docs(docs): update problem page paths to use (problems)/<num>_<slug>.mdx format and adjust related examples

.claude/skills/problem-approach/SKILL.md

@@ -5,7 +5,7 @@ description: Write the `## Approach` section — a Mermaid flowchart that traces
 
 # Problem approach diagrams
 
-Every solution page (`apps/docs/content/(<phase>)/<topic>/<num>-<slug>.mdx`) has a
+Every solution page (`apps/docs/content/(<phase>)/<topic>/(problems)/<num>_<slug>.mdx`) has a
 hand-owned section before the script-owned one:
 
 ```
@@ -100,7 +100,7 @@ flowchart TD
   The base case is the first decision after entry.
 - **Classes** (design problems) use one `subgraph name["method(args)"]` per public
   method, plus a `state["…"]` subgraph describing the fields, with `state --> method`
-  edges — see `(hash-table)/146-lru-cache.mdx`. Private helpers are named inside the
+  edges — see `hybrid-structures/(problems)/146_lru-cache.mdx`. Private helpers are named inside the
   method nodes (`"_remove_node then _add_node — move it beside the tail"`), not drawn.
 - **Annotate the why with an em dash** inside the node, sparingly (one clause, a few
   per diagram): `"nums.sort() — duplicates become adjacent"`, `"map = {0: 1} — the
@@ -122,7 +122,7 @@ flowchart TD
 ### Code that does not run
 
 Trace it anyway — the diagram documents what was submitted — and put a `::::warning`
-callout **before** the fence naming exactly why it fails (`(array)/121-best-time-to-buy-and-sell-stock.mdx`):
+callout **before** the fence naming exactly why it fails (`sliding-window/(problems)/121_best-time-to-buy-and-sell-stock.mdx`):
 
 ````md
 ## Approach

AGENTS.md

@@ -48,7 +48,7 @@ flowchart LR
 |---|---|
 | `work/<1\|3\|7>/<Difficulty>/<Category>/<num>.<slug>.{js,py}` | Solutions, e.g. `work/1/Easy/Array/1.two-sum.py`. The top directory is the spaced-repetition bucket: `1` = first solve, `3`/`7` = the blind re-solves of that problem 3 and 7 days later. Machine-parsed header comment (title / `Difficulty:` / URL / `─` rule / statement) — preserve its exact shape |
 | `apps/cli/` | Flat Bun TS workspace: automation entries (shebang + top-level await) and libraries (no shebang, side-effect-free on import). Root `bun run` scripts delegate here |
-| `apps/docs/` | Blume site (`blume.config.ts`, `content/`, `pages/`, `components/` + `components.ts`, `islands/`, `public/`). `content/(0N-<phase>)/<topic>/<num>-<slug>.mdx` plus one `meta.ts` per phase and per topic folder, all generated by sync (a phase's once, then hand-owned): the phase folder is a `(group)` (sidebar section, no route segment), the topic folder is the README campaign topic slug (`tree-dfs/`, `heap-priority-queue/`) and a real route segment (`/tree-dfs/invert-binary-tree`), the `meta.ts` files carry the exact labels, phase/topic numbers and icons so the sidebar reads in curriculum order with each topic a collapsible group. A problem page's badge row (between the description and the body) is rendered, not written: the MDX `wrapper` (`components/ProblemBadges.astro`, registered as `mdx.wrapper` in `components.ts` — Blume's page template renders the title and description itself with no slot before the body, so the wrapper, which MDX hands no route, reads it off `Astro.url`) reads the page's `topics:` (LeetCode's topic tags, from sync) and `video:` (NeetCode YouTube id, from `bun run videos`) frontmatter — both declared via `frontmatter.extend` in `blume.config.ts`, hand-rolled Standard Schemas, no zod — and links a tag the campaign teaches to its topic landing page (filled), any other tag to its card on the Appendix glossary `/appendix#<slug>` (outlined; LeetCode's problem list if the tag has no term, gray and iconless), and the video as a red `Explanation` badge. Every badge in the row is a pill. A tag badge carries the icon its target shows (a landing's: the topic `meta.ts` icon read off `data.navigation`; an