MathComps

Use this skill to build a defense-conversation fixture for the AI examiner engine — author a problem plus a candidate persona defending a solution (anywhere from fully correct, through a subtly flawed one, to confident nonsense), then drive a full conversation by playing that candidate against the examiner CLI turn by turn. Produces a complete fixture (problem + reference + transcript) under `data/defense-fixtures/`. Do NOT use to evaluate an existing transcript — use `judge`.

Use this skill to evaluate an AI-examiner defense transcript — whether the examiner leaked earned progress, whether its challenges were sharp and probed the real weakness, and whether every mathematical claim it made is correct. Fans out one blind reviewer per dimension, then synthesizes a verdict plus concrete prompt-fix ideas. Do NOT use to produce a transcript — use `generate-conversation`.

Use this skill to finalize a handout — promote it from draft to published. Updates web/src/content/handouts.json, runs the Handouts CLI to build JSONs/PDFs, and validates. Trigger words: "finalize", "publish", "release", "ship" a handout. Do NOT use for writing or editing .tex content — use the `handout-editor` skill for that.

Use this skill to make a target-language variant of a handout consistent with the source — whether the target file doesn't exist yet (translate end-to-end) or already exists and just needs the latest changes synced (propagate delta). Operates on the PlainTeX+AMS-TeX+OPmac stack used by this project, CS / SK / EN. Trigger phrases: "translate this handout to SK", "preložte do češtiny", "translate the EN version", "propagate this to SK", "sync the EN version", "apply these changes to other languages", "ensure this is in CS too", "update the other languages". Do NOT use for editing a single language variant in place (use `handout-editor`).

Use this skill when adding a competition's problems to the site database through the bulk-import draft pipeline — registering a brand-new competition in the taxonomy if it isn't there yet, authoring the draft folder (statements + solutions + images, one original language plus translations), and running the bulk-import CLI validate until it passes. Trigger phrases: "add a new competition", "import a contest's problems into the DB", "register a competition in the taxonomy", "create a bulk-import draft", "add a round/year of a competition". Do NOT use for editing handouts (use the handout-* skills). The skill ends at `validate`; `apply` runs only on the user's explicit say-so (see "Validate" below).

Use this skill to pull figures out of a vector competition PDF as small, faithful SVGs for the bulk-import pipeline — auto-detecting each diagram, cropping it (keeping the real glyph outlines, not retypeset text), and rendering a PNG preview of every crop to verify. Trigger phrases: "extract the figures from this PDF", "crop the diagrams out of a competition PDF as SVGs", "get the figure for problem N", "I need the images from this competition PDF". Hands the cropped SVGs to the add-problems skill for placement. Do NOT use for raster/scanned PDFs (it only handles vector drawings), or for handling problem text.

Use this skill when editing one olympiad math handout file — filling solutions, reformatting/transcribing, adding problems, or polishing prose. Operates on the PlainTeX+AMS-TeX+OPmac stack used by this project. Do NOT use for translating or propagating changes between CS/SK/EN language variants (use `handout-translate`).

Use this skill to proofread a handout .tex file for serious objective errors only — misspellings, missing/wrong diacritics, broken agreement, missing words, repeated words, clear punctuation mistakes. Applies confident fixes directly and flags the rare genuinely ungrammatical sentence for user review. Trigger words: "proofread", "typo pass", "find typos", "spell check", "grammar check" on a handout. Languages: CS, SK, EN. Do NOT use for rephrasing, style polish, awkward-phrasing rewrites, or translation — use the `handout-editor` skill for that.

Use this skill when editing or adding handout figures — Asymptote `.asy` files in `data/handouts/Images/`. Adding/modifying geometry, angle marks, fills, colors, labels, then re-rendering to PDF + SVG. Trigger phrases: "add a 60° angle to that figure", "change the color in the figure", "redraw", "fix the figure", "make X visible", anything touching a `.asy` under handouts. Do NOT use for editing the `.tex` that embeds the figure — that's `handout-editor`.

Use this skill to math-check the solutions in one olympiad math handout `.tex` file. For each `\Problem` with a non-empty solution, spawns one parallel reviewer agent that verifies mathematical correctness — logical gaps, unstated assumptions, case-analysis errors, wrong lemmas — and produces a punch list. Trigger phrases: "review the math", "are these solutions correct", "math-check this handout", "verify the proofs". Do NOT use for spelling/typo proofreading (use `handout-typos`), prose/style polish (use `handout-editor`), or full-handout translation review (use `handout-translate`).