Add a 404 page concept and a spring-physics motion primitive

404: "Page Fault" — a SIGSEGV/memory-fault framing distinct from the
retired terminal easter egg, still fitting the CS-flavored identity.
Plain/unstyled for now like the rest of the placeholder layout;
restyle once the design system lands.

src/lib/spring.ts: a small CSS+Web Animations API spring utility
(damped harmonic oscillator -> keyframe progress values), per the
locked "no animation library" decision. Not wired into any component
yet — this is the foundational primitive the design system's motion
work will build on, kept free of any visual/component opinions.

apps/site/src/lib/spring.ts

@@ -0,0 +1,66 @@
+export interface SpringOptions {
+  stiffness?: number;
+  damping?: number;
+  mass?: number;
+  /** Stop simulating once position and velocity are both within this of rest. */
+  precision?: number;
+}
+
+/**
+ * Simulates a damped harmonic oscillator from 0 to 1 and returns per-frame
+ * progress values (60fps), for use as Web Animations API keyframes. Pure
+ * physics simulation, no DOM/CSS opinions — see `animateSpring` below for
+ * the usual way to consume it.
+ */
+export function springProgress({
+  stiffness = 170,
+  damping = 26,
+  mass = 1,
+  precision = 0.005,
+}: SpringOptions = {}): number[] {
+  const frames: number[] = [];
+  let position = 0;
+  let velocity = 0;
+  const dt = 1 / 60;
+  const maxDuration = 4; // seconds, safety cap against under-damped configs
+  for (let t = 0; t < maxDuration; t += dt) {
+    const acceleration =
+      (-stiffness * (position - 1) - damping * velocity) / mass;
+    velocity += acceleration * dt;
+    position += velocity * dt;
+    frames.push(position);
+    if (Math.abs(1 - position) < precision && Math.abs(velocity) < precision)
+      break;
+  }
+  frames.push(1);
+  return frames;
+}
+
+/**
+ * Animates `element` from `from` to `to` along a spring curve, via the
+ * native Web Animations API — no animation library dependency. `toKeyframe`
+ * shapes each interpolated value into whatever CSS properties you need,
+ * e.g. `(v) => ({ transform: \`translateY(${(1 - v) * 20}px)\`, opacity: v })`.
+ * Honors `prefers-reduced-motion` by jumping straight to the end state.
+ */
+export function animateSpring(
+  element: HTMLElement,
+  options: SpringOptions & {
+    from: number;
+    to: number;
+    toKeyframe: (value: number) => Keyframe;
+  },
+): Animation {
+  const { from, to, toKeyframe, ...spring } = options;
+  if (window.matchMedia("(prefers-reduced-motion: reduce)").matches) {
+    return element.animate([toKeyframe(to)], { duration: 1, fill: "forwards" });
+  }
+  const progress = springProgress(spring);
+  const keyframes = progress.map((p) => toKeyframe(from + (to - from) * p));
+  const durationMs = (progress.length / 60) * 1000;
+  return element.animate(keyframes, {
+    duration: durationMs,
+    fill: "forwards",
+    easing: "linear",
+  });
+}

apps/site/src/pages/404.astro

@@ -0,0 +1,14 @@
+---
+import Base from "../layouts/Base.astro";
+---
+
+<Base title="Page Fault" description="404 — this page is not mapped in this process's address space.">
+  <h1>Page Fault</h1>
+  <p class="meta">SIGSEGV — the address you requested was never mapped.</p>
+  <p>
+    Whatever used to live here has been moved, renamed, or never existed in
+    this address space to begin with. Unlike a real page fault, there's no
+    handler that's going to page this back in for you.
+  </p>
+  <p><a href="/">Return to a valid address →</a></p>
+</Base>