feat(levels): D5 three-rotation prototype

The shipped 1000 levels have a hole: 568 of them need no rotation at all, and
none needs more than two — the mechanic the game is built on is mostly
decoration. This fills the empty band with levels that need at least three.

createDeepLock builds a four-piece chain where each link only releases at a
later orientation, and growDeepLevel packs the rest of the board around it
without opening a shortcut. Candidate pools are built per orientation and left
untruncated; ranking by bend count first starved the packer and capped levels
at four to six pieces instead of twelve.

deadTurnAudit enumerates every reachable (orientation, remaining-set) state to
prove no dead ends exist, and counts how long a player can be left with
nothing to do — solvable and feeling solvable are different things, which is
what "level 2 is impossible" turned out to be about.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>

labs/d5/app.js

@@ -0,0 +1,159 @@
+import { Game, available, trace, solveRotations } from '../../src/core.js';
+import { TapQueue } from '../../src/tap-queue.js';
+import { layout, hitCell } from '../../src/geometry.js';
+import { CanvasPainter, drawScene } from '../../src/renderer.js';
+import { TILE_ATLAS } from '../../src/sprites.js';
+import { exitTiming } from '../../src/exit-animation.js';
+import { MOTION } from '../../src/design-tokens.js';
+import { unlockAudio, playSound } from '../../src/audio.js';
+
+const $ = id => document.getElementById(id);
+const canvas = $('board'), context = canvas.getContext('2d'), painter = new CanvasPainter(context);
+const taps = new TapQueue();
+const reduced = matchMedia('(prefers-reduced-motion: reduce)').matches;
+let levels = [], current = null, game = null, view, width, height, animation = null, turning = null, hint = null, path = null, frame = 0;
+
+const pct = value => `${Math.round(value * 100)}%`;
+function describeWitness(actions, tiles) {
+  // Compress the solver reference into "+1 · 3 枚 · +1 · 2 枚 · −1 · 4 枚".
+  const parts = []; let taps = 0;
+  for (const action of actions) {
+    if (action.type === 'rotate') { if (taps) parts.push(`${taps} 枚`); taps = 0; parts.push(action.direction === 1 ? '右转' : '左转'); }
+    else taps++;
+  }
+  if (taps) parts.push(`${taps} 枚`);
+  return `参考解：${parts.join(' · ')}（共 ${tiles.length} 枚）`;
+}
+function showEvidence() {
+  const p = current.prototype, s = p.stats;
+  const rows = [
+    ['底盘 / 棋子', `${current.cells.length} 格 · ${s.pieces} 枚 · ${p.family} r${p.radius} · seed ${p.seed}`],
+    ['最少旋转', `${s.rotations} 次`],
+    ['开局被锁住', `${s.lockedAtStart} / ${s.pieces} 枚（${pct(s.lockedShare)}）`],
+    ['每次旋转释放', s.releasePerTurn.join(' / ') + ' 枚'],
+    ['首转方向', s.firstTurnDirections === 1 ? '只有一侧能开路' : '两侧都能开路'],
+    ['主角路线', `${p.lock.heroBends} 弯`],
+    ['随机玩家 动作 ÷ 棋子', p.monkeyActionsPerPiece.toFixed(2) + '（v0.5 全库 1.67）'],
+  ];
+  $('evidence').innerHTML = rows.map(([k, v]) => `<div><dt>${k}</dt><dd>${v}</dd></div>`).join('');
+  $('witness').textContent = describeWitness(current.experience.actions, current.tiles);
+}
+// Stuck-state idle hint: when nothing can leave, wait, then point at the turn
+// that opens something. This is the §07 rule — the direction is never shown
+// instantly, so "which way" stays the player's move first.
+let idleTimer = null;
+function clearIdleHint() { clearTimeout(idleTimer); idleTimer = null; for (const id of ['left', 'right']) $(id).classList.remove('hinted'); }
+function scheduleIdleHint() {
+  clearIdleHint();
+  if (!game || game.won || animation || turning || available(game.level, game.tiles).length) return;
