docs(docs): add Carousel component and embed in topological‑sort page, replace static spine image with interactive component

apps/docs/components/Carousel.astro

@@ -0,0 +1,170 @@
+---
+/**
+ * A horizontal carousel of <CarouselImage> slides, built the way Blume's own
+ * content components are: static markup, a custom element for the behaviour,
+ * no framework. The track is a CSS scroll-snap strip (so it also swipes on
+ * touch and the browser does the animation); prev/next sit outside it and
+ * the play toggle sits below with a "n / N" counter.
+ *
+ * `time` is seconds per slide while playing (default 1.25); `autoplay` starts
+ * playing on load. Play wraps around, pauses whenever the tab is hidden, and
+ * never starts on its own for a reader who prefers reduced motion — the
+ * button still works for them. Manual navigation (buttons, arrow keys, swipe)
+ * does not stop playback; it only restarts the interval so a step is never
+ * doubled.
+ */
+import Icon from "blume/components/Icon.astro";
+
+interface Props {
+  /** Seconds each slide stays while playing. */
+  time?: number;
+  autoplay?: boolean;
+}
+
+const { time = 1.25, autoplay = false } = Astro.props;
+
+const buttonClass =
+  "inline-flex size-9 shrink-0 cursor-pointer items-center justify-center rounded-full border border-border bg-background text-muted-foreground transition-colors hover:border-foreground hover:text-foreground disabled:cursor-default disabled:opacity-40";
+---
+
+<blume-carousel
+  class="not-prose my-6 block"
+  data-time={String(time)}
+  data-autoplay={autoplay ? "" : undefined}
+  role="region"
+  aria-roledescription="carousel"
+>
+  <div class="flex items-center gap-3">
+    <button class={buttonClass} data-prev type="button" aria-label="Previous slide">
+      <Icon class="rtl:-scale-x-100" name="chevron-left" size={18} />
+    </button>
+    <div
+      class="flex min-w-0 flex-1 snap-x snap-mandatory overflow-x-auto scroll-smooth rounded-blume [scrollbar-width:none] [&::-webkit-scrollbar]:hidden"
+      data-track
+      tabindex="0"
+      aria-live="polite"
+    >
+      <slot />
+    </div>
+    <button class={buttonClass} data-next type="button" aria-label="Next slide">
+      <Icon class="rtl:-scale-x-100" name="chevron-right" size={18} />
+    </button>
+  </div>
+  <div class="mt-3 flex items-center justify-center gap-3">
+    <button class={buttonClass} data-play type="button" aria-label="Play" aria-pressed="false">
+      <Icon class="[[aria-pressed=true]_&]:hidden" name="play" size={16} />
+      <Icon class="[[aria-pressed=false]_&]:hidden" name="pause" size={16} />
+    </button>
+    <span class="text-muted-foreground text-xs tabular-nums leading-5" data-count></span>
+  </div>
+</blume-carousel>
+
+<script>
+  class BlumeCarousel extends HTMLElement {
+    #track!: HTMLElement;
+    #play!: HTMLButtonElement;
+    #count!: HTMLElement;
+    #timer: number | null = null;
+    #index = 0;
+
+    connectedCallback() {
+      this.#track = this.querySelector("[data-track]")!;
+      this.#play = this.querySelector("[data-play]")!;
+      this.#count = this.querySelector("[data-count]")!;
+      const prev = this.querySelector<HTMLButtonElement>("[data-prev]")!;
+      const next = this.querySelector<HTMLButtonElement>("[data-next]")!;
+
+      const slides = this.#slides().length;
+      if (slides < 2) {
+        for (const b of [prev, next, this.#play]) b.disabled = true;
+      }
+      this.#render();
+
+      prev.addEventListener("click", () => this.#step(-1));
+      next.addEventListener("click", () => this.#step(1));
+      this.#play.addEventListener("click", () => (this.#timer === null ? this.#start() : this.#stop()));
+      this.addEventListener("keydown", (event) => {
+        if (event.key === "ArrowLeft") this.#step(-1);
+        else if (event.key === "ArrowRight") this.#step(1);
+        else return;
+        event.preventDefault();
+      });
+      // Swipes and trackpad scrolls move the track without #step; follow them
+      // once the scroll settles. Settle-only, not per event: a long smooth
+      // scroll from #step passes over intermediate slides and must not be
+      // read back as the reader's position mid-flight.
+      let settle: number | undefined;
+      this.#track.addEventListener(
+        "scroll",
+        () => {
+          window.clearTimeout(settle);
+          settle = window.setTimeout(() => this.#syncFromScroll(), 150);
+        },
+        { passive: true }
+      );
+      document.addEventListener("visibilitychange", this.#onVisibility);
+
+      const reduced = matchMedia("(prefers-reduced-motion: reduce)").matches;
+      if (this.hasAttribute("data-autoplay") && slides > 1 && !reduced) this.#start();
+    }
+
+    disconnectedCallback() {
+      this.#stop();
+      document.removeEventListener("visibilitychange", this.#onVisibility);
+    }
+
+    #slides(): HTMLElement[] {
+      return [...this.#track.querySelectorAll<HTMLElement>(":scope > blume-carousel-image")];
+    }
+
+    #step(delta: number) {
+      const slides = this.#slides();
+      this.#index = (this.#index + delta + slides.length) % slides.length;
+      slides[this.#index]!.scrollIntoView({ block: "nearest", inline: "start", behavior: "smooth" });
+      this.#render();
+      if (this.#timer !== null) this.#start(); // restart the interval from this slide
+    }
+
+    #syncFromScroll() {
+      const at = Math.round(this.#track.scrollLeft / this.#track.clientWidth);
+      if (at !== this.#index && Number.isFinite(at)) {
+        this.#index = Math.min(Math.max(at, 0), this.#slides().length - 1);
+        this.#render();
+      }
+    }
+
+    #start() {
+      this.#stop();
+      const ms = Number(this.dataset.time) * 1000;
+      this.#timer = window.setInterval(() => this.#step(1), ms > 0 ? ms : 1250);
+      this.#play.setAttribute("aria-pressed", "true");
+      this.#play.setAttribute("aria-label", "Pause");
+    }
+
+    #stop() {
+      if (this.#timer !== null) window.clearInterval(this.#timer);
+      this.#timer = null;
+      this.#play.setAttribute("aria-pressed", "false");
+      this.#play.setAttribute("aria-label", "Play");
+    }
+
+    // A background tab keeps its timers but not its layout; resume on return.
+    #wasPlaying = false;
+    #onVisibility = () => {
+      if (document.hidden) {
+        this.#wasPlaying = this.#timer !== null;
+        this.#stop();
+      } else if (this.#wasPlaying) this.#start();
+    };
+
+    #render() {
+      const slides = this.#slides();
+      this.#count.textContent = `${this.#index + 1} / ${slides.length}`;
+      slides.forEach((s, i) => s.setAttribute("aria-hidden", i === this.#index ? "false" : "true"));
+    }
+  }
+
+  if (!customElements.get("blume-carousel")) {
+    customElements.define("blume-carousel", BlumeCarousel);
+  }
+</script>

