diff --git a/docs/angrybirds-build-plan.md b/docs/angrybirds-build-plan.md
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+# Angry Birds — build plan
+
+Living plan doc. Survives context clears: **read this file first**, pick the next unchecked item, update the checkboxes and the Status line as work lands.
+
+## Status
+
+**Wave 0 complete 2026-07-30 — the gate is passed.** `node tools/verifyAngryBirds.js` → **51 checks green**. A 10-box tower settles in 0.68s, sleeps, drifts <1px sideways, and tilts 6.1e-3 rad (0.35°, invisible). A 15-box pyramid settles too. The solver runs a 6-second, 41-body shot in **254ms** headless.
+
+Next: Wave 1, the playable core.
+
+## Decisions taken up front
+
+| Question | Answer |
+|---|---|
+| Slug / category / iconFrame | `angrybirds` / `arcade-console-pc` ("Video Games") / **92** (next free after Excitebike's 91) |
+| Physics | **Bespoke deterministic rigid-body solver.** Matter.js ships inside the CDN Phaser build and would work in-browser, but it is not importable in bare Node and not reproducible — that forfeits the verifier, the generator's measured star thresholds, and the editor's winnability gate. |
+| Visual treatment | **No CRT overlay, no scanlines, no pixel font.** It's a 2009 touch game, not an arcade cabinet. Clean cartoon look, app's normal fonts. |
+| Campaign scale | **63 levels, 3 episodes of 21** — Poached Eggs / Mighty Hoax / Danger Above. |
+| Art | Procedural, with a `data/angrybirds-artwork.json` drop-in hook so real sprites can replace the fallbacks later with no code change. Procedural fallbacks must always work standalone. |
+| Bird roster | All 8 — Red, Chuck, Blue, Bomb, Matilda, Terence, Hal, Bubbles. |
+| Modes | Single-player campaign only. `maxOpponents: 0`, so it skips `OpponentSelect` entirely. |
+
+## Files
+
+| File | Role | State |
+|---|---|---|
+| `src/games/angrybirds/AngryBirdsPhysics.js` | Rigid-body solver. Zero imports. | 🔨 Wave 0 |
+| `src/games/angrybirds/AngryBirdsLogic.js` | Materials, damage, birds, scoring, `stepSim`. Zero imports. | ⬜ Wave 1 |
+| `src/games/angrybirds/AngryBirdsGame.js` | Phaser scene, key `AngryBirdsGame`. | ⬜ Wave 1 |
+| `src/games/angrybirds/AngryBirdsArt.js` | Procedural textures + artwork-JSON resolution. | ⬜ Wave 5 |
+| `src/games/angrybirds/AngryBirdsEditor.js` | Level editor, key `AngryBirdsEditor`. | ⬜ Wave 3 |
+| `src/games/angrybirds/AngryBirdsAuto.js` | Reference bot / winnability gate. In `src/` so the editor button and the verifier run the same gate. | ⬜ Wave 3 |
+| `src/games/angrybirds/tutorial.md` | Tutorial copy. | ⬜ Wave 5 |
+| `tools/genAngryBirds.js` | Level-bank generator; **measures** star thresholds. | ⬜ Wave 3 |
+| `tools/verifyAngryBirds.js` | Node harness. | 🔨 Wave 0 |
+| `assets/gamedata/angrybirds/` | `levels.json` manifest + 63 level files. | ⬜ Wave 4 |
+| `data/angrybirds-artwork.json` | Drop-in sprite map. | ⬜ Wave 5 |
+
+Wiring touchpoints: `src/data/gamesRegistry.js`, `src/main.js` (import + scene array, both scenes), `src/scenes/GameRoomScene.js:26` (`slugDispatch`), `src/data/assetManifest.js`, `src/scenes/PreloadScene.js` (manifest JSON + `?angrybirds-editor=1` entrance).
+
+---
+
+## Wave 0 — the rigid-body solver — ✅ DONE 2026-07-30
+
+- [x] Convex polygon + circle bodies, mass/inertia derived from geometry
+- [x] Uniform-grid AABB broadphase
+- [x] SAT narrowphase with reference-face clipping → 2-point manifolds
+- [x] Sequential-impulse solver with warm starting
+- [x] Coulomb friction clamped against the accumulated normal impulse
+- [x] **Split-impulse** position correction with penetration slop (not plain Baumgarte — see finding 1)
+- [x] Island-based sleeping
+- [x] `cloneWorld` / `hashWorld` for determinism tests
+- [x] Verifier green — all four gate conditions pass
+
+### The gate — all four passed
+
+1. ✅ 10-box tower settles in 0.68s, every body asleep, drift 0.00px, tilt 6.1e-3 rad. A 15-box pyramid also settles.
+2. ✅ Box on a 15° slope with µ=0.9 does not creep; a µ=0.2 box on 40° does slide.
+3. ✅ Bit-identical replay; 1/60 frame == 4 substeps exactly; ragged frame pacing matches even pacing.
+4. ✅ 12 monkey seeds × 900 substeps: no NaN, no overspeed, nothing sinks.
+
+### Wave 0 findings
+
+1. **Plain Baumgarte is not good enough for a 10-high stack, and the failure looks like a bug when it isn't.** Feeding position error back as bias velocity makes a contact behave like a stiff spring, so penetration is proportional to load — the bottom contact of a 10-box tower carries 9 boxes and sinks ~9× deeper than the top one. Measured sag was 12.85px. Switching to **split impulse** (a separate pseudo-velocity accumulator, added into the position integration then discarded) removes a fixed fraction of the excess per substep *regardless of load*, and never leaks the correction back as bounce energy. Sag dropped to 0.46px per contact, which is exactly `SLOP` — i.e. the remaining sag is the slop band we deliberately allow, not solver error. **Do not "simplify" this back to a single bias term.**
+2. **Total stack sag is bounded by `SLOP × contactCount`, by design.** The verifier asserts against that budget rather than a flat pixel value. Shrinking `SLOP` tightens stacks but reintroduces resting-contact jitter — 0.5px on a 40px block is the sweet spot.
+3. **Warm starting must key on a stable feature id, not array position.** Contact points are matched across substeps by `(refFace << 8) | incidentVert`, with a flip bit. Matching by index scrambles impulses the moment the clip order changes and the stack sags visibly.
+4. **The reference-face choice needs hysteresis.** Preferring A unless B is deeper by a relative margin (`0.1 × |sepA| + 0.01`) keeps the choice stable frame to frame, which is what keeps feature ids — and therefore warm starting — stable for a resting contact.
+5. **Sequential impulses are Gauss-Seidel, so solve order genuinely changes the answer.** Bit-identical results across different body *creation* orders are not achievable and were never the goal; the verifier asserts the dependence stays sub-pixel (measured 0.4px). What must be exact — and is — is that a *given* scene replays identically.
+6. **Island sleeping, not per-body sleeping.** Union-find over contacts; an island sleeps only when its slowest member has been slow for `SLEEP_TIME`. Per-body sleeping freezes half a tower while the rest still moves. Sleeping is also how the rules layer knows a shot is over, so it is not just an optimization.
+7. **Anti-tunnelling is a design constraint, not a runtime check.** `MAX_SPEED × SUBSTEP_DT < MIN_HALF_EXTENT` (10px < 12px) is asserted by the verifier, which is what forced `SUBSTEP_DT` to 1/240 and `MAX_SPEED` to 2400. No block may be thinner than 24px.
+8. **String keys dominated the profile.** Numeric composite keys for the grid and contact maps, plus building the contact list in already-sorted pair order instead of re-sorting it four times per substep, took a 6-second shot from 368ms to 254ms with bit-identical output.
+9. **Contacts cache direct body references, so `cloneWorld` must rewire them.** A shallow spread leaves the clone's contacts pointing at the original's bodies — the clone then drives the world it was supposed to leave alone. The winnability bot and shot preview both depend on this; the verifier now asserts it explicitly.
+
+### Baselines
+
+```
+node tools/verifyAngryBirds.js              -> 51 checks green
+node tools/verifyAngryBirds.js --seeds=40   -> slower monkey soak, still green
+```
+
+---
+
+## Wave 1 — playable core — ⬜ NEXT
+
+- [ ] Materials: wood / stone / ice with distinct density, friction, restitution, hp, damage threshold
+- [ ] Damage as a **health model** — impulse above threshold subtracts hp; 2/3 and 1/3 crossings emit crack stages
+- [ ] Pigs take damage from debris, not just direct hits
+- [ ] Slingshot: drag, clamp to max draw, release
+- [ ] Win/lose evaluated only once the world is settled or `MAX_SHOT_TIME` expires
+- [ ] `stepSim(state, dt) → events[]` contract
+- [ ] Phaser scene with sim-space→screen-space mapping, camera pan/zoom
+- [ ] Trajectory memory (dotted trail of previous shots)
+
+---
+
+## Wave 2 — the full roster, TNT, scoring — ⬜
+
+- [ ] 8 birds, abilities fire on tap mid-flight
+- [ ] TNT blocks detonate when damaged
+- [ ] Scoring: 5,000/pig + material destruction points + 10,000 per unused bird
+
+---
+
+## Wave 3 — editor and generator — ⬜
+
+- [ ] `?angrybirds-editor=1` entrance, authoring in play coordinates
+- [ ] **Settle** button so levels export already at rest
+- [ ] **Test Winnable** button running the same gate as the verifier
+- [ ] `AngryBirdsAuto` beam search over (angle, power, ability timing)
+- [ ] Blob export of `level-NNN.json` + regenerated `levels.json`
+
+Gate is **one-directional**: if the bot wins, a human can. A bot failure is *not* proof a level is impossible.
+
+---
+
+## Wave 4 — the 63-level campaign — ⬜
+
+- [ ] Poached Eggs (1-21) — wood then stone; Red, Chuck, Blue
+- [ ] Mighty Hoax (22-42) — ice, TNT, taller structures; adds Bomb, Matilda
+- [ ] Danger Above (43-63) — mixed materials, elevated structures; adds Terence, Hal, Bubbles
+
+Every level needs a **load-bearing** support whose removal collapses the structure. That, not bird variety, is what makes a shot feel clever.
