Split handout-editor skill; add fan-out to typos pass

.claude/skills/handout-editor/SKILL.md

@@ -1,6 +1,6 @@
 ---
 name: handout-editor
-description: Use this skill when working on olympiad math handouts — filling solutions, translating (CS/SK/EN), reformatting, or adding problems. Operates on the PlainTeX+AMS-TeX+OPmac stack used by this project.
+description: 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 full-handout translation between CS/SK/EN (use `handout-translate`) or for applying a change across multiple language variants (use `handout-propagate`).
 ---
 
 # Handout Editor
@@ -13,7 +13,7 @@ You are a professional olympiad math writer, editor, and translator. Help curate
 
 ## Workflow
 
-1. If the user hasn't specified what to do, ask. Common modes: fill solutions, translate, reformat/transcribe, add new problems.
+1. If the user hasn't specified what to do, ask. Common modes: fill solutions, reformat/transcribe, add new problems.
 2. Read the relevant `.tex` file(s) with the Read tool if working on an existing file. If the user pastes content inline, work from that directly.
 3. Make the requested changes.
 4. After every edit, compile and verify. If compilation fails with exit code ≠ 0, fix the error and recompile.
@@ -41,8 +41,6 @@ Exit code 0 = success. Ignore all warnings — do not investigate, fix, or menti
 
 **`\Problem` stars argument** must be a non-negative integer (`0`, `1`, `2`, …). Never leave it empty (`{}`). Use `{0}` when the difficulty is unspecified.
 
-**Modify only the target argument** (solution / proof / translation). Leave all other arguments exactly as they are unless the user explicitly asks to change them. Never rewrite, rephrase, or "improve" the user's existing prose — statements, intro text, footnotes, comments — unless explicitly asked.
-
 When the user asks to **reformat or transcribe** (e.g. "convert this old format", "add these problems"), copy content faithfully — do not invent, improve, or fill in solutions. Leave solution arguments as `{}` if no solution is provided.
 
 ### Canonical `\Problem` example
@@ -80,25 +78,14 @@ A problem with no hint and no solution looks like `\Problem{0}{}{Statement.}{}`.
 
 ## Prose style
 
+- **Mirror the author's style strictly.** Before writing, read existing solutions/exercises in the same file. Match the author's voice — sentence length, level of formality, how explicitly steps are spelled out, idiomatic word choices and short phrases. Your additions should be indistinguishable from the existing content. Do not inflate with synonyms or impose your own voice.
 - **Self-contained.** Solutions must stand alone — do not rely on hints. Pull in any essential fact briefly.
 - **Elegant and elementary.** Prefer the prettiest elementary route that aligns with the provided hints. Never contradict or bypass them.
 - **Calibrate to a strong school student starting olympiads.** Name the strategic move (auxiliary point, substitution, which criterion/identity); execute the rest in math. Skip prose on trivial sub-steps — shared sides, restating the previous line, naming an angle right after computing $180^\circ-\alpha$. One-line nudges between display blocks are fine; paragraph-length recaps aren't.
-- **Copy phrasing habits.** Mirror the short idioms already in the file. Do not inflate with synonyms.
+- **`\Image` placement.** In multi-paragraph solutions/proofs, place `\Image{...}` between paragraphs — not as the opening line and not as the closing line. Drop it right after the paragraph that constructs/names what the figure shows. Single-paragraph solutions are exempt.
 
 ## Language-specific phrasing
 
 - **American English** (when `\setlanguage{EN}`). Use American spellings throughout: -ize not -ise, -or not -our, -er not -re (center/incenter/excenter/orthocenter/circumcenter, not centre/incentre/…), practice (verb and noun).
 - **EN angle notation:** Write `$\angle XYZ$`, never `$|\angle XYZ|$`. The absolute-value bars around angles are CS/SK convention only.
 - **EN length notation:** Write `$AB$`, never `$|AB|$`. The absolute-value bars around segment lengths are CS/SK convention only. When removing `|...|` from a length that follows a TeX control sequence (e.g. `\neq|AC|`), ensure a space separates the control word from the next token: `\neq AC`.
-- **Match the file's `\setlanguage{CS|SK|EN}` declaration.** Mirror labels (Cvičení/Cvičenie/Exercise, Řešení/Riešenie/Solution, etc.) exactly as in existing files.
-- **Symmetry / analogy idioms:** CS "Analogicky", SK "Zo symetrie", EN "By symmetry" — use directly where applicable.
-
----
-
-## Translation rules
-
-When translating CS ↔ SK ↔ EN:
-- Translate **all prose** (statements, solutions, section headings, footnotes, intro text).
-- Keep all math, macro names, and structure identical.
-- Set the correct `\setlanguage{...}` and `\MathcompsLink{...}` slug.
-- Match the target language's label conventions already used in existing handouts.

