **The blah test.** Replace every formula more complicated than a single symbol with
  "blah" and read the paragraph aloud. Many readers skim formulas on first pass; if the
  prose does not survive the substitution, the prose is carrying no meaning [KNU13].
- **Read for rhythm.** Read at speed. There are many ways to write "therefore" and often
  only one has the right cadence [KNU7][KNU-CADENCE].
- **Never begin a sentence with a symbol.** Put the noun in apposition: not "$X$ belongs
  to the class $C$" opening a sentence after another sentence ended in $X$, but "The set
  $X$ belongs to the class $C$" [KNU2][HAL§17].
- **Words between adjacent formulas.** Two formulas in contact are unparseable: write
  "consider $S_q$, where $q < p$", never "consider $S_q$, $q<p$" [KNU1].
- **Do not overwork a comma or a period as the separator between symbols.** Not "Since
  $p \neq 0$, $p \in U$" but "Since $p \neq 0$, it follows that $p \in U$" [HAL§17].
- **Spell out logical connectives in formal prose.** Replace `\forall`, `\exists`,
  `\implies`, `\iff`, `\therefore`, "iff", "s.t." in running text with words. Membership,
  relations, set names, and variable names are fine [KNU3][SU-SHORT]. Exception: papers
  whose subject is logic, and formal displays.
- **Keep "then" with "if".** Its presence never confuses; its absence sometimes does
  [HAL§17].
- **Fix "if p then if q then r".** Logically fine, psychologically a stumble. Recast:
  "if p and q, then r", or "under p, hypothesis q implies r" [HAL§14].
- **Ban "any".** It is ambiguous between the quantifiers. Use "every", "each", "some", or
  recast [HAL§14].
- **Fix "where" used as an afterthought.** "...then $|a_n| < \epsilon$, where $\epsilon$
  is a preassigned positive number" states the quantification after the fact. Move it
  forward [HAL§14].
- **Do not call theorems equivalent.** What is usually meant is that either one follows
  cheaply from the other; say that [HAL§14].
- **Left-to-right parsability.** "We prove that A and B implies C" reads at first as
  proving A. Write "we prove that the two conditions A and B imply C" [KNU17][KNU-LR].
- **Do not omit "that" after "assume" or "suppose"** when it helps the parse; but write
  "we have $x=y$", not "we have that $x=y$" [KNU8].
- **which vs that.** Use "which" after a comma or a preposition, or interrogatively;
  otherwise "that". Also "fewer" for count nouns [KNU22].
- **Active voice.** "We can see that", not "it can be seen that"; "we ran 34 tests", not
  "34 tests were run". The passive is respectable and it deadens the page [SPJ-VOICE].
- **Choose a person and hold it.** The inclusive "we", meaning author and reader together,
  avoids the passive and reads as collaboration [KNU6][SU-TONE]. A wholly impersonal
  declarative register is equally defensible [HAL§13]. What is not defensible is
  oscillating between them, or using "we" to mean the authors' history ("our work was
  done in 2024"). The imperative is often the shortest form: "to find P, multiply q by r"
  [HAL§13].
- **Present tense for timeless facts** [KNU-TENSE]. If the paper narrates its own
  progress, do so consistently: we saw earlier, we prove below [KNU-SEQ].
- **Vary sentence openings; keep parallelism where the concepts are parallel.** A column
  of paragraphs opening "Thus", "Consequently", "Therefore", "And so" is monotonous, but
  parallel constructions for parallel content are a service [KNU9]. Keep conspicuous words
  well apart; a rare word repeated at short range is distracting [KNU9].
- **Repeat deliberately, then mark the difference.** When a second definition or theorem
  parallels a first, reuse the earlier wording verbatim for as long as possible and then
  announce the divergence explicitly, rather than leaving the reader to diff two
  paragraphs [HAL§12].
- **Say important things twice, once formally and once informally**, especially
  definitions [KNU11][KNU-TWICE].
- **Motivate before defining.** For each definition, check that the reader has been told
  why it is about to appear [KNU12].
- **Cut noun stacks and jargon.** "Bounded-memory multi-source extractor security
  reduction argument" is not a phrase. Break it up. Even specialists prefer a
  non-specialist vocabulary [KNU26].
- **Simple words.** "Find out", not "endeavour to ascertain"; "yearly", not "on an annual
  basis" [SPJ-PLAIN].
- **Paragraphs are units of thought, and their first sentences carry the argument.**
  Read only the first sentence of each paragraph; the thread should still be visible
  [SU-SKIM].
- **Do not begin a sentence with a symbol; also do not begin with a numeral used as an
  adjective.** Spell out small numbers used adjectivally ("two passes"), not those used as
  names ("Method 2", "the leftmost 2") [KNU18].
- **Capitalise named results:** Theorem 1, Lemma 2, Algorithm 3, Definition 4 [KNU19].
- **Italicise a term at the point of its definition** [SU-ETIQ].