+
+---
+
+## Wave 5 — art, audio, progress, polish — ⬜
+
+- [ ] Procedural art + artwork-JSON drop-in
+- [ ] Progress via `/puzzles/angrybirds/{progress,complete}`, per-level best/stars in `ab-best-N` / `ab-stars-N`
+- [ ] Match history — use `{ slug, score, opponentScores, result }`. ⚠️ Goo Tower gets this **wrong** (`GooTowerGame.js:879-881`); copy `RushHourGame.js:513-516` instead.
+- [ ] `tutorial.md` + `hasTutorial: true`
+- [ ] Paint `game-icons.png` frame 92 (row 6, col 2 → 44×44 at x=88, y=264)
+
+---
+
+## How difficulty is decided
+
+`TUNING` in `AngryBirdsLogic.js` owns damage thresholds and material hp — tune there, not in level files. Star thresholds are **measured** by `tools/genAngryBirds.js` from the bot's achieved score, never hand-authored (same discipline as Excitebike's `qualifyMs`).
+
+## Sources for original-game behaviour
+
+- Rovio *Angry Birds* (2009) — material behaviour, bird abilities, 5,000/pig and 10,000/unused-bird scoring.
+- Episode structure: Poached Eggs, Mighty Hoax, Danger Above — 21 levels each.
diff --git a/src/games/angrybirds/AngryBirdsPhysics.js b/src/games/angrybirds/AngryBirdsPhysics.js
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+// Angry Birds — rigid-body physics. Zero imports, deterministic, Node-testable.
+//
+// Generic 2D rigid-body solver: it knows about convex polygons and circles and
+// nothing at all about birds, pigs or scoring. AngryBirdsLogic.js layers the
+// game on top.
+//
+// ── WHY A BESPOKE SOLVER ────────────────────────────────────────────────────
+// Matter.js ships inside the CDN Phaser build and would have worked in the
+// browser, but it cannot be imported in bare Node and is not reproducible.
+// This repo's whole quality apparatus — tools/verifyAngryBirds.js, the level
+// generator's MEASURED star thresholds, and the editor's winnability gate —
+// depends on replaying a shot headlessly and getting the same answer twice.
+//
+// Neither existing engine could be extended into this. PeggleLogic collides a
+// moving circle against STATIC pegs with no rotation and no persistent
+// contacts; GooTowerLogic has no angular state anywhere, because its rigidity
+// is emergent from triangulation. A toppling tower of boxes needs both
+// rotation and lasting contacts, so this is new code.
+//
+// ── THE THREE THINGS THAT MAKE STACKS STAND UP ──────────────────────────────
+//  1. TWO-POINT MANIFOLDS. A single contact point cannot resist rotation, so a
+//     box resting on a box rocks forever. Reference-face clipping yields up to
+//     2 points per pair, which is what makes a face-to-face rest contact rigid.
+//  2. WARM STARTING. Each contact point remembers last substep's accumulated
+//     impulse — keyed by a FEATURE ID that survives across frames, not by array
+//     position — and reapplies it before iterating. Without it a 6-box tower
+//     visibly sags every frame because the solver spends all its iterations
+//     rediscovering gravity from zero.
+//  3. ISLAND SLEEPING. Bodies are grouped by contact into islands; an island
+//     sleeps only when EVERY member has been slow for SLEEP_TIME. Per-body
+//     sleeping would let half a tower freeze while the other half moves.
+//     Sleeping is load-bearing three times over: stack stability, perf, and the
+//     "shot is finished" test the rules layer waits on.
+//
+// ── UNITS AND CONVENTIONS ───────────────────────────────────────────────────
+// Pixels, seconds, radians. Y IS DOWN (screen convention). Polygon winding is
+// normalized on insert so the shoelace area is positive; the outward normal of
+// edge v[i]->v[i+1] is then (e.y, -e.x). Contact normals point from A to B.
+//
+// Determinism rules, all load-bearing:
+//   * bodies and contacts are always iterated in ascending id order;
+//   * no Math.random() anywhere — callers pass a seeded rng if they need one;
+//   * no Date/performance reads;
+//   * nothing that affects the result may depend on Map/Set iteration order —
+//     broadphase pairs are sorted by (aId, bId) and the solver walks that list.
+
+export const PHYS = {
+  SUBSTEP_DT: 1 / 240,
+  VEL_ITERS: 8,           // sequential-impulse passes per substep
+  GRAVITY: 1400,          // px/s²
+  BAUMGARTE: 0.25,        // fraction of excess penetration removed per substep
+  SLOP: 0.5,              // allowed penetration, px — stops resting contacts buzzing
+  REST_THRESHOLD: 120,    // approach speed below which restitution is ignored
+  MAX_SPEED: 2400,        // px/s
+  MAX_OMEGA: 40,          // rad/s
+  LINEAR_DAMPING: 0.002,
+  ANGULAR_DAMPING: 0.004,
+  SLEEP_LIN: 14,          // px/s
+  SLEEP_ANG: 0.14,        // rad/s
+  SLEEP_TIME: 0.5,        // s below both thresholds before an island sleeps
+  GRID_CELL: 96,          // broadphase cell size, px
+  MIN_HALF_EXTENT: 12,    // smallest half-extent any body may have (anti-tunnel)
+};
+
+// ── Small math helpers ──────────────────────────────────────────────────────
+
+const cross = (ax, ay, bx, by) => ax * by - ay * bx;
+const clamp = (v, lo, hi) => (v < lo ? lo : v > hi ? hi : v);
+
+// Numeric composite keys. Body ids are dense and small, so this is exact well
+// past any level we'd author, and it keeps Map lookups off the string path.
+const PAIR_STRIDE = 1 << 20;
+const pairKey = (aId, bId) => aId * PAIR_STRIDE + bId;
+// Grid cells can be negative, so bias into non-negative space before packing.
+const GRID_BIAS = 1 << 14;
+const cellKey = (gx, gy) => (gx + GRID_BIAS) * (1 << 15) + (gy + GRID_BIAS);
+
+// ── Mass properties ─────────────────────────────────────────────────────────
+
+// Signed shoelace area. Positive means the winding matches our normal formula.
+function signedArea(verts) {
+  let a = 0;
+  for (let i = 0; i < verts.length; i += 1) {
+    const [x0, y0] = verts[i];
+    const [x1, y1] = verts[(i + 1) % verts.length];
+    a += x0 * y1 - x1 * y0;
+  }
+  return a * 0.5;
+}
+
+// Area, centroid and second moment of a convex polygon, integrated over the
+// triangle fan from the origin. Inertia comes out about the ORIGIN, so it is
+// shifted to the centroid with the parallel-axis theorem before returning.
+function polyMassData(verts, density) {
+  let area = 0;
+  let cx = 0;
+  let cy = 0;
+  let inertia = 0;
+  for (let i = 0; i < verts.length; i += 1) {
+    const [x0, y0] = verts[i];
+    const [x1, y1] = verts[(i + 1) % verts.length];
+    const c = x0 * y1 - x1 * y0;
+    area += c;
+    cx += (x0 + x1) * c;
+    cy += (y0 + y1) * c;
+    inertia += c * (x0 * x0 + x0 * x1 + x1 * x1 + y0 * y0 + y0 * y1 + y1 * y1);
+  }
+  area *= 0.5;
+  const inv6A = 1 / (6 * area);
+  cx *= inv6A;
+  cy *= inv6A;
+  const mass = density * Math.abs(area);
+  let I = density * Math.abs(inertia) / 12;
+  I -= mass * (cx * cx + cy * cy);   // parallel axis: origin -> centroid
+  return { mass, cx, cy, I: Math.max(I, 1e-6) };
+}
+
+// ── World ───────────────────────────────────────────────────────────────────
+
+export function createWorld(opts = {}) {
+  return {
+    bodies: [],
+    byId: new Map(),
+    // Keyed by pairKey(a,b) — a NUMBER, not a string. Contact lookup runs a few
+    // thousand times a substep and string keys dominated the profile.
+    contacts: new Map(),
+    // Rebuilt in pair order each substep; the solver iterates this, never the
+    // Map, so nothing depends on Map insertion history.
+    contactList: [],
+    nextId: 1,
+    gravity: opts.gravity ?? PHYS.GRAVITY,
+    accum: 0,
+    time: 0,
+  };
+}
+
+function addBody(world, body) {
+  body.id = world.nextId;
+  world.nextId += 1;
+  world.bodies.push(body);
+  world.byId.set(body.id, body);
+  return body;
+}
+
+function baseBody(o) {
+  return {
+    id: 0,
+    x: o.x, y: o.y, angle: o.angle ?? 0,
+    vx: 0, vy: 0, omega: 0,
+    // Pseudo-velocity for the split-impulse position solve. Accumulated during
+    // the bias pass, added into the position integration, then zeroed. It never
+    // survives a substep, so it can't inject energy into the real velocity.
+    psx: 0, psy: 0, psw: 0,
+    friction: o.friction ?? 0.5,
+    restitution: o.restitution ?? 0.1,
+    isStatic: !!o.isStatic,
+    sleeping: false,
+    sleepTimer: 0,
+    // Free-form pointer the rules layer hangs blocks/pigs/birds off. The solver
+    // never reads it, which is what keeps this file game-agnostic.
+    userData: o.userData ?? null,
+    aabb: { minx: 0, miny: 0, maxx: 0, maxy: 0 },
+  };
+}
+
+/** Convex polygon from local-space verts (any winding, recentred on centroid). */
+export function addPoly(world, o) {
+  let verts = o.verts.map(([x, y]) => [x, y]);
+  if (signedArea(verts) < 0) verts.reverse();
+  const md = polyMassData(verts, o.density ?? 1);
+  // Recentre so the body origin IS the centre of mass; the solver assumes it.