Appendix term's: its `icon` in `appendix.ts`) and the tag's own colour from `lib/tag-colors.ts` — unique per tag site-wide, assigned greedily over every tag with a landing or a term so tags that share problem pages sit furthest apart in OKLab, in a lightness band that keeps ≥ 3:1 contrast in both themes (Blume's Badge takes one hex for both). The reverse direction is the `PageFooter` slot (`components/BacklinksList.astro`): an Obsidian-style `<num> <name>` list under every topic landing page of the problems whose badges link there, plus a topic's own folder members (so a topic no tag names, `hybrid-structures`, still lists its problems), in a native `<details>` open on load whose top-right chevron collapses it (no JS); problem pages are recognised by their `<num>. <name>` title and render no list. Which tags the campaign teaches is ONE map, `apps/docs/topic-landings.ts` (tag slug → landing routes), and where a badge points is ONE function beside it, `tagTarget()` — read by both components and the Appendix page (so badges, backlinks and term cards cannot disagree) and the map by sync. Every other tag a problem carries is ONE hand-written table, `apps/docs/appendix.ts` (`APPENDIX`: slug → `{ name, icon, category, definition }`), rendered by ONE custom page, `pages/appendix.astro` — a glossary with an A–Z letter index and a filter box (an `<appendix-filter>` custom element over static markup; no JS, the full list), one card per term (icon tinted the tag's colour, category, definition, LeetCode list link, and a `<details>` "Solved" list of the problem pages whose badge `tagTarget()` sends there, paged `PAGE_SIZE` (5) rows at a time by numbered buttons under it — a `<solved-pages>` custom element; without JS every row shows and the buttons stay hidden), each card `id`'d by slug and highlighted as `:target`. It is no content folder, so it enters neither the sidebar tree nor prev/next: `navigation.featured` pins it above the tree. Sync writes nothing for it — it warns about a carried tag with no term, a term whose tag a topic now teaches (delete it), and a term `icon` that is a `TOPIC_ICONS` value or another term's. The former per-term pages `/appendix/<slug>` are exact redirects to `/appendix#<slug>` in `blume.config.ts`, generated from `APPENDIX`'s keys. A hand-written `(0N-<phase>)/<topic>/index.mdx` (`hidden: true`) is that topic's landing page: Blume ≥ 1.7.3 links the sidebar group row to it (`sliding-window/index.mdx` → `/sliding-window`) and the hidden flag drops the duplicate row. Two kinds of custom MDX component, both import-free on every page: `islands/<Name>.tsx` is hydrated React (auto-discovered; the five `/progress` cards `SolvedRing`/`SubmissionHeatmap`/`SubmissionChart`/`TopicBubbles`/`RecentSolves`, and `DependencySpine` — the README topic map as data, zoom/pan, nodes link to whatever route Blume's `/api/docs/navigation.json` reports for the topic folder, inert until a topic has pages), `components/<Name>.astro` registered in `components.ts` is static markup plus a custom element for behaviour, the way Blume's own `Frame` is built (`Carousel`/`CarouselImage`: `src` takes a URL, `/file.png`, or the page-relative `../../public/file.png`) |
+| `apps/docs/` | Blume site (`blume.config.ts`, `content/`, `pages/`, `components/` + `components.ts`, `islands/`, `public/`). `content/(0N-<phase>)/<topic>/(problems)/<num>_<slug>.mdx` plus one `meta.ts` per phase and per topic folder, all generated by sync (a phase's once, then hand-owned): the phase folder is a `(group)` (sidebar section, no route segment), the topic folder is the README campaign topic slug (`tree-dfs/`, `heap-priority-queue/`) and a real route segment, and `(problems)` is a second `(group)` inside it, so `tree-dfs/(problems)/226_invert-binary-tree.mdx` routes to `/tree-dfs/invert-binary-tree` (Blume sorts by the `<num>_` prefix and strips it