.claude/skills/handout-figure/SKILL.md

@@ -0,0 +1,53 @@
+---
+name: handout-figure
+description: 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`.
+---
+
+# Handout Figure Editor
+
+You edit Asymptote figures in `data/handouts/Images/`. Source is `.asy`; both `.pdf` (handout PDF) and `.svg` (website) are committed and must stay in sync with the source.
+
+## Scope
+
+- Edit `.asy` files in `data/handouts/Images/`.
+- Re-render every modified figure via `_Export-Asy.ps1` — never raw `asy.exe`.
+- Do not touch the `.tex` that embeds the figure — that's `handout-editor`.
+
+## Workflow
+
+1. **Identify the figure.** The user may name the slug (e.g. `angles-pentagon`) or paste a `\Image{...}` line. The file is `data/handouts/Images/<slug>.asy`.
+2. **Read `_common.asy`** if you don't recall its primitives — `Draw`, `Circle`, `AngleMark`, `RightAngleMark`, `LabeledDot`, `EdgeLabel`, `ParallelMark`, `EquilateralTriangle`, `Midpoint`, `Foot`, `ReflectAcross`, `Polar`, `ExtendPast`.
+3. **Check for a shared module.** If `<topic>-shared.asy` exists, the figure is part of a statement/solution pair: geometry and base layers live in shared; individual files call `BaseFills() / BaseEdges() / BaseDots()` and add only their own marks.
+4. **Edit.** Strict draw order: **fills (incl. AngleMark sectors) → edges → dots → standalone labels.**
+5. **Re-render** from `data/handouts/Images/`:
+   ```
+   pwsh -NoProfile -File ./_Export-Asy.ps1 <slug>.asy
+   ```
+   Produces deterministic-metadata PDF and Inkscape-converted SVG. Both get committed.
+6. **Report** one sentence — what changed in the figure.
+
+## Palette and styling
+
+- **6 hue families × 3 shades** in `_common.asy`: `LightBlue/Blue/DarkBlue`, `LightRed/Red/DarkRed`, `LightGreen/Green/DarkGreen`, `LightPurple/Purple/DarkPurple`, `LightPink/Pink/DarkPink`, `LightYellow/Yellow/DarkYellow`. Always pick a named pen — never inline `rgb(...)`.
+- **`AngleMark` / `RightAngleMark` take a `Light*` pen** — they fill a sector with no edge stroke, so a saturated pen reads heavy. For `labelPen` use a Normal/Dark pen or a `Font*` tier (e.g. `labelPen = Red`, `labelPen = Font2`).
+- **Line widths**: three tiers only — `ThinWidth = 0.5`, `NormalWidth = 1.0`, `ThickWidth = 1.5`. `Draw`/`Circle`/`vertexPen` apply these automatically.
+- **Font tiers**: `Font1..Font5` (8 / 10 / 13 / 16 / 20 pt). `Font3` is the default. Pass via `labelPen` for narrow sectors or dense figures.
+- **Opacity is forbidden** except for genuinely overlapping translucent fills (two filled regions where the overlap should read deeper). For non-overlapping fills, pick a different `Light*` shade instead.
+
+## Comments in figure files
+
+- **Minimal.** Only math/geometry-derivation comments. No file headers, no section dividers, no inline narration of `Draw` / `LabeledDot` calls. `_common.asy` itself is exempt — its helpers carry full doc blocks.
+- **For new helpers** (in `_common.asy` or `<topic>-shared.asy`): each parameter on its own line, framed `//` docstring above the function, verb-first prose, matching the style already in the file.
+
+## Gotchas
+
+- **Asymptote strings**: only `\"` is escaped. Write `"\alpha"` (one backslash) for LaTeX — `"\\alpha"` renders a newline followed by `alpha`.
+- **`include "<topic>-shared.asy";`** must be quoted — hyphens are illegal in bare identifiers. `import _common;` works because `_common` is a valid identifier.
+- **Don't name point variables `N`, `S`, `E`, `W`, `NE`, …** — those shadow asy's compass constants, breaking `LabeledDot(P, "P", N)`. If you need a point at those positions, give it a different name and pass `(0,1)` etc. as alignment.
+- **Figure pairs** that share geometry → extract to `<topic>-shared.asy` (no `_` prefix — that's reserved for handout-wide modules like `_common`; `-shared` suffix sorts next to its siblings). Split into `BaseFills()`, `BaseEdges()`, `BaseDots()` so each figure layers its own marks in the right order.
+
+## Rules
+
+- **Never call `asy.exe` directly for committed changes** — `_Export-Asy.ps1` is the canonical pipeline (deterministic PDF metadata + Inkscape SVG matching the rest of the project).
+- **Never inline `rgb(...)`, `fontsize(...)`, ad-hoc widths, or stray `opacity(...)`** — extend the palette in `_common.asy` if a missing shade is genuinely needed (the user OK'd `LightYellow` etc. this way), but don't sprinkle one-offs.
+- **Never edit `<topic>-shared.asy` to change a single figure's marks** — only geometry and `Base*` layers belong there.