+  verts = verts.map(([x, y]) => [x - md.cx, y - md.cy]);
+
+  const b = baseBody(o);
+  b.kind = 'poly';
+  b.verts = verts;
+  b.normals = verts.map(([x0, y0], i) => {
+    const [x1, y1] = verts[(i + 1) % verts.length];
+    const ex = x1 - x0;
+    const ey = y1 - y0;
+    const len = Math.hypot(ex, ey) || 1;
+    return [ey / len, -ex / len];
+  });
+  b.wverts = verts.map(() => [0, 0]);
+  b.wnormals = verts.map(() => [0, 0]);
+  b.radius = Math.max(...verts.map(([x, y]) => Math.hypot(x, y)));
+  b.invMass = o.isStatic ? 0 : 1 / md.mass;
+  b.invI = o.isStatic ? 0 : 1 / md.I;
+  b.mass = o.isStatic ? Infinity : md.mass;
+  addBody(world, b);
+  syncTransform(b);
+  return b;
+}
+
+/** Axis-aligned-at-rest box helper; `angle` still rotates it. */
+export function addBox(world, o) {
+  const hw = o.w / 2;
+  const hh = o.h / 2;
+  return addPoly(world, {
+    ...o,
+    verts: [[-hw, -hh], [hw, -hh], [hw, hh], [-hw, hh]],
+  });
+}
+
+export function addCircle(world, o) {
+  const b = baseBody(o);
+  b.kind = 'circle';
+  b.radius = o.r;
+  const mass = (o.density ?? 1) * Math.PI * o.r * o.r;
+  b.invMass = o.isStatic ? 0 : 1 / mass;
+  b.invI = o.isStatic ? 0 : 1 / (0.5 * mass * o.r * o.r);
+  b.mass = o.isStatic ? Infinity : mass;
+  addBody(world, b);
+  syncTransform(b);
+  return b;
+}
+
+export function removeBody(world, body) {
+  const i = world.bodies.indexOf(body);
+  if (i >= 0) world.bodies.splice(i, 1);
+  world.byId.delete(body.id);
+  for (const [key, c] of [...world.contacts]) {
+    if (c.aId === body.id || c.bId === body.id) world.contacts.delete(key);
+  }
+  world.contactList = world.contactList.filter((c) => c.aId !== body.id && c.bId !== body.id);
+}
+
+// Recompute world-space verts/normals and the AABB after a transform change.
+function syncTransform(b) {
+  const c = Math.cos(b.angle);
+  const s = Math.sin(b.angle);
+  if (b.kind === 'poly') {
+    let minx = Infinity; let miny = Infinity; let maxx = -Infinity; let maxy = -Infinity;
+    for (let i = 0; i < b.verts.length; i += 1) {
+      const [lx, ly] = b.verts[i];
+      const wx = b.x + lx * c - ly * s;
+      const wy = b.y + lx * s + ly * c;
+      b.wverts[i][0] = wx;
+      b.wverts[i][1] = wy;
+      const [nx, ny] = b.normals[i];
+      b.wnormals[i][0] = nx * c - ny * s;
+      b.wnormals[i][1] = nx * s + ny * c;
+      if (wx < minx) minx = wx;
+      if (wy < miny) miny = wy;
+      if (wx > maxx) maxx = wx;
+      if (wy > maxy) maxy = wy;
+    }
+    b.aabb.minx = minx; b.aabb.miny = miny; b.aabb.maxx = maxx; b.aabb.maxy = maxy;
+  } else {
+    b.aabb.minx = b.x - b.radius; b.aabb.miny = b.y - b.radius;
+    b.aabb.maxx = b.x + b.radius; b.aabb.maxy = b.y + b.radius;
+  }
+}
+
+export function wakeBody(b) {
+  if (b.isStatic) return;
+  b.sleeping = false;
+  b.sleepTimer = 0;
+}
+
+export function applyImpulse(b, ix, iy, px, py) {
+  if (b.isStatic) return;
+  wakeBody(b);
+  b.vx += ix * b.invMass;
+  b.vy += iy * b.invMass;
+  if (px !== undefined) b.omega += cross(px - b.x, py - b.y, ix, iy) * b.invI;
+}
+
+// ── Broadphase ──────────────────────────────────────────────────────────────
+
+// Uniform grid over AABBs, rebuilt each substep. Bodies here are large relative
+// to their per-substep travel, so a rebuild is cheaper than incremental upkeep.
+function broadphase(world) {
+  const cell = PHYS.GRID_CELL;
+  const grid = new Map();
+  const bodies = world.bodies;
+  for (let i = 0; i < bodies.length; i += 1) {
+    const b = bodies[i];
+    const x0 = Math.floor(b.aabb.minx / cell);
+    const x1 = Math.floor(b.aabb.maxx / cell);
+    const y0 = Math.floor(b.aabb.miny / cell);
+    const y1 = Math.floor(b.aabb.maxy / cell);
+    for (let gx = x0; gx <= x1; gx += 1) {
+      for (let gy = y0; gy <= y1; gy += 1) {
+        const key = cellKey(gx, gy);
+        let bucket = grid.get(key);
+        if (!bucket) { bucket = []; grid.set(key, bucket); }
+        bucket.push(b);
+      }
+    }
+  }
+
+  const pairs = [];
+  const seen = new Set();
+  for (const bucket of grid.values()) {
+    for (let i = 0; i < bucket.length; i += 1) {
+      for (let j = i + 1; j < bucket.length; j += 1) {
+        let a = bucket[i];
+        let b = bucket[j];
+        if (a.id > b.id) { const t = a; a = b; b = t; }
+        // A pair where neither side can move produces no useful contact. A
+        // sleeping body against a static one is already at rest by definition.
+        if (a.isStatic && b.isStatic) continue;
+        if (a.sleeping && b.sleeping) continue;
+        if (a.sleeping && b.isStatic) continue;
+        if (b.sleeping && a.isStatic) continue;
+        const key = pairKey(a.id, b.id);
+        if (seen.has(key)) continue;
+        seen.add(key);
+        if (a.aabb.maxx < b.aabb.minx || b.aabb.maxx < a.aabb.minx) continue;
+        if (a.aabb.maxy < b.aabb.miny || b.aabb.maxy < a.aabb.miny) continue;
+        pairs.push(a, b);   // flat, to avoid a per-pair array allocation
+      }
+    }
+  }
+  // Sorted so the solve order never depends on Map/Set iteration order.
+  const order = [];
+  for (let i = 0; i < pairs.length; i += 2) order.push(i);
+  order.sort((p, q) => (pairs[p].id - pairs[q].id) || (pairs[p + 1].id - pairs[q + 1].id));
+  const sorted = [];
+  for (const i of order) sorted.push(pairs[i], pairs[i + 1]);
+  return sorted;
+}
+
+// ── Narrowphase ─────────────────────────────────────────────────────────────
+
+// Largest separation of B's verts from any of A's faces. Negative => overlap.
+function maxSeparation(a, b) {
+  let best = -Infinity;
+  let bestFace = 0;
+  for (let i = 0; i < a.wverts.length; i += 1) {
+    const [nx, ny] = a.wnormals[i];
+    const [vx, vy] = a.wverts[i];
+    // Support point of B in direction -n: the deepest vert against this face.
+    let lowest = Infinity;
+    for (let j = 0; j < b.wverts.length; j += 1) {
+      const d = (b.wverts[j][0] - vx) * nx + (b.wverts[j][1] - vy) * ny;
+      if (d < lowest) lowest = d;
+    }
+    if (lowest > best) { best = lowest; bestFace = i; }
+  }
+  return { sep: best, face: bestFace };
+}
+
+// The face of `inc` most anti-parallel to the reference normal.
+function incidentFace(inc, refNx, refNy) {
+  let best = Infinity;
+  let bestFace = 0;
+  for (let i = 0; i < inc.wnormals.length; i += 1) {
+    const d = inc.wnormals[i][0] * refNx + inc.wnormals[i][1] * refNy;
+    if (d < best) { best = d; bestFace = i; }
+  }
+  return bestFace;
+}
+
+// Clip a segment against a half-plane, keeping the portion where
+// dot(n, p) - offset <= 0. Feature ids ride along so warm starting can match
+// points across frames even when clipping order changes.
+function clipSegment(pts, nx, ny, offset) {
+  const out = [];
+  const d0 = pts[0].x * nx + pts[0].y * ny - offset;
+  const d1 = pts[1].x * nx + pts[1].y * ny - offset;
+  if (d0 <= 0) out.push(pts[0]);
+  if (d1 <= 0) out.push(pts[1]);
+  if (d0 * d1 < 0) {
+    const t = d0 / (d0 - d1);
+    out.push({
+      x: pts[0].x + t * (pts[1].x - pts[0].x),
+      y: pts[0].y + t * (pts[1].y - pts[0].y),
+      fid: d0 > 0 ? pts[1].fid : pts[0].fid,
+    });
+  }
+  return out;
+}
+
+function collidePolyPoly(a, b) {
+  const sa = maxSeparation(a, b);
+  if (sa.sep > 0) return null;
+  const sb = maxSeparation(b, a);
+  if (sb.sep > 0) return null;
+
+  // Prefer A as reference unless B is clearly deeper — the small bias keeps the
+  // choice stable frame to frame, which keeps feature ids (and warm starting)
+  // stable for a resting contact.
+  let ref = a; let inc = b; let refFace = sa.face; let flip = false;
+  if (sb.sep > sa.sep + 0.1 * Math.abs(sa.sep) + 0.01) {
+    ref = b; inc = a; refFace = sb.face; flip = true;
+  }
+
+  const [rnx, rny] = ref.wnormals[refFace];
+  const rv0 = ref.wverts[refFace];
+  const rv1 = ref.wverts[(refFace + 1) % ref.wverts.length];
+
+  const incFace = incidentFace(inc, rnx, rny);
+  const iv0 = inc.wverts[incFace];
+  const iv1 = inc.wverts[(incFace + 1) % inc.wverts.length];
+
+  // Tangent of the reference face; clip the incident edge to its side planes.