from the route). The `meta.ts` files carry the exact labels, phase/topic numbers and icons so the sidebar reads in curriculum order; every topic meta is `display: "page"`, so a topic is one sidebar row whose panel holds its landing page and a "Problems" section. A problem page's badge row (between the description and the body) is rendered, not written: the MDX `wrapper` (`components/ProblemBadges.astro`, registered as `mdx.wrapper` in `components.ts` — Blume's page template renders the title and description itself with no slot before the body, so the wrapper, which MDX hands no route, reads it off `Astro.url`) reads the page's `topics:` (LeetCode's topic tags, from sync) and `video:` (NeetCode YouTube id, from `bun run videos`) frontmatter — both declared via `frontmatter.extend` in `blume.config.ts`, hand-rolled Standard Schemas, no zod — and links a tag the campaign teaches to its topic landing page (filled), any other tag to its card on the Appendix glossary `/appendix#<slug>` (outlined; LeetCode's problem list if the tag has no term, gray and iconless), and the video as a red `Explanation` badge. Every badge in the row is a pill. A tag badge carries the icon its target shows (a landing's: the topic `meta.ts` icon read off `data.navigation`; an Appendix term's: its `icon` in `appendix.ts`) and the tag's own colour from `lib/tag-colors.ts` — unique per tag site-wide, assigned greedily over every tag with a landing or a term so tags that share problem pages sit furthest apart in OKLab, in a lightness band that keeps ≥ 3:1 contrast in both themes (Blume's Badge takes one hex for both). The reverse direction is the `PageFooter` slot (`components/BacklinksList.astro`): an Obsidian-style `<num> <name>` list under every topic landing page of the problems whose badges link there, plus a topic's own folder members (so a topic no tag names, `hybrid-structures`, still lists its problems), in a native `<details>` open on load whose top-right chevron collapses it (no JS); problem pages are recognised by their `<num>. <name>` title and render no list. Which tags the campaign teaches is ONE map, `apps/docs/topic-landings.ts` (tag slug → landing routes), and where a badge points is ONE function beside it, `tagTarget()` — read by both components and the Appendix page (so badges, backlinks and term cards cannot disagree) and the map by sync. Every other tag a problem carries is ONE hand-written table, `apps/docs/appendix.ts` (`APPENDIX`: slug → `{ name, icon, category, definition }`), rendered by ONE custom page, `pages/appendix.astro` — a glossary with an A–Z letter index and a filter box (an `<appendix-filter>` custom element over static markup; no JS, the full list), one card per term (icon tinted the tag's colour, category, definition, LeetCode list link, and a `<details>` "Solved" list of the problem pages whose badge `tagTarget()` sends there, paged `PAGE_SIZE` (5) rows at a time by numbered buttons under it — a `<solved-pages>` custom element; without JS every row shows and the buttons stay hidden), each card `id`'d by slug and highlighted as `:target`. It is no content folder, so it enters neither the sidebar tree nor prev/next: `navigation.featured` pins it above the tree. Sync writes nothing for it — it warns about a carried tag with no term, a term whose tag a topic now teaches (delete it), and a term `icon` that is a `TOPIC_ICONS` value or another term's. The former per-term pages `/appendix/<slug>` are exact redirects to `/appendix#<slug>` in `blume.config.ts`, generated from `APPENDIX`'s keys. A hand-written `(0N-<phase>)/<topic>/index.mdx` (`hidden: true`) is that topic's landing page: Blume ≥ 1.7.3 links the sidebar group row to it (`sliding-window/index.mdx` → `/sliding-window`) and the hidden flag drops the duplicate row. Two kinds of custom MDX component, both import-free on every page: `islands/<Name>.tsx` is hydrated React (auto-discovered; the five `/progress` cards `SolvedRing`/`SubmissionHeatmap`/`SubmissionChart`/`TopicBubbles`/`RecentSolves`, and `DependencySpine` — the README topic map as data, zoom/pan, nodes link to whatever route Blume's `/api/docs/navigation.json` reports for the topic folder, inert until a topic has pages), `components/<Name>.astro` registered in `components.ts` is static markup plus aLine truncated