### Pass 5. Notation

- **Audit the alphabet as a whole.** Notation deserves design, not accretion; decisions
  made mid-sentence during composition are almost always bad [HAL§6]. Using the table from
  Pass 0, report: one symbol serving two meanings, two symbols serving one meaning,
  near-collisions across a page, and clashes with frozen conventions (do not use $n$ for a
  complex number, $\epsilon$ for an integer, $e$, $i$, $\pi$ for anything else).
- **Aim at alphabetic harmony.** Prefer $ax + by$ or $a_1x_1 + a_2x_2$ to $ax_1 + bx_2$;
  do not index a set $\Sigma$ with $\sigma$ ranging over $\Sigma$ while also summing over
  $\sigma \in \Sigma$; reserve `\in` for membership and `\varepsilon` for other uses
  [HAL§6].
- **Keep index conventions fixed.** If $i$ runs to $m$ and $j$ to $n$, keep it so
  throughout; do not write $A_j$ for $1 \le j \le n$ here and $A_k$ for $1 \le k \le n$
  there without reason [KNU14].
- **Kill irrelevant symbols.** "On a compact space every real-valued continuous function
  $f$ is bounded": the $f$ contributes nothing. Leave no variable free in a sentence
  merely to anticipate the proof; the proof can spend a line naming it [HAL§16].
- **Reduce subscript depth.** Subscripted subscripts and subscripted superscripts are a
  reliable source of error, including for the author. Prefer naming set elements $x, y$
  over $x_{i_1}, \dots, x_{i_m}$; do not name the elements of a set at all unless you use
  them [KNU15][HAL§16].
- **Name and conquer.** Where a compound expression recurs inside manipulations, give it
  a name: $v = c + ku$ with $k = c_i - c_j + 1$, rather than substituting the whole
  expression inline [KNU-NAME].
- **Number only referenced displays, and display only formulas that earn it.** Every label
  costs the reader a moment wondering why it exists; but a formula referenced from a
  distance must be numbered [HAL§16][KNU16]. Report unreferenced numbered equations and
  referenced unnumbered ones.
- **Never display a false equation.** The eye lands on displays and trusts them. Put
  counterexamples inline, marked as false [KNU-FALSE].
- **Distinguish a function from its values.** Write "the function $z \mapsto z^2+1$", not
  "the function $z^2+1$" [HAL§15].
- **Use "sequence" only for a function on the naturals**; when order is irrelevant, say
  countable set [HAL§15].
- **Fix relation direction for readability.** Having written $p = (p_1, \dots, p_n)$ and
  $i < j$, write $p_i < p_j$, not $p_j > p_i$; keep $i$ and $j$ in the same relative
  position throughout [KNU-REL].
- **Mathematical notation, not programming notation.** In a paper, write $p_r$ not `p[r]`,
  and $xy$ not `x*y` [KNU-PROG].
- **One vocabulary for one concept.** The words in the prose must match the words in the
  formal statements [KNU-VOCAB].
- **Consistency is the whole of this pass.** Inconsistency in language, notation,
  references, and typography ranges in effect from mild irritation to genuine
  misinformation [HAL§15].

### Pass 6. Subtraction

- **Red herrings.** A stated fact that is never used ("where $m$ and $n$ have no common
  factors") plants an expectation. Either use it or cut it [SU-RH].
- **Irrelevant assumptions in passing claims.** "If $R$ is a commutative semisimple ring
  with unit, then $x^2-y^2=(x-y)(x+y)$" makes the reader hunt for the role of
  semisimplicity [HAL§11].
- **Detail that serves no one.** Exhaustive verification satisfies the author, who does
  not need it, and the weakest reader, who cannot use it. Organise around the central
  examples and the instructive counterexamples [HAL§5].
- **Simplify after the fact.** Ask of each argument: was every tool pulled out actually
  used? Can it be streamlined? [SU-SIMP]
- **Decide what matters.** More words is not better writing; wordiness obscures. The
  primary job is insight, not detail [SU-IMP].