+  const tx = rv1[0] - rv0[0];
+  const ty = rv1[1] - rv0[1];
+  const tlen = Math.hypot(tx, ty) || 1;
+  const utx = tx / tlen;
+  const uty = ty / tlen;
+
+  let pts = [
+    { x: iv0[0], y: iv0[1], fid: (refFace << 8) | incFace },
+    { x: iv1[0], y: iv1[1], fid: (refFace << 8) | ((incFace + 1) % inc.wverts.length) },
+  ];
+  pts = clipSegment(pts, -utx, -uty, -(rv0[0] * utx + rv0[1] * uty));
+  if (pts.length < 2) return null;
+  pts = clipSegment(pts, utx, uty, rv1[0] * utx + rv1[1] * uty);
+  if (pts.length < 2) return null;
+
+  const offset = rv0[0] * rnx + rv0[1] * rny;
+  const points = [];
+  for (const p of pts) {
+    const sep = p.x * rnx + p.y * rny - offset;
+    if (sep <= 0) points.push({ x: p.x, y: p.y, sep, fid: p.fid | (flip ? 0x10000 : 0) });
+  }
+  if (!points.length) return null;
+
+  // Normal must always point A -> B.
+  return { nx: flip ? -rnx : rnx, ny: flip ? -rny : rny, points };
+}
+
+function collideCirclePoly(c, p, circleIsA) {
+  // Work in the polygon's local frame so the face tests are cheap.
+  const cs = Math.cos(-p.angle);
+  const sn = Math.sin(-p.angle);
+  const dx = c.x - p.x;
+  const dy = c.y - p.y;
+  const lx = dx * cs - dy * sn;
+  const ly = dx * sn + dy * cs;
+
+  let best = -Infinity;
+  let bestFace = 0;
+  for (let i = 0; i < p.verts.length; i += 1) {
+    const [nx, ny] = p.normals[i];
+    const [vx, vy] = p.verts[i];
+    const d = (lx - vx) * nx + (ly - vy) * ny;
+    if (d > c.radius) return null;
+    if (d > best) { best = d; bestFace = i; }
+  }
+
+  const [v0x, v0y] = p.verts[bestFace];
+  const [v1x, v1y] = p.verts[(bestFace + 1) % p.verts.length];
+  let nlx; let nly; let sep;
+
+  if (best < 1e-6) {
+    // Centre is inside the polygon — push straight out along the closest face.
+    [nlx, nly] = p.normals[bestFace];
+    sep = best - c.radius;
+  } else {
+    // Voronoi regions: nearest to v0, to v1, or to the face interior.
+    const ex = v1x - v0x;
+    const ey = v1y - v0y;
+    const t = clamp(((lx - v0x) * ex + (ly - v0y) * ey) / (ex * ex + ey * ey), 0, 1);
+    const px = v0x + ex * t;
+    const py = v0y + ey * t;
+    const ddx = lx - px;
+    const ddy = ly - py;
+    const dist = Math.hypot(ddx, ddy);
+    if (dist > c.radius) return null;
+    if (dist < 1e-9) { [nlx, nly] = p.normals[bestFace]; } else { nlx = ddx / dist; nly = ddy / dist; }
+    sep = dist - c.radius;
+  }
+
+  // Back to world space. Local normal points polygon -> circle.
+  const wc = Math.cos(p.angle);
+  const ws = Math.sin(p.angle);
+  const nwx = nlx * wc - nly * ws;
+  const nwy = nlx * ws + nly * wc;
+  const contactX = c.x - nwx * (c.radius + sep * 0.5);
+  const contactY = c.y - nwy * (c.radius + sep * 0.5);
+
+  // Caller's A is `circleIsA ? c : p`; normal must run A -> B.
+  const sign = circleIsA ? -1 : 1;
+  return {
+    nx: nwx * sign, ny: nwy * sign,
+    points: [{ x: contactX, y: contactY, sep, fid: 1 }],
+  };
+}
+
+function collideCircleCircle(a, b) {
+  const dx = b.x - a.x;
+  const dy = b.y - a.y;
+  const r = a.radius + b.radius;
+  const d2 = dx * dx + dy * dy;
+  if (d2 >= r * r) return null;
+  const d = Math.sqrt(d2);
+  let nx; let ny;
+  if (d < 1e-9) { nx = 0; ny = -1; } else { nx = dx / d; ny = dy / d; }
+  return {
+    nx, ny,
+    points: [{ x: a.x + nx * a.radius, y: a.y + ny * a.radius, sep: d - r, fid: 1 }],
+  };
+}
+
+function collide(a, b) {
+  if (a.kind === 'circle' && b.kind === 'circle') return collideCircleCircle(a, b);
+  if (a.kind === 'circle') return collideCirclePoly(a, b, true);
+  if (b.kind === 'circle') return collideCirclePoly(b, a, false);
+  return collidePolyPoly(a, b);
+}
+
+// ── Contact bookkeeping ─────────────────────────────────────────────────────
+
+// Rebuild manifolds, carrying accumulated impulses across from last substep by
+// feature id. This is the warm-starting half of stack stability; matching by
+// array index instead would scramble impulses the moment a clip order flips.
+function updateContacts(world, pairs) {
+  const live = new Set();
+  const list = [];
+  for (let pi = 0; pi < pairs.length; pi += 2) {
+    const a = pairs[pi];
+    const b = pairs[pi + 1];
+    const m = collide(a, b);
+    const key = pairKey(a.id, b.id);
+    if (!m) { world.contacts.delete(key); continue; }
+    live.add(key);
+
+    const prev = world.contacts.get(key);
+    const points = m.points.map((p) => {
+      const old = prev?.points.find((q) => q.fid === p.fid);
+      return {
+        x: p.x, y: p.y, sep: p.sep, fid: p.fid,
+        pn: old?.pn ?? 0, pt: old?.pt ?? 0,
+        pnBias: 0,                     // never warm-started: position error is transient
+        massNormal: 0, massTangent: 0, bias: 0, restTarget: 0,
+        rax: 0, ray: 0, rbx: 0, rby: 0,
+      };
+    });
+    const contact = {
+      aId: a.id, bId: b.id, a, b,
+      nx: m.nx, ny: m.ny,
+      friction: Math.sqrt(a.friction * b.friction),
+      restitution: Math.max(a.restitution, b.restitution),
+      points,
+      maxImpulse: 0,   // peak |pn| this substep — the damage signal the rules read
+    };
+    world.contacts.set(key, contact);
+    list.push(contact);
+  }
+  for (const [key] of [...world.contacts]) {
+    if (!live.has(key)) world.contacts.delete(key);
+  }
+  // Pairs arrive pre-sorted by (aId, bId), so this list is already in the
+  // canonical solve order and needs no further sorting.
+  world.contactList = list;
+}
+
+// The solver's contact iteration order. Never iterate world.contacts directly:
+// Map order depends on insertion history, which would make the sim depend on
+// the order bodies happened to be created in.
+function orderedContacts(world) {
+  return world.contactList;
+}
+
+function prestep(world, h) {
+  const invH = 1 / h;
+  for (const c of orderedContacts(world)) {
+    const a = c.a;
+    const b = c.b;
+    const { nx, ny } = c;
+    const tx = -ny;
+    const ty = nx;
+
+    for (const p of c.points) {
+      p.rax = p.x - a.x; p.ray = p.y - a.y;
+      p.rbx = p.x - b.x; p.rby = p.y - b.y;
+
+      const rnA = cross(p.rax, p.ray, nx, ny);
+      const rnB = cross(p.rbx, p.rby, nx, ny);
+      p.massNormal = 1 / (a.invMass + b.invMass + a.invI * rnA * rnA + b.invI * rnB * rnB);
+
+      const rtA = cross(p.rax, p.ray, tx, ty);
+      const rtB = cross(p.rbx, p.rby, tx, ty);
+      p.massTangent = 1 / (a.invMass + b.invMass + a.invI * rtA * rtA + b.invI * rtB * rtB);
+
+      // Position error is corrected by a SEPARATE pseudo-velocity pass (split
+      // impulse), not by biasing the real velocity. With plain Baumgarte the
+      // steady-state penetration is proportional to the load, so the bottom
+      // contact of a 10-box tower sinks ~10x deeper than the top one and the
+      // stack visibly sags. Driving position through pseudo-velocities removes
+      // a fixed fraction of the excess per substep regardless of load, and the
+      // correction never leaks into the real velocity as bounce energy.
+      p.bias = -PHYS.BAUMGARTE * invH * Math.min(0, p.sep + PHYS.SLOP);
+      p.pnBias = 0;
+
+      // Restitution, sampled once from the APPROACH velocity. Sampling it every
+      // iteration would let a resting box slowly bounce itself apart.
+      const rvx = (b.vx - p.rby * b.omega) - (a.vx - p.ray * a.omega);
+      const rvy = (b.vy + p.rbx * b.omega) - (a.vy + p.rax * a.omega);
+      const vn = rvx * nx + rvy * ny;
+      p.restTarget = vn < -PHYS.REST_THRESHOLD ? -c.restitution * vn : 0;
+    }
+  }
+  for (const b of world.bodies) { b.psx = 0; b.psy = 0; b.psw = 0; }
+}
+
+function warmStart(world) {
+  for (const c of orderedContacts(world)) {
+    const a = c.a;
+    const b = c.b;
+    const { nx, ny } = c;
+    const tx = -ny;
+    const ty = nx;
+    for (const p of c.points) {
+      const ix = p.pn * nx + p.pt * tx;
+      const iy = p.pn * ny + p.pt * ty;
+      if (!a.isStatic) {
+        a.vx -= ix * a.invMass; a.vy -= iy * a.invMass;
+        a.omega -= cross(p.rax, p.ray, ix, iy) * a.invI;
+      }
+      if (!b.isStatic) {
+        b.vx += ix * b.invMass; b.vy += iy * b.invMass;
+        b.omega += cross(p.rbx, p.rby, ix, iy) * b.invI;
+      }
+    }
+  }
+}
+
+function solveVelocities(world) {
+  const contacts = orderedContacts(world);
+  for (let iter = 0; iter < PHYS.VEL_ITERS; iter += 1) {
+    for (const c of contacts) {
+      const a = c.a;
+      const b = c.b;
+      const { nx, ny } = c;
+      const tx = -ny;
+      const ty = nx;
+
+      for (const p of c.points) {
+        // Normal impulse. Accumulate then clamp to >= 0, applying only the
+        // delta — clamping the per-iteration impulse instead would let a
+        // contact pull bodies together.