 | `apps/api/` | Cloudflare Worker workspace: `src/` modules, `data/schedule.json` (the plan: `date → { topics | problems | review | gate | sweep }`, human-edited, bundled at deploy), `migrations/` (append-only; `0002` is the +3/+7 ladder rebuild) |
 | `.github/workflows/` | deploy (docs → Pages with `GITHUB_TOKEN` for the releases-backed changelog, Worker → Cloudflare with the `OPENROUTER_API_KEY` Actions secret put into it first, on every main push), close-solved (issues + `/admin/solved` + Project `Set`/`Difficulty`, needs `SRS_ADMIN_KEY` and `PROJECT_PAT`; then the `release` job: timever tag + release per finished topic, `contents: write`), close-topics, sync-d1 (issue edits → `/admin/reconcile`), spaced-repetition (daily 06:00 ET cron → today's review issue; `GITHUB_TOKEN` only, no secrets) |
 | `.githooks/` | Tracked git hooks; `bun install` points `core.hooksPath` here (root `prepare` script, no husky). `pre-commit` runs `bun run sync` and stages only what sync changed (pages, `apps/docs/redirects.ts`), so a solution, its page and its `/<num>` short link land in one commit; it refuses to run while `work/1` has anything unstaged (sync reads the tree, so the page would not match the commit), and leaves pre-existing dirt under `apps/docs/content` (in-progress `## Approach` prose) unstaged. `git commit --no-verify` for a deliberate partial commit |
@@ -113,7 +113,7 @@ curl -X POST -H "Authorization: Bearer $LINK_KEY" \
 - `apps/api/src/ask.ts` — `POST /ask`, the docs assistant's backend. Blume's own assistant route is server-rendered and cannot ship in the static Pages build (`BLUME_SERVER_FEATURE_REQUIRED`), so `blume.config.ts` sets `ai.assistant.endpoint` to this route instead of a `provider`. It speaks the Blume island's wire contract (`{ messages, page: { path } }` in, a plain-text stream out, a 503 "The assistant is not configured…" when the key is missing), validates like Blume's generated route (1–40 user/assistant messages, 24 000 chars, 64 KB — no caller system prompt), grounds on the published `llms-full.txt` (current page first, then keyword-ranked excerpts in Blume's 6 × 2 000 / 10 000-char budget, cached 5 min), and streams OpenRouter's chat completions over plain `fetch` — no AI SDK — for the `ASK_MODEL` var. `:free` models share an upstream pool and often answer 429, which the island shows as its rate-limit notice.
 - `apps/api/src/digest.ts` / `apps/api/src/email.tsx` — the daily digest, split data/presentation. `digest.ts` reads D1 into a `DigestData`; `email.tsx` owns every colour and every sentence, and renders both the HTML and (via its own `plainDigest`, not React Email's `plainText` mode, which flattens the tables) the text alternative. The retrieval rules hold by construction: `DigestRow` has no title and no issue field, so a review or drill line *cannot* leak the topic or a solution link. Subject is `(Day N/<CAMPAIGN_DAYS>) LeetCode Daily Digest` — 79 with the plan ending Nov 3; booking a later day in `schedule.json` lengthens it, and the heatmaps and `/api/stats` `heat` with it.
 - `apps/api/src/png.ts` — hand-rolled PNG encoder (RGB8, one IDAT, zlib via `CompressionStream("deflate")`, CRC32, 5×7 bitmap font). It exists because every major email client refuses remote SVG, so `/chart/heatmap.png` rasters the heatmap for the digest while `/chart/heatmap.svg` keeps serving the README byte-for-byte. Both come from one `heatmapCells()` so the two pictures cannot drift.