apps/docs/components/CarouselImage.astro

@@ -0,0 +1,45 @@
+---
+/**
+ * One slide of a <Carousel>: Blume's own <Frame> around an <img>, so a slide
+ * is pixel-identical to a framed image elsewhere on the site — `alt` doubles
+ * as the frame's hint line and `caption` is Markdown, exactly as in Frame.
+ *
+ * `src` accepts what MDX authors already write for images: a URL, a
+ * root-relative `/file.png` (served from public/, prefixed with the deploy
+ * base), or the page-relative `../../public/file.png` form. A relative path
+ * that does not pass through public/ has nothing to serve it, so it is a
+ * build error rather than a silent 404.
+ */
+import Frame from "blume/components/content/Frame.astro";
+import { withBase } from "blume/components/islands/base-path.ts";
+
+interface Props {
+  src: string;
+  alt?: string;
+  caption?: string;
+}
+
+const { src, alt, caption } = Astro.props;
+
+const resolveSrc = (value: string): string => {
+  if (URL.canParse(value)) return value;
+  if (value.startsWith("/")) return withBase(value);
+  const at = value.indexOf("public/");
+  if (at === -1) {
+    throw new Error(
+      `<CarouselImage src="${value}">: a relative src must point into public/ (or use /file.png)`
+    );
+  }
+  return withBase(`/${value.slice(at + "public/".length)}`);
+};
+---
+
+<blume-carousel-image
+  class="block w-full shrink-0 snap-center [&_blume-frame]:my-0"
+  role="group"
+  aria-roledescription="slide"
+>
+  <Frame caption={caption} hint={alt}>
+    <img alt={alt ?? ""} src={resolveSrc(src)} loading="lazy" draggable="false" />
+  </Frame>
+</blume-carousel-image>