+        let rvx = (b.vx - p.rby * b.omega) - (a.vx - p.ray * a.omega);
+        let rvy = (b.vy + p.rbx * b.omega) - (a.vy + p.rax * a.omega);
+        const vn = rvx * nx + rvy * ny;
+        let dPn = p.massNormal * (-vn + p.restTarget);
+        const pn0 = p.pn;
+        p.pn = Math.max(pn0 + dPn, 0);
+        dPn = p.pn - pn0;
+
+        let ix = dPn * nx;
+        let iy = dPn * ny;
+        if (!a.isStatic) {
+          a.vx -= ix * a.invMass; a.vy -= iy * a.invMass;
+          a.omega -= cross(p.rax, p.ray, ix, iy) * a.invI;
+        }
+        if (!b.isStatic) {
+          b.vx += ix * b.invMass; b.vy += iy * b.invMass;
+          b.omega += cross(p.rbx, p.rby, ix, iy) * b.invI;
+        }
+
+        // Split-impulse position pass, run on pseudo-velocities only.
+        const pvx = (b.psx - p.rby * b.psw) - (a.psx - p.ray * a.psw);
+        const pvy = (b.psy + p.rbx * b.psw) - (a.psy + p.rax * a.psw);
+        const pvn = pvx * nx + pvy * ny;
+        let dPb = p.massNormal * (-pvn + p.bias);
+        const pb0 = p.pnBias;
+        p.pnBias = Math.max(pb0 + dPb, 0);
+        dPb = p.pnBias - pb0;
+
+        const bx = dPb * nx;
+        const by = dPb * ny;
+        if (!a.isStatic) {
+          a.psx -= bx * a.invMass; a.psy -= by * a.invMass;
+          a.psw -= cross(p.rax, p.ray, bx, by) * a.invI;
+        }
+        if (!b.isStatic) {
+          b.psx += bx * b.invMass; b.psy += by * b.invMass;
+          b.psw += cross(p.rbx, p.rby, bx, by) * b.invI;
+        }
+
+        // Coulomb friction, clamped against the ACCUMULATED normal impulse.
+        rvx = (b.vx - p.rby * b.omega) - (a.vx - p.ray * a.omega);
+        rvy = (b.vy + p.rbx * b.omega) - (a.vy + p.rax * a.omega);
+        const vt = rvx * tx + rvy * ty;
+        let dPt = p.massTangent * -vt;
+        const maxPt = c.friction * p.pn;
+        const pt0 = p.pt;
+        p.pt = clamp(pt0 + dPt, -maxPt, maxPt);
+        dPt = p.pt - pt0;
+
+        ix = dPt * tx;
+        iy = dPt * ty;
+        if (!a.isStatic) {
+          a.vx -= ix * a.invMass; a.vy -= iy * a.invMass;
+          a.omega -= cross(p.rax, p.ray, ix, iy) * a.invI;
+        }
+        if (!b.isStatic) {
+          b.vx += ix * b.invMass; b.vy += iy * b.invMass;
+          b.omega += cross(p.rbx, p.rby, ix, iy) * b.invI;
+        }
+      }
+    }
+  }
+  for (const c of contacts) {
+    let peak = 0;
+    for (const p of c.points) if (p.pn > peak) peak = p.pn;
+    c.maxImpulse = peak;
+  }
+}
+
+// ── Islands and sleeping ────────────────────────────────────────────────────
+
+// Union-find over contacts between dynamic bodies. An island sleeps only when
+// every member has been slow for SLEEP_TIME — per-body sleeping would freeze
+// half a tower while the rest still moves.
+function updateSleeping(world, h) {
+  const parent = new Map();
+  const find = (x) => {
+    let r = x;
+    while (parent.get(r) !== r) r = parent.get(r);
+    while (parent.get(x) !== r) { const nx = parent.get(x); parent.set(x, r); x = nx; }
+    return r;
+  };
+  const union = (x, y) => {
+    const rx = find(x);
+    const ry = find(y);
+    if (rx !== ry) parent.set(rx > ry ? rx : ry, rx > ry ? ry : rx);
+  };
+
+  for (const b of world.bodies) if (!b.isStatic) parent.set(b.id, b.id);
+  for (const c of orderedContacts(world)) {
+    const a = c.a;
+    const b = c.b;
+    if (!a.isStatic && !b.isStatic) union(a.id, b.id);
+  }
+
+  // Per-body slow timer.
+  for (const b of world.bodies) {
+    if (b.isStatic || b.sleeping) continue;
+    const slow = Math.hypot(b.vx, b.vy) < PHYS.SLEEP_LIN && Math.abs(b.omega) < PHYS.SLEEP_ANG;
+    b.sleepTimer = slow ? b.sleepTimer + h : 0;
+  }
+
+  // An island's timer is its slowest member's.
+  const islandTimer = new Map();
+  for (const b of world.bodies) {
+    if (b.isStatic) continue;
+    const root = find(b.id);
+    const t = b.sleeping ? Infinity : b.sleepTimer;
+    const cur = islandTimer.get(root);
+    if (cur === undefined || t < cur) islandTimer.set(root, t);
+  }
+
+  for (const b of world.bodies) {
+    if (b.isStatic) continue;
+    const t = islandTimer.get(find(b.id)) ?? 0;
+    if (t >= PHYS.SLEEP_TIME) {
+      b.sleeping = true;
+      b.vx = 0; b.vy = 0; b.omega = 0;
+    } else if (t < PHYS.SLEEP_TIME && b.sleeping) {
+      // A neighbour woke up; the whole island comes with it.
+      b.sleeping = false;
+      b.sleepTimer = 0;
+    }
+  }
+}
+
+// ── Integration ─────────────────────────────────────────────────────────────
+
+function integrateVelocities(world, h) {
+  for (const b of world.bodies) {
+    if (b.isStatic || b.sleeping) continue;
+    b.vy += world.gravity * h;
+    b.vx *= 1 - PHYS.LINEAR_DAMPING;
+    b.vy *= 1 - PHYS.LINEAR_DAMPING;
+    b.omega *= 1 - PHYS.ANGULAR_DAMPING;
+  }
+}
+
+function integratePositions(world, h) {
+  for (const b of world.bodies) {
+    if (b.isStatic || b.sleeping) continue;
+    const sp = Math.hypot(b.vx, b.vy);
+    if (sp > PHYS.MAX_SPEED) { const k = PHYS.MAX_SPEED / sp; b.vx *= k; b.vy *= k; }
+    b.omega = clamp(b.omega, -PHYS.MAX_OMEGA, PHYS.MAX_OMEGA);
+    // Pseudo-velocity moves the body but is then discarded, so position error
+    // is repaired without the correction showing up as momentum next substep.
+    b.x += (b.vx + b.psx) * h;
+    b.y += (b.vy + b.psy) * h;
+    b.angle += (b.omega + b.psw) * h;
+    b.psx = 0; b.psy = 0; b.psw = 0;
+    syncTransform(b);
+  }
+}
+
+// ── The frame ───────────────────────────────────────────────────────────────
+
+export function substep(world, h) {
+  integrateVelocities(world, h);
+  const pairs = broadphase(world);
+  updateContacts(world, pairs);
+  prestep(world, h);
+  warmStart(world);
+  solveVelocities(world);
+  integratePositions(world, h);
+  updateSleeping(world, h);
+  world.time += h;
+}
+
+/**
+ * Advance by `dt` seconds in whole fixed substeps. Any leftover is carried in
+ * world.accum, which is what makes 1/60 and 1/120 frames produce identical
+ * trajectories — the property tools/verifyAngryBirds.js asserts.
+ */
+export function step(world, dt) {
+  world.accum += Math.min(dt, 0.05);   // a backgrounded tab must not teleport
+  let steps = 0;
+  while (world.accum >= PHYS.SUBSTEP_DT && steps < 16) {
+    substep(world, PHYS.SUBSTEP_DT);
+    world.accum -= PHYS.SUBSTEP_DT;
+    steps += 1;
+  }
+  return steps;
+}
+
+/** True when nothing is moving — the rules layer's "shot is over" test. */
+export function isSettled(world) {
+  for (const b of world.bodies) {
+    if (b.isStatic) continue;
+    if (!b.sleeping) return false;
+  }
+  return true;
+}
+
+/** Peak normal impulse seen on each body this substep, keyed by body id. */
+export function contactImpulses(world) {
+  const out = new Map();
+  for (const c of world.contacts.values()) {
+    if (c.maxImpulse <= 0) continue;
+    for (const id of [c.aId, c.bId]) {
+      const cur = out.get(id) ?? 0;
+      if (c.maxImpulse > cur) out.set(id, c.maxImpulse);
+    }
+  }
+  return out;
+}
+
+/** Radial impulse + falloff, used by Bomb and TNT. Returns bodies affected. */
+export function applyExplosion(world, x, y, radius, power) {
+  const hit = [];
+  for (const b of world.bodies) {
+    if (b.isStatic) continue;
+    const dx = b.x - x;
+    const dy = b.y - y;
+    const d = Math.hypot(dx, dy);
+    if (d > radius) continue;
+    const falloff = 1 - d / radius;
+    const nx = d < 1e-6 ? 0 : dx / d;
+    const ny = d < 1e-6 ? -1 : dy / d;
+    const j = power * falloff * b.mass;
+    applyImpulse(b, nx * j, ny * j, b.x, b.y);
+    hit.push({ body: b, falloff, dist: d });
+  }
+  return hit;
+}
+
+// ── Determinism helpers ─────────────────────────────────────────────────────
+
+export function cloneWorld(world) {
+  const copy = createWorld({ gravity: world.gravity });
+  copy.nextId = world.nextId;
+  copy.accum = world.accum;
+  copy.time = world.time;
+  for (const b of world.bodies) {
+    const nb = { ...b, aabb: { ...b.aabb } };
+    if (b.kind === 'poly') {
+      nb.verts = b.verts.map((v) => [v[0], v[1]]);
+      nb.normals = b.normals.map((v) => [v[0], v[1]]);
+      nb.wverts = b.wverts.map((v) => [v[0], v[1]]);
+      nb.wnormals = b.wnormals.map((v) => [v[0], v[1]]);
+    }
+    copy.bodies.push(nb);
+    copy.byId.set(nb.id, nb);
+  }
+  // Contacts cache direct body references for speed, so a shallow spread would
+  // leave the clone's contacts pointing at the ORIGINAL world's bodies — the
+  // clone would silently drive the thing it was supposed to leave untouched.
