LaTeX: formulas, theorems, proofs, slides

Compilable LaTeX for mathematically dense text on any subject. Open the references by mode; do not keep everything in your head.

Step 1. Pick the mode

Check Beamer first: it has the clearest signals.

Beamer Mode: the words slides, presentation, beamer, talk, slide deck, a request to prepare a talk from a paper or draft, "title slide" and similar section names. Use references/preamble.md (Beamer part) and references/beamer.md. Do not use the Document Mode preamble or structure.

• A finished manuscript or paper exists: move its content onto slides exactly, without distortion.
• Only a title or theses: build the full skeleton with \todo{} in the empty places.
• Never invent theorems, lemmas or numerical results that were not given.

Document Mode: a theorem / lemma / proposition / corollary / definition (with or without a proof), a multi-step derivation, a convergence analysis, an algorithm with justification, an introduction or literature review, a self-contained report or preprint. Deliver a full .tex file.

Snippet Mode: one formula or system of formulas, an algorithm or pseudocode alone, a results table, a TikZ/pgfplots plot, any fragment to paste into someone else's template. Only the body (no \documentclass, no preamble), in the chat as a code block, not a file (unless a file was asked for).

Unsure which mode: one question, "the whole document, a fragment, or slides?".

References by step

Required before delivery

• Every \begin{} is closed by \end{}; every numbered environment has a \label{}; every \ref{} / \eqref{} / \cref{} resolves. The detailed checklist: references/writing-quality.md.
• No proof given by the user: do not invent one; put \begin{proof} with a \todo{} plan instead of a finished argument.
• Author, institution, talk topic not given: put \todo{} or ask; never copy the sample data from the references.
• If a TeX distribution is installed, compile and read the log before delivering; if it is not, say the file was not compiled.