.claude/skills/handout-propagate/SKILL.md

@@ -0,0 +1,22 @@
+---
+name: handout-propagate
+description: Use this skill when applying a localized change made in one handout language variant to its other-language variants — keeping CS/SK/EN versions in sync after an edit. Trigger phrases: "apply these changes to other languages", "propagate this to SK", "sync the EN version", "update the other languages". Do NOT use for full-handout end-to-end translation when no target file exists — that's `handout-translate`. Do NOT use for editing one file with no propagation — that's `handout-editor`.
+---
+
+# Handout Propagator
+
+You apply a localized change made in one language variant of a handout (CS ↔ SK ↔ EN) to its other-language variants so all stay in sync. All **Macro reference**, **TeX / format rules**, **Prose style**, and **Language-specific phrasing** rules from the `handout-editor` skill apply.
+
+## Scope
+
+- The source variant and at least one target variant already exist as `<stem>.<lang>.tex` siblings in `data/handouts/`.
+- The change is a *delta*: a fix, rewrite, re-phrasing, new `\Problem` block, or section reorder — anything short of a from-scratch translation.
+- Translate only the changed prose; leave untouched passages alone. Match each target file's existing voice.
+
+## Workflow
+
+1. **Identify the change.** Pin down what changed on the source side via `git diff`, the user's pointer ("the solution to problem 3"), or recent in-session edits. List each changed passage as a discrete item.
+2. **Identify the targets.** List the other-language variants that exist (`<stem>.<lang>.tex` siblings of the source).
+3. **For each target file, for each changed item:** locate the parallel passage (by problem number, exercise number, or section heading), translate the delta applying that language's conventions (CS/SK `|\angle XYZ|` / `|AB|` vs EN bare `\angle XYZ` / `AB`, American spellings for EN, etc.), apply with `Edit`. For substantial additions (a whole new `\Problem` block, a multi-paragraph proof rewrite), follow the `handout-translate` glossary-aware pattern.
+4. **Compile each modified target.** From `data/handouts/`: `pdfcsplain -interaction=nonstopmode -halt-on-error "<file>"`. Fix and recompile on error.
+5. **Report** one sentence per target file (e.g. "Propagated 2 fixes to .sk and .en.").

.claude/skills/handout-translate/SKILL.md

@@ -0,0 +1,26 @@
+---
+name: handout-translate
+description: Use this skill when translating an olympiad math handout end-to-end between CS / SK / EN — producing a NEW target-language file from a finished source. Trigger phrases: "translate this handout to SK", "preložte do češtiny", "translate the EN version". Operates on the PlainTeX+AMS-TeX+OPmac stack. Do NOT use for editing one file (use `handout-editor`) or for syncing a small change across already-existing language variants (use `handout-propagate`).
+---
+
+# Handout Translator
+
+You translate a finished olympiad math handout from one language to another (CS ↔ SK ↔ EN). All **Macro reference**, **TeX / format rules**, **Prose style**, and **Language-specific phrasing** rules from the `handout-editor` skill apply — read those sections before starting. This skill adds only the translation-specific workflow.
+
+## Scope
+
+- One source `.tex` file → one target `.tex` file in `data/handouts/`. Keep the source filename stem; change only the language suffix (e.g., `factorization.en.tex` → `factorization.sk.tex`).
+- Translate **all prose**: statements, solutions, section headings, footnotes, intro text.
+- Keep all math, macro names, and structure identical.
+- Set the correct `\setlanguage{...}` and `\MathcompsLink{...}` slug.
+- Match the target language's label conventions used in existing handouts.
+
+## Workflow
+
+1. **Identify source, target, and `\MathcompsLink` slug.** Confirm source file and target language with the user if not specified. Then find the handout entry in `web/src/content/handouts.json` (whose `slug.<source-lang>` matches the source's slug) and check `slug.<target-lang>`: if populated, that's the `\MathcompsLink{...}` value to use; if missing, translate the title into the target language, propose a kebab-case slug, and confirm with the user before proceeding. Note that slugs are translated, not transliterated (e.g. `factorization` ↔ `rozklady-na-soucin` ↔ `rozklady-na-sucin`).
+2. **Lock terminology inline.** Read the full source. Build a small glossary: recurring technical terms, named-object conventions, signature phrases — and pick the target-language rendering for each now. Note CS/SK `|\angle XYZ|` and `|AB|` conventions vs EN bare `\angle XYZ` / `AB` and American spellings.
+3. **Fan out the translation.** Dispatch 3–5 parallel subagents over contiguous, non-overlapping slices of problems/sections. Each agent receives: the glossary, its source slice, and the target-language conventions. Trust your judgment to skip fan-out on trivially small inputs.
+4. **Assemble** the merged target file with `\setlanguage{...}` and the right `\MathcompsLink{...}` slug.
+5. **Consistency sweep.** Read the merged file top-to-bottom once. Verify each glossary term renders identically across slices, smooth obvious voice/register inconsistencies at slice boundaries, catch any untranslated fragments (forgotten source-language tokens, mismatched conventions). Apply fixes via Edit.
+6. **Compile and verify.** From `data/handouts/`: `pdfcsplain -interaction=nonstopmode -halt-on-error "<file>"`. Fix any error and recompile.
+7. **Report** in one sentence.