+  // Rewire every reference through the copy's id map.
+  for (const [key, c] of world.contacts) {
+    copy.contacts.set(key, {
+      ...c,
+      a: copy.byId.get(c.aId),
+      b: copy.byId.get(c.bId),
+      points: c.points.map((p) => ({ ...p })),
+    });
+  }
+  copy.contactList = world.contactList.map((c) => copy.contacts.get(pairKey(c.aId, c.bId))).filter(Boolean);
+  return copy;
+}
+
+// FNV-1a over the Float64 bit patterns of every body's transform and velocity.
+// Hashing the bits rather than rounded values means a 1-ULP divergence still
+// shows up, which is the point.
+export function hashWorld(world) {
+  const buf = new ArrayBuffer(8);
+  const f64 = new Float64Array(buf);
+  const u32 = new Uint32Array(buf);
+  let h = 0x811c9dc5;
+  const mix = (v) => {
+    f64[0] = v;
+    for (let i = 0; i < 2; i += 1) {
+      h ^= u32[i];
+      h = Math.imul(h, 0x01000193) >>> 0;
+    }
+  };
+  const sorted = [...world.bodies].sort((a, b) => a.id - b.id);
+  for (const b of sorted) {
+    mix(b.x); mix(b.y); mix(b.angle);
+    mix(b.vx); mix(b.vy); mix(b.omega);
+    mix(b.sleeping ? 1 : 0);
+  }
+  return h >>> 0;
+}
+
+/** Run until everything sleeps (or `maxSeconds` elapses). Used by the editor. */
+export function settle(world, maxSeconds = 10) {
+  const limit = Math.ceil(maxSeconds / PHYS.SUBSTEP_DT);
+  for (let i = 0; i < limit; i += 1) {
+    substep(world, PHYS.SUBSTEP_DT);
+    if (isSettled(world)) return true;
+  }
+  return isSettled(world);
+}
diff --git a/tools/verifyAngryBirds.js b/tools/verifyAngryBirds.js
new file mode 100644
index 0000000..a3ad24a
--- /dev/null
+++ b/tools/verifyAngryBirds.js
@@ -0,0 +1,471 @@
+// Headless verification for Angry Birds.
+//   node tools/verifyAngryBirds.js
+// Exits non-zero on any failure.
+//
+// 1. Physics invariants — mass properties, resting contacts, stack stability,
+//    friction, restitution, anti-tunnel bound, explosion falloff.
+// 2. Determinism — seeded replay, frame-rate independence, clone independence.
+// 3. Robustness — random-impulse monkey test for NaN / overspeed / sinking.
+//
+// Rendering, slingshot feel, camera and the editor's Blob export are
+// browser-only and must be smoke-tested manually.
+
+import {
+  PHYS, createWorld, addBox, addPoly, addCircle, removeBody,
+  step, substep, settle, isSettled, applyImpulse, applyExplosion,
+  cloneWorld, hashWorld, contactImpulses,
+} from '../src/games/angrybirds/AngryBirdsPhysics.js';
+
+let failures = 0;
+let passes = 0;
+function check(name, cond, detail = '') {
+  if (cond) { passes += 1; console.log(`  ok  ${name}`); }
+  else { failures += 1; console.error(`FAIL  ${name}${detail ? ` — ${detail}` : ''}`); }
+}
+const near = (a, b, tol) => Math.abs(a - b) <= tol;
+
+function section(title) { console.log(`\n── ${title} ${'─'.repeat(Math.max(0, 60 - title.length))}`); }
+
+// Deterministic RNG for the monkey test (never Math.random — see the header
+// contract in AngryBirdsPhysics.js).
+function mulberry32(seed) {
+  let a = seed >>> 0;
+  return () => {
+    a = (a + 0x6d2b79f5) >>> 0;
+    let t = Math.imul(a ^ (a >>> 15), 1 | a);
+    t = (t + Math.imul(t ^ (t >>> 7), 61 | t)) ^ t;
+    return ((t ^ (t >>> 14)) >>> 0) / 4294967296;
+  };
+}
+
+/** Ground plane spanning the test area. */
+function withGround(world, y = 800) {
+  addBox(world, { x: 600, y: y + 50, w: 4000, h: 100, isStatic: true, friction: 0.7 });
+  return world;
+}
+
+// ── 1. Mass properties ──────────────────────────────────────────────────────
+
+section('1. Mass properties');
+{
+  const w = createWorld();
+  const b = addBox(w, { x: 0, y: 0, w: 40, h: 20, density: 2 });
+  const expectMass = 2 * 40 * 20;
+  check('box mass = density x w x h', near(b.mass, expectMass, 1e-6), `${b.mass} vs ${expectMass}`);
+
+  const expectI = (expectMass * (40 * 40 + 20 * 20)) / 12;
+  check('box inertia = m(w^2+h^2)/12', near(1 / b.invI, expectI, expectI * 1e-6),
+    `${1 / b.invI} vs ${expectI}`);
+
+  const c = addCircle(w, { x: 0, y: 0, r: 10, density: 3 });
+  const cMass = 3 * Math.PI * 100;
+  check('circle mass = density x pi r^2', near(c.mass, cMass, 1e-6), `${c.mass} vs ${cMass}`);
+
+  const s = addBox(w, { x: 0, y: 0, w: 10, h: 10, isStatic: true });
+  check('static body has zero inverse mass', s.invMass === 0 && s.invI === 0);
+}
+{
+  // Winding must be normalized: a CW polygon must produce the same body as CCW.
+  const w = createWorld();
+  const ccw = addPoly(w, { x: 0, y: 0, verts: [[-10, -10], [10, -10], [10, 10], [-10, 10]], density: 1 });
+  const cw = addPoly(w, { x: 0, y: 0, verts: [[-10, 10], [10, 10], [10, -10], [-10, -10]], density: 1 });
+  check('polygon winding normalized', near(ccw.mass, cw.mass, 1e-9) && near(ccw.invI, cw.invI, 1e-12),
+    `${ccw.mass}/${cw.mass}`);
+
+  // Outward normals must point away from the centroid.
+  const outward = ccw.normals.every(([nx, ny], i) => {
+    const [vx, vy] = ccw.verts[i];
+    return vx * nx + vy * ny > 0;
+  });
+  check('polygon normals point outward', outward);
+}
+{
+  // Verts are recentred on the centroid, so an off-centre polygon still
+  // rotates about its true centre of mass.
+  const w = createWorld();
+  const b = addPoly(w, { x: 0, y: 0, verts: [[0, 0], [40, 0], [40, 20], [0, 20]], density: 1 });
+  const cx = b.verts.reduce((s, v) => s + v[0], 0) / b.verts.length;
+  const cy = b.verts.reduce((s, v) => s + v[1], 0) / b.verts.length;
+  check('polygon recentred on centroid', near(cx, 0, 1e-9) && near(cy, 0, 1e-9), `${cx},${cy}`);
+}
+
+// ── 2. Anti-tunnelling bound ────────────────────────────────────────────────
+
+section('2. Anti-tunnelling');
+{
+  const travel = PHYS.MAX_SPEED * PHYS.SUBSTEP_DT;
+  check('MAX_SPEED x SUBSTEP_DT < MIN_HALF_EXTENT',
+    travel < PHYS.MIN_HALF_EXTENT, `${travel.toFixed(2)} !< ${PHYS.MIN_HALF_EXTENT}`);
+}
+{
+  // A fast circle fired at a thin static wall must not pass through it.
+  const w = createWorld();
+  addBox(w, { x: 400, y: 300, w: 20, h: 400, isStatic: true });
+  const ball = addCircle(w, { x: 100, y: 300, r: 12, density: 1 });
+  ball.vx = PHYS.MAX_SPEED;
+  w.gravity = 0;
+  for (let i = 0; i < 240; i += 1) substep(w, PHYS.SUBSTEP_DT);
+  check('fast body does not tunnel through a wall', ball.x < 400, `x=${ball.x.toFixed(1)}`);
+}
+
+// ── 3. Resting contacts and stack stability (THE WAVE 0 GATE) ───────────────
+
+section('3. Resting contacts and stacks');
+{
+  const w = withGround(createWorld());
+  const b = addBox(w, { x: 600, y: 700, w: 60, h: 60, density: 1 });
+  for (let i = 0; i < 600; i += 1) substep(w, PHYS.SUBSTEP_DT);
+  // Ground top is y=800; a 60-tall box rests with its centre at 770.
+  check('single box rests on ground', near(b.y, 770, PHYS.SLOP + 0.5), `y=${b.y.toFixed(3)}`);
+  check('resting box does not sink', b.y < 772, `y=${b.y.toFixed(3)}`);
+  check('resting box falls asleep', b.sleeping, `timer=${b.sleepTimer.toFixed(2)}`);
+}
+{
+  // THE GATE: a 10-box tower must settle, sleep, and not drift.