-- `apps/cli/sync.ts` — work→docs contract: on existing pages only the frontmatter `icon:` and the `## Solution` section are regenerated, and `topics:` (LeetCode's `topicTags` as `{ name, slug }`, fetched by GraphQL) and `issue:` (the URL of the problem's `problem`-labelled GitHub issue, `LC <num> · …`, listed via `github()` — rendered as the neutral `Issue #N` badge after `Explanation`) are filled once — on create, or on any run that finds them missing — never refreshed (delete a key to refetch; offline or without `gh` auth, the page is written without it and the next sync retries; a sync with nothing missing makes no request). Only a problem the README plan lists gets `issue:` — an unplanned warm-up has no catalog issue, so it is never looked up. `## Solution` is the latter bounded by `solutionEnd()` at the next unfenced top-level heading; human prose before it and any sections after it are never touched. Never hand-write solution pages or edit inside `## Solution`. Two classifications, two homes: the sidebar group is the README topic (`readmeTopics()`, first listing wins for a problem under two topics; a warm-up outside the plan groups under its category at `order: 0`, ahead of topic 1) and the `work/1/<Difficulty>/<Category>/` category, which only places an unplanned problem — the page's topic badges are LeetCode's tags, not either classification. Topics nest under their README phase (`## Phase N — Name` headings, shortened via `PHASE_ALIASES`): `content/(0N-<phase>)/<topic>/`. The topic `meta.ts` is script-owned and rewritten every run (label, curriculum order, `TOPIC_ICONS` icon, `display: "group"`); the phase `meta.ts` is written once when missing (`Phase N: Name`, `order: N`) and hand-owned after — rename its title freely. Never rewriting it loses nothing: its order and name are also the folder name, so a README change to either lands in a new folder with a fresh meta. The phase folder is a Blume `(group)` — no route segment, so `/tree-dfs` is unchanged and a landing page there is one level deep, never at `/` — and the topic folder is the real segment; never put a topic `index.mdx` directly inside a `(group)`. A page is `rename`d when its topic or phase changes; a folder every page has left is deleted (climbing into an emptied phase folder) unless it still holds a hand-written `index.mdx` (sync never writes, moves, or deletes one — so page-relative asset paths in a moved landing page are yours to fix). Slugs come from `slugify()`, which glues a leading number to the next token (`1d-dynamic-programming`) because Blume strips `<digits>-` prefixes from routes. The hand-owned parts have their own owners: `## Approach` (a Mermaid flowchart tracing the page's code, placed *before* `## Solution` so a re-sync keeps it) is written per the `problem-approach` skill (`/problem-approach` fills every page missing one); the frontmatter `video:` (the NeetCode walkthrough, rendered as the red `Explanation` badge) is added by `bun run videos --write` (`apps/cli/videos.ts`).
+- `apps/cli/sync.ts` — work→docs contract: on existing pages only the frontmatter `icon:` and the `## Solution` section are regenerated, and `topics:` (LeetCode's `topicTags` as `{ name, slug }`, fetched by GraphQL) and `issue:` (the URL of the problem's `problem`-labelled GitHub issue, `LC <num> · …`, listed via `github()` — rendered as the neutral `Issue #N` badge after `Explanation`) are filled once — on create, or on any run that finds them missing — never refreshed (delete a key to refetch; offline or without `gh` auth, the page is written without it and the next sync retries; a sync with nothing missing makes no request). Only a problem the README plan lists gets `issue:` — an unplanned warm-up has no catalog issue, so it is never looked up. `## Solution` is the latter bounded by `solutionEnd()` at the next unfenced top-level heading; human prose before it and any sections after it are never touched. Never hand-write solution pages or edit inside `## Solution`. Two classifications, two homes: the sidebar group is the README topic (`readmeTopics()`, first listing wins for a problem under two topics; a warm-up outside the plan groups under its category at `order: 0`, ahead of topic 1) and the `work/1/<Difficulty>/<Category>/` category, which only places an unplanned problem — the page's topic badges are LeetCode's tags, not either classification. Topics nest under their README phase (`## Phase N — Name` headings, shortened via `PHASE_ALIASES`): `content/(0N-<phase>)/<topic>/`, with every problem page in the topic's `(problems)/` group as `<num>_<slug>.mdx` (a page is found by its frontmatter title, wherever it sits, so a layout change is one sync of `rename`s). The topic `meta.ts` is script-owned and rewritten every run (label, curriculum order, `TOPIC_ICONS` icon, `display: "page"`); the phase `meta.ts` is written once when missing (`Phase N: Name`, `order: N`) and hand-owned after — rename its title freely. Never rewriting it loses nothing: its order and name are also the folder name, so a README change to either lands in a new folder with a fresh meta. The phase folder is a Blume `(group)` — no route segment, so `/tree-dfs` is unchanged and a landing page there is one level deep, never at `/` — and the topic folder is the real segment; never put a topic `index.mdx` directly inside a `(group)`. A page is `rename`d when its topic or phase changes; a folder every page has left is deleted (climbing through an emptied `(problems)` and topic into an emptied phase folder) unless it still holds a hand-written `index.mdx` (sync never writes, moves, or deletes one — so page-relative asset paths in a moved landing page are yours to fix). Slugs come from `slugify()`, which glues a leading number to the next token (`1d-dynamic-programming`) because Blume strips `<digits>-` prefixes from routes. The hand-owned parts have their own owners: `## Approach` (a Mermaid flowchart tracing the page's code, placed *before* `## Solution` so a re-sync keeps it) is written per the `problem-approach` skill (`/problem-approach` fills every page missing one); the frontmatter `video:` (the NeetCode walkthrough, rendered as the red `Explanation` badge) is added by `bun run videos --write` (`apps/cli/videos.ts`).