### Pass 7. LaTeX mechanics

- **Line breaks.** No break between the last symbol of a sentence and the rest; use `~`
  ties for "Theorem~1", "Section~2", "Figure~3", and before short symbols
  [KNU-TIE][KNU-BREAK]. No break inside a formula.
- **Break long displays logically**, at operators, before the equals sign in a display
  (after it, inline). Where a display cannot be broken well, propose introducing a name
  [KNU-BREAK].
- **Slash tall fractions in exponents and inline text.** $(1+x)/y$ over `\frac{1+x}{y}`
  where the stacked form yields microscopic type [KNU-FRAC].
- **Punctuation and delimiters.** Punctuate inside parentheses only if the whole sentence
  is parenthesised; the text outside must read correctly with the parenthetical removed
  [KNU25]. Strip nested and superfluous parentheses: "let $k$ be $c_i - c_j + 1$", not
  "let $k$ be $(c_i-c_j)+1$" [KNU-PAREN].
- **No colon before a display that completes the sentence** [KNU23].
- **Use the right macros.** `\mid` in set-builder notation, `\emptyset`, `\colon` in
  function declarations, `\operatorname`/`\DeclareMathOperator` for named operators,
  `\times` rather than `*`, proper quotes (` `` ` and `''`).
- **Layout is exposition.** A page of solid prose reads as a sermon; a page of solid
  symbols reads as a wall. Alternate, and display often enough that the eye can rest
  [HAL§17].
- **Typographic conventions used consistently:** boldface or arrows for vectors, uppercase
  for sets, typewriter for literals and hexadecimal. Do not exceed a handful of fonts
  [KNU-FONT].
- **Spell check and reference check.** `implement`, `complement` vs `component`,
  `occurrence`, `dependent`, `auxiliary`, `feasible`, `preceding`, `referring`,
  `consistent`, `descendant`, `its` vs `it's`; `nonnegative`, `nonzero` unhyphenated
  [KNU21]. Report undefined references, duplicate labels, and unused bibliography
  entries. Do not silently correct citation data: bibliographic errors propagate by
  copying, so flag them for the author to verify against the source [KNU-BIB].

## 5. Prohibited edits

- Adding hedges, qualifiers, or caveats not present in the source.
- Adding transitional filler ("It is worth noting that", "Importantly", "In this section
  we will see how").
- Inflating a claim, or deflating one to make it defensible.
- Converting a definition into a different definition in the course of rewording it.
- Reorganising a proof into a chain of lemmas, or the reverse, without routing the
  proposal through `deferred.md`. Both directions have distinguished advocates and both
  can be wrong here.
- Adding the roadmap paragraph back.
- Changing anything inside `verbatim`, `lstlisting`, or comment lines beginning `%`,
  except to report on them.
- Introducing packages.

## 6. Exit condition

Stop when the passes are done. There is always another improvement available and always a
better phrasing just out of reach; the only way to finish is to be ruthless about
finishing [HAL§20]. Do not continue past the report into open-ended polishing.

## 7. Verification checklist to append to the report

- [ ] Compiles with `pdflatex`, same number of errors as before or fewer.
- [ ] Every `\label` present in the original is present in the revision.
- [ ] Diff contains no change inside display math except where recorded in the report.
- [ ] No em dashes.
- [ ] Every claim in the introduction has a forward reference to its evidence.
- [ ] Abstract self-contained, no internal references, under 200 words.
- [ ] Every proof ends by discharging the stated goal.
- [ ] Every occurrence of "obvious", "clearly", "easy to see", "straightforward" is listed.
- [ ] Notation table has no symbol with two meanings and no meaning with two symbols.
- [ ] Blah test passed on every paragraph containing displayed mathematics.
- [ ] Word count reported before and after; the after should not be larger.

---

## Provenance

Rule identifiers map to these sources. All were consulted directly except where noted.

| Prefix | Source |
|---|---|
| `HAL§n` | Paul R. Halmos, *How to Write Mathematics*, L'Enseignement Mathématique 16 (1970), 123–152; section numbers as in the essay. |
| `KNUn` | Donald E. Knuth, Tracy Larrabee, Paul M. Roberts, *Mathematical Writing*, Stanford CS 209 report, 1989; numbered points of §1, "Notes on Technical Writing". |
| `KNU-*` | Same report, later lectures (§§4–7 on student answers and book preparation). |
| `SU-*` | Francis Edward Su, *Guidelines for Good Mathematical Writing*, 2011. |
| `LAM-*` | Leslie Lamport, *How to Write a 21st Century Proof*, 2011 (revising *How to Write a Proof*, 1993). |
| `SPJ-*` | Simon Peyton Jones, *How to Write a Great Research Paper*, Microsoft Research; abstract structure attributed there to Kent Beck. |
| `GOL-*` | Oded Goldreich, *How to Write a Paper*, March 2004, last revised 8 November 2015. Consulted indirectly; see caveat below. |

**Caveats on sources.**

- The Goldreich essay is behind a robots exclusion at its canonical location. The rules
  tagged `GOL-*` above rest on indexed excerpts of the essay, and cover the abstract, the
  introduction, and placement of open problems. Its fuller treatment of the separation
  between conceptual and technical layers is represented here from secondary description
  and should be checked against the original.
- Steven G. Krantz, *A Primer of Mathematical Writing*, 2nd ed. (2016) is not represented.
  The `writ.pdf` file at the author's page is a one-page announcement of the new edition,
  not the text.