+  const w = withGround(createWorld());
+  const boxes = [];
+  // Ground top is y=800, boxes are 40 tall, so box i rests centred at 780-40i.
+  // Spawning them exactly at rest isolates solver sag from free-fall settling.
+  for (let i = 0; i < 10; i += 1) {
+    boxes.push(addBox(w, { x: 600, y: 780 - i * 40, w: 60, h: 40, density: 1, friction: 0.6 }));
+  }
+  const startX = boxes.map((b) => b.x);
+
+  let sleptAt = -1;
+  for (let i = 0; i < 720; i += 1) {          // 3 simulated seconds at 1/240
+    substep(w, PHYS.SUBSTEP_DT);
+    if (sleptAt < 0 && isSettled(w)) sleptAt = i;
+  }
+  check('10-box tower settles within 3s', sleptAt >= 0, `never settled`);
+  check('10-box tower is fully asleep', boxes.every((b) => b.sleeping),
+    `${boxes.filter((b) => !b.sleeping).length} awake`);
+
+  const drift = Math.max(...boxes.map((b, i) => Math.abs(b.x - startX[i])));
+  check('tower horizontal drift < 1px', drift < 1, `max drift ${drift.toFixed(3)}px`);
+
+  // Total sag is bounded by SLOP per contact — the solver deliberately stops
+  // correcting once penetration is inside the slop band, so 10 stacked
+  // contacts can each give up to SLOP. Anything beyond that is real sag.
+  const sag = boxes[9].y - (780 - 9 * 40);
+  const sagBudget = PHYS.SLOP * 10;
+  check('tower sag within the slop budget', Math.abs(sag) < sagBudget,
+    `sag ${sag.toFixed(3)}px vs budget ${sagBudget}px`);
+
+  const tilt = Math.max(...boxes.map((b) => Math.abs(b.angle)));
+  check('tower stays upright', tilt < 0.02, `max |angle| ${tilt.toFixed(4)} rad`);
+}
+{
+  // A pyramid is the harder stacking case: contacts are shared sideways.
+  const w = withGround(createWorld());
+  const bodies = [];
+  for (let row = 0; row < 5; row += 1) {
+    const n = 5 - row;
+    for (let i = 0; i < n; i += 1) {
+      bodies.push(addBox(w, {
+        x: 600 - (n - 1) * 35 + i * 70,
+        y: 770 - row * 40,
+        w: 64, h: 40, density: 1, friction: 0.6,
+      }));
+    }
+  }
+  for (let i = 0; i < 600; i += 1) substep(w, PHYS.SUBSTEP_DT);
+  check('pyramid settles and sleeps', bodies.every((b) => b.sleeping),
+    `${bodies.filter((b) => !b.sleeping).length} awake`);
+  const maxTilt = Math.max(...bodies.map((b) => Math.abs(b.angle)));
+  check('pyramid stays upright', maxTilt < 0.05, `max |angle| ${maxTilt.toFixed(4)}`);
+}
+
+// ── 4. Friction ─────────────────────────────────────────────────────────────
+
+section('4. Friction');
+{
+  // 15 degrees, mu = 0.8 -> tan(15) = 0.27 < 0.8, so the box must not creep.
+  const w = createWorld();
+  const slope = 15 * Math.PI / 180;
+  addBox(w, { x: 600, y: 800, w: 2000, h: 60, angle: slope, isStatic: true, friction: 0.9 });
+  const b = addBox(w, { x: 600, y: 745, w: 60, h: 40, angle: slope, density: 1, friction: 0.9 });
+  const x0 = b.x;
+  for (let i = 0; i < 900; i += 1) substep(w, PHYS.SUBSTEP_DT);
+  check('box on 15deg slope does not creep', Math.abs(b.x - x0) < 2,
+    `moved ${(b.x - x0).toFixed(2)}px`);
+  check('box on slope sleeps', b.sleeping);
+}
+{
+  // 40 degrees, mu = 0.2 -> tan(40) = 0.84 > 0.2, so it must slide.
+  const w = createWorld();
+  const slope = 40 * Math.PI / 180;
+  addBox(w, { x: 600, y: 800, w: 3000, h: 60, angle: slope, isStatic: true, friction: 0.2 });
+  const b = addBox(w, { x: 400, y: 800 - 200 * Math.tan(slope) - 52, w: 60, h: 40, angle: slope, density: 1, friction: 0.2 });
+  const x0 = b.x;
+  for (let i = 0; i < 600; i += 1) substep(w, PHYS.SUBSTEP_DT);
+  check('low-friction box slides down a steep slope', b.x - x0 > 20,
+    `moved ${(b.x - x0).toFixed(2)}px`);
+}
+
+// ── 5. Restitution ──────────────────────────────────────────────────────────
+
+section('5. Restitution');
+{
+  const w = withGround(createWorld());
+  const ball = addCircle(w, { x: 600, y: 400, r: 20, density: 1, restitution: 0.8 });
+  let peakUp = 0;
+  for (let i = 0; i < 400; i += 1) {
+    substep(w, PHYS.SUBSTEP_DT);
+    if (ball.vy < peakUp) peakUp = ball.vy;
+  }
+  check('bouncy ball rebounds upward', peakUp < -100, `peak vy ${peakUp.toFixed(1)}`);
+}
+{
+  const w = withGround(createWorld());
+  const dead = addCircle(w, { x: 600, y: 400, r: 20, density: 1, restitution: 0 });
+  for (let i = 0; i < 900; i += 1) substep(w, PHYS.SUBSTEP_DT);
+  check('zero-restitution ball comes to rest', dead.sleeping && near(dead.y, 780, 1.5),
+    `y=${dead.y.toFixed(2)} sleeping=${dead.sleeping}`);
+}
+
+// ── 6. Shape-pair coverage ──────────────────────────────────────────────────
+
+section('6. Shape pairs');
+{
+  const w = createWorld();
+  w.gravity = 0;
+  const a = addCircle(w, { x: 100, y: 300, r: 20, density: 1 });
+  const b = addCircle(w, { x: 200, y: 300, r: 20, density: 1 });
+  a.vx = 200;
+  for (let i = 0; i < 200; i += 1) substep(w, PHYS.SUBSTEP_DT);
+  check('circle-circle transfers momentum', b.vx > 50 && a.vx < 200, `a=${a.vx.toFixed(1)} b=${b.vx.toFixed(1)}`);
+}
+{
+  const w = createWorld();
+  w.gravity = 0;
+  const c = addCircle(w, { x: 100, y: 300, r: 20, density: 1 });
+  const p = addBox(w, { x: 300, y: 300, w: 60, h: 60, density: 1 });
+  c.vx = 300;
+  for (let i = 0; i < 240; i += 1) substep(w, PHYS.SUBSTEP_DT);
+  check('circle-poly transfers momentum', p.vx > 20, `box vx=${p.vx.toFixed(1)}`);
+  check('circle-poly does not overlap after impact',
+    Math.hypot(c.x - p.x, c.y - p.y) > 40, `dist ${Math.hypot(c.x - p.x, c.y - p.y).toFixed(1)}`);
+}
+{
+  // A circle dropped into a closed V must wedge, not squeeze through the seam.
+  // Two slabs tilted toward each other, overlapping at the bottom so there is
+  // no gap for the ball to slip through.
+  const w = createWorld();
+  addBox(w, { x: 480, y: 780, w: 400, h: 40, angle: -0.6, isStatic: true, friction: 0.6 });
+  addBox(w, { x: 720, y: 780, w: 400, h: 40, angle: 0.6, isStatic: true, friction: 0.6 });
+  const ball = addCircle(w, { x: 600, y: 300, r: 25, density: 1 });
+  for (let i = 0; i < 1800; i += 1) substep(w, PHYS.SUBSTEP_DT);
+  check('circle wedges in a V without escaping', ball.y < 820 && ball.sleeping,
+    `y=${ball.y.toFixed(1)} sleeping=${ball.sleeping}`);
+}
+
+// ── 7. Sleeping and waking ──────────────────────────────────────────────────
+
+section('7. Sleeping');
+{
+  const w = withGround(createWorld());
+  const stack = [];
+  for (let i = 0; i < 4; i += 1) stack.push(addBox(w, { x: 600, y: 770 - i * 40, w: 60, h: 40, density: 1 }));
+  for (let i = 0; i < 600; i += 1) substep(w, PHYS.SUBSTEP_DT);
+  check('stack asleep before impact', stack.every((b) => b.sleeping));
+
+  // A projectile must wake the whole island, not just the box it touches.