 - `apps/cli/work.ts` — the `work/` layout: bucket paths, `isSolution()`/`solvedInBucket()` (the stub test, shared with `close-solved.ts`), `firstSolved()` (one `git log`, ET dates, keyed by LC number so past layout moves don't matter), and `reviewQueues()` (what each window still owes). Everything that needs to know where a solution file lives, or when it was solved, goes through here.
 - `apps/api/src/stats.ts` / `apps/cli/stats.ts` / `apps/cli/tui.ts` / `apps/cli/api.ts` / `apps/docs/lib/stats.ts` — the read side. `buildStats()` is the ONE aggregation: phases, ladder, difficulty, `attempting` (open misses, via `MISS_WHERE` in `srs.ts` — the sweep day's definition), per-topic temperature, gates, the 14-day due queue, `heat` (every campaign day, zeros and future days included — the TUI windows its tail rather than asking a second question), `recent` (the ten problems most recently solved, dated by each one's first pass) and `year` (the 365 days ending today — always the calendar year to date — each split by difficulty into attempts and first solves; the docs cards window and bucket it themselves). Two readers consume it, the docs `/progress` islands and `bun run stats`, so its shape is their contract: change the Worker and both readers together (additive fields a reader ignores are safe). `tui.ts` is hand-rolled ANSI (bars, sparklines, heat cells, alternate screen) on charts.ts's palette, and every chart differs by GLYPH as well as by colour so a piped or `NO_COLOR` dashboard still reads. The TUI recomputes nothing: the only local fact it shows is the `work/` solution count, which is inventory, not schedule.
 - `README.md` live charts are Worker endpoints (`/chart/*.svg`, `/badge/gate.svg`, 5-min Camo cache). The docs `/progress` page is five LeetCode-style islands — `SolvedRing` (difficulty gauge + "Attempting"), `SubmissionHeatmap` and `SubmissionChart` sharing one row (the heatmap: the last six months in month blocks, the README's colour ramp as theme.css `--heat-0..4`, its attempts / active days / max streak counted from the cells it draws; the chart: this calendar year as stacked Easy/Med./Hard bars per month or week, first solves or every attempt, via two shadcn `ToggleGroup`s), `TopicBubbles` (the campaign topics circle-packed by `d3-hierarchy`, filled by solved share), `RecentSolves` (the ten most recent, linked through `redirects.ts`) — composed from shadcn/ui (`components/ui/{card,chart,skeleton,toggle,toggle-group}.tsx`, Recharts under `chart`, Radix under the toggles) on Blume's tokens: `apps/docs/theme.css` maps shadcn's names onto `--blume-*` (never `accent`, which is Blume's brand colour — vendored components that use it, like `toggle.tsx`, are retokened to `background`/`muted`) and gives shadcn's `data-slot` parts their border colour. They share `lib/stats.ts` (`useStats()`), so the page makes ONE `/api/stats` request however many islands hydrate. shadcn sources live outside `islands/` (every `.tsx` there becomes an island) and import `lib/utils` relatively; `components.json` + `tsconfig.json` exist for the shadcn CLI and `tsc`, so after `shadcn add` rewrite `@/…` imports to relative ones (house style) — and check `package.json`: the CLI has twice installed an unrelated `cn` package for `lib/utils` and skipped real deps (`class-variance-authority`). Blume turns every tsconfig `paths` target into a Vite alias AND a dev dep-scan glob (`<target>/**/*.astro`…), so `paths` maps only `@/components`, `@/lib`, `@/hooks` — each bare and `/*`, since `components.json` names the bare forms — never `@/*` → `./*`: that glob reaches through `node_modules/blume`, where Vite's scanner reads a `<script>` inside a `RootLayout.astro` comment as a tag and `blume dev` skips dependency pre-bundling. Blume's `.prose :where(a, p, ol)` rules ignore `not-prose`, so island markup overrides them with `!` utilities, as Blume's own components do.