Mathematical writing: the research article, its template, and the structure of a proof

How a mathematical research article and each proof in it should be laid out so the reader finds the result, judges it, and sees why it holds.

Steps: frame · protocol · sources · review · state of the art · position · against · baseline · bibliography

Claims

Claim	Grade	Where
Mathematics articles follow Introduction-Results, without Methods or Discussion	measured, descriptive	review.md 2
21 of 22 pure-mathematics openings announce the principal findings	measured, descriptive	review.md 2
Half of the 22 articles have no conclusion section	measured, descriptive	review.md 2
State the main results first, in self-contained one-sentence theorems	convention, untested	review.md 1
Abstracts carry no citations; at least one primary MSC code is required	convention, enforced by the publisher	review.md 2
The DTP style records results but loses how understanding is passed on	supported with caveat	review.md 3, against.md 4
Leron-style structured proofs help readers identify the summary	measured, one study	state-of-the-art.md Q4
The same structure slightly lowers scores on justifications, transfer and examples	measured, one study, mostly not significant	against.md 1
Narrated e-Proofs lowered retention after two weeks	measured	against.md 2
Generic proofs did not improve comprehension	measured	against.md 2
Self-explanation training of the reader raises comprehension, d = 0.95	measured, replicated by the same team	state-of-the-art.md Q4
Experts look for implicit warrants between consecutive lines	measured	review.md 5
Mathematicians do not share one standard of proof validity	measured	against.md 5
About 4 to 10 steps per level, and few levels, keep a structured proof readable	convention, untested	review.md 4
Writing the dependencies of each lemma exposes missing hypotheses	supported with caveat (case reports)	review.md 6
Societies and publishers regulate the abstract and theorem styles, not the layout of introductions or proofs	convention, enforced by the publisher	review.md 2
Practitioners split on whether to postpone proofs after the introduction	convention, untested; contested	review.md 1.1, against.md 5
About 40 formalisation projects list a blueprint with uses labels	measured, descriptive (the repository's own count)	review.md 6
No review found compares layouts of a research article or a proof	this search did not find one	review.md 0
Whether any layout helps research mathematicians read papers	not known	position.md