+  const shot = addCircle(w, { x: 200, y: 700, r: 16, density: 4 });
+  shot.vx = 1200;
+  let allAwake = false;
+  for (let i = 0; i < 240; i += 1) {
+    substep(w, PHYS.SUBSTEP_DT);
+    if (stack.every((b) => !b.sleeping)) { allAwake = true; break; }
+  }
+  check('impact wakes the whole island', allAwake,
+    `${stack.filter((b) => b.sleeping).length} still asleep`);
+}
+{
+  const w = withGround(createWorld());
+  const b = addBox(w, { x: 600, y: 700, w: 60, h: 60, density: 1 });
+  settle(w, 10);
+  check('settle() reaches rest', isSettled(w) && b.sleeping);
+  const yRest = b.y;
+  for (let i = 0; i < 600; i += 1) substep(w, PHYS.SUBSTEP_DT);
+  check('sleeping body does not drift', near(b.y, yRest, 1e-9), `${b.y} vs ${yRest}`);
+}
+
+// ── 8. Explosions ───────────────────────────────────────────────────────────
+
+section('8. Explosions');
+{
+  const w = withGround(createWorld());
+  const near1 = addBox(w, { x: 620, y: 700, w: 40, h: 40, density: 1 });
+  const far1 = addBox(w, { x: 900, y: 700, w: 40, h: 40, density: 1 });
+  const outside = addBox(w, { x: 1400, y: 700, w: 40, h: 40, density: 1 });
+  const hit = applyExplosion(w, 600, 700, 400, 600);
+  check('explosion hits bodies inside the radius', hit.length === 2, `hit ${hit.length}`);
+  check('explosion falls off with distance',
+    Math.hypot(near1.vx, near1.vy) > Math.hypot(far1.vx, far1.vy),
+    `${Math.hypot(near1.vx, near1.vy).toFixed(1)} vs ${Math.hypot(far1.vx, far1.vy).toFixed(1)}`);
+  check('explosion spares bodies outside the radius',
+    outside.vx === 0 && outside.vy === 0);
+  check('explosion pushes away from the centre', near1.vx > 0 && far1.vx > 0);
+  check('explosion wakes sleeping bodies', !near1.sleeping);
+}
+
+// ── 9. Determinism ──────────────────────────────────────────────────────────
+
+section('9. Determinism');
+function scene() {
+  const w = withGround(createWorld());
+  for (let i = 0; i < 6; i += 1) addBox(w, { x: 600, y: 770 - i * 40, w: 60, h: 40, density: 1 });
+  addBox(w, { x: 660, y: 730, w: 30, h: 120, density: 0.8 });
+  const ball = addCircle(w, { x: 200, y: 600, r: 16, density: 4 });
+  ball.vx = 900; ball.vy = -120;
+  return w;
+}
+{
+  const a = scene();
+  const b = scene();
+  for (let i = 0; i < 300; i += 1) { substep(a, PHYS.SUBSTEP_DT); substep(b, PHYS.SUBSTEP_DT); }
+  check('identical scenes replay bit-identically', hashWorld(a) === hashWorld(b),
+    `${hashWorld(a)} vs ${hashWorld(b)}`);
+}
+{
+  // Frame-rate independence: one 1/60 frame must equal exactly N substeps.
+  const perFrame = Math.round((1 / 60) / PHYS.SUBSTEP_DT);
+  const c = scene();
+  const d = scene();
+  for (let i = 0; i < 300; i += 1) {
+    step(c, 1 / 60);
+    for (let k = 0; k < perFrame; k += 1) substep(d, PHYS.SUBSTEP_DT);
+  }
+  check(`1/60 step == ${perFrame}x substep`, hashWorld(c) === hashWorld(d),
+    `${hashWorld(c)} vs ${hashWorld(d)}`);
+}
+{
+  // Ragged frame pacing: the accumulator only ever runs WHOLE substeps, so N
+  // substeps reached through jittery frame times must be bit-identical to N
+  // substeps reached evenly. (Total elapsed time can differ by up to one
+  // substep's worth of carry — that leftover is the accumulator's whole job —
+  // so the comparison is on substeps run, not on wall time.)
+  const e = scene();
+  const f = scene();
+  const rng = mulberry32(99);
+  let ran = 0;
+  for (let i = 0; i < 400; i += 1) ran += step(e, 0.004 + rng() * 0.02);
+  for (let i = 0; i < ran; i += 1) substep(f, PHYS.SUBSTEP_DT);
+  check('ragged frame pacing matches even pacing', hashWorld(e) === hashWorld(f),
+    `${ran} substeps: ${hashWorld(e)} vs ${hashWorld(f)}`);
+}
+{
+  const src = scene();
+  for (let i = 0; i < 60; i += 1) substep(src, PHYS.SUBSTEP_DT);
+  const before = hashWorld(src);
+  const copy = cloneWorld(src);
+  check('clone starts hash-identical', before === hashWorld(copy));
+
+  // Stepping the clone must not disturb the original by any route — including
+  // through the body references cached on contacts. simulatePreview and the
+  // winnability bot both depend on this being airtight.
+  for (let i = 0; i < 120; i += 1) substep(copy, PHYS.SUBSTEP_DT);
+  check('stepping a clone leaves the original untouched', hashWorld(src) === before,
+    `${hashWorld(src)} vs ${before}`);
+  check('clone diverges from a stationary original', hashWorld(copy) !== before);
+
+  for (let i = 0; i < 120; i += 1) substep(src, PHYS.SUBSTEP_DT);
+  check('clone and original converge when stepped equally', hashWorld(src) === hashWorld(copy),
+    `${hashWorld(src)} vs ${hashWorld(copy)}`);
+}
+{
+  // Sequential impulses are Gauss-Seidel, so solve order genuinely affects the
+  // answer — bit-identical results across creation orders are NOT achievable
+  // and not required. What matters is that the dependence stays sub-pixel, so
+  // an author reordering blocks in the editor can't change whether a level
+  // works. Exact reproducibility of a GIVEN scene is covered above.
+  const build = (reverse) => {
+    const w = withGround(createWorld());
+    const spec = [];
+    for (let i = 0; i < 5; i += 1) spec.push({ x: 600, y: 770 - i * 40 });
+    const order = reverse ? [...spec].reverse() : spec;
+    for (const s of order) addBox(w, { ...s, w: 60, h: 40, density: 1 });
+    return w;
+  };
+  const fwd = build(false);
+  const rev = build(true);
+  for (let i = 0; i < 480; i += 1) { substep(fwd, PHYS.SUBSTEP_DT); substep(rev, PHYS.SUBSTEP_DT); }
+  const fy = [...fwd.bodies].filter((b) => !b.isStatic).map((b) => b.y).sort((a, b) => a - b);
+  const ry = [...rev.bodies].filter((b) => !b.isStatic).map((b) => b.y).sort((a, b) => a - b);
+  const worst = Math.max(...fy.map((v, i) => Math.abs(v - ry[i])));
+  check('creation order shifts results by under 1px', worst < 1, `worst ${worst.toFixed(3)}px`);
+}
+
+// ── 10. Robustness monkey test ──────────────────────────────────────────────
+
+section('10. Robustness');
+{
+  const seeds = Number((process.argv.find((a) => a.startsWith('--seeds=')) ?? '--seeds=12').split('=')[1]);
+  let bad = 0;
+  let sank = 0;
+  let overspeed = 0;
+  for (let s = 0; s < seeds; s += 1) {
+    const rng = mulberry32(1000 + s);
+    const w = withGround(createWorld());
+    const bodies = [];
+    for (let i = 0; i < 14; i += 1) {
+      const b = rng() < 0.3
+        ? addCircle(w, { x: 400 + rng() * 400, y: 300 + rng() * 400, r: 10 + rng() * 18, density: 0.5 + rng() })
+        : addBox(w, { x: 400 + rng() * 400, y: 300 + rng() * 400, w: 24 + rng() * 60, h: 24 + rng() * 60, angle: rng() * Math.PI, density: 0.5 + rng() });
+      bodies.push(b);
+    }
+    for (let i = 0; i < 900; i += 1) {
+      if (i % 60 === 0) {
+        const b = bodies[Math.floor(rng() * bodies.length)];
+        applyImpulse(b, (rng() - 0.5) * 4e5, (rng() - 0.5) * 4e5, b.x, b.y);
+      }
+      substep(w, PHYS.SUBSTEP_DT);
+      for (const b of bodies) {
+        if (!Number.isFinite(b.x) || !Number.isFinite(b.y) || !Number.isFinite(b.angle)
+          || !Number.isFinite(b.vx) || !Number.isFinite(b.vy) || !Number.isFinite(b.omega)) bad += 1;
+        if (Math.hypot(b.vx, b.vy) > PHYS.MAX_SPEED + 1e-6) overspeed += 1;
+        if (b.y > 1000) sank += 1;
+      }
+    }
+  }
+  check(`no NaN across ${seeds} monkey seeds`, bad === 0, `${bad} non-finite samples`);
+  check('nothing exceeds MAX_SPEED', overspeed === 0, `${overspeed} samples`);
+  check('nothing sinks through the ground', sank === 0, `${sank} samples`);
+}
+{
+  // Bodies must be removable mid-sim without leaving dangling contacts.
+  const w = withGround(createWorld());
+  const boxes = [];
+  for (let i = 0; i < 5; i += 1) boxes.push(addBox(w, { x: 600, y: 770 - i * 40, w: 60, h: 40, density: 1 }));
+  for (let i = 0; i < 120; i += 1) substep(w, PHYS.SUBSTEP_DT);
+  removeBody(w, boxes[2]);
+  let threw = false;
+  try { for (let i = 0; i < 480; i += 1) substep(w, PHYS.SUBSTEP_DT); } catch (e) { threw = true; }
+  check('removing a mid-stack body is safe', !threw);
+  check('stack recovers after a removal', boxes.filter((b, i) => i !== 2).every((b) => b.sleeping),
+    `${boxes.filter((b, i) => i !== 2 && !b.sleeping).length} awake`);
+}
+{
+  // contactImpulses is the damage signal the rules layer reads — a hard hit
+  // must report a much larger impulse than a resting contact.
+  const w = withGround(createWorld());
+  const target = addBox(w, { x: 600, y: 770, w: 60, h: 60, density: 1 });
+  settle(w, 5);
+  substep(w, PHYS.SUBSTEP_DT);
+  const resting = contactImpulses(w).get(target.id) ?? 0;
+
+  const shot = addCircle(w, { x: 200, y: 740, r: 16, density: 6 });
+  shot.vx = 1800;
+  let peak = 0;
+  for (let i = 0; i < 240; i += 1) {
+    substep(w, PHYS.SUBSTEP_DT);
+    peak = Math.max(peak, contactImpulses(w).get(target.id) ?? 0);
+  }
+  check('impact impulse exceeds resting impulse', peak > resting * 3,
+    `peak ${peak.toFixed(0)} vs resting ${resting.toFixed(0)}`);
+}
+
+// ── Summary ─────────────────────────────────────────────────────────────────
+
+console.log(`\n${passes} passed, ${failures} failed`);
+process.exit(failures ? 1 : 0);