+  idleTimer = setTimeout(() => {
+    const action = solveRotations({ ...game.level, tiles: game.tiles, moveLimit: game.moves }).actions[0];
+    if (!action || action.type !== 'rotate') return;
+    $(action.direction === 1 ? 'right' : 'left').classList.add('hinted');
+    $('message').textContent = `这个朝向没有出口。试试向${action.direction === 1 ? '右' : '左'}转。`;
+  }, 3000);
+}
+function stats() {
+  const busy = !!(animation || turning);
+  if (!busy) scheduleIdleHint();
+  $('remaining').textContent = game.tiles.length;
+  $('progress').textContent = game.won ? '清盘 · 三转到位' : `已放行 ${current.tiles.length - game.tiles.length} / ${current.tiles.length} · 旋转 ${game.rotations}${taps.ids.length ? ` · 待出发 ${taps.ids.length}` : ''}`;
+  for (const id of ['left', 'right', 'hint']) $(id).disabled = busy || game.won;
+  $('undo').disabled = busy || !game.history.length;
+  if (game.won && !busy) $('message').textContent = `清盘。用了 ${game.rotations} 次旋转，参考解 ${current.prototype.stats.rotations} 次。`;
+}
+function draw(now = performance.now()) {
+  cancelAnimationFrame(frame);
+  if (!view || !game) return;
+  context.clearRect(0, 0, width, height);
+  const state = { hint, path, reduced, queued: taps.ids };
+  if (animation) {
+    const progress = Math.min(1, (now - animation.start) / animation.duration);
+    state.animation = { route: animation.route, progress };
+    if (progress >= 1) animation = null;
+  }
+  if (turning) {
+    const progress = Math.min(1, (now - turning.start) / turning.duration);
+    state.boardAngle = -turning.direction * Math.PI / 3 * Math.pow(1 - progress, 3);
+    if (progress >= 1) turning = null;
+  }
+  drawScene(painter, game.level, game.tiles, view, state);
+  if (!animation && !turning) {
+    const next = taps.take(game.tiles);
+    if (next) { tap(next); return; }
+  }
+  stats();
+  if (animation || turning) frame = requestAnimationFrame(draw);
+}
+function resize() {
+  if (!game) return;
+  const rect = canvas.getBoundingClientRect(), dpr = Math.min(devicePixelRatio || 1, 3);
+  width = rect.width; height = rect.height;
+  canvas.width = Math.round(width * dpr); canvas.height = Math.round(height * dpr);
+  context.setTransform(dpr, 0, 0, dpr, 0, 0);
+  view = layout(game.level.cells, width, height); draw();
+}
+function clearEffects() { taps.clear(); cancelAnimationFrame(frame); animation = null; turning = null; hint = null; path = null; clearIdleHint(); }
+canvas.addEventListener('pointerdown', clearIdleHint, { passive: true });
+for (const id of ['left', 'right', 'undo', 'reset', 'hint']) $(id).addEventListener('pointerdown', clearIdleHint, { passive: true });
+function load(index) {
+  current = levels[index]; clearEffects(); game = new Game(current);
+  const free = available(game.level, game.tiles).length;
+  $('message').textContent = free ? `开局有 ${free} 枚能走，其余都在等旋转。` : '开局没有任何棋子能走。转一下，看哪一层松开了。';
+  $('meta').textContent = `${current.cells.length} 格 · ${current.tiles.length} 枚 · 最少 ${current.prototype.stats.rotations} 转`;
+  showEvidence(); resize();
+}
+function tap(tile) {
+  if (game.won) return;
+  if (animation || turning) { if (taps.add(tile.id, animation?.route.tile.id)) draw(); return; }
+  hint = null; path = null;
+  const before = new Set(available(game.level, game.tiles).map(t => t.id));
+  const result = game.tap(tile.id);
+  if (result.status === 'exit') {
+    animation = { route: result, start: performance.now(), duration: reduced ? 100 : exitTiming(result).duration };
+    const opened = available(game.level, game.tiles).filter(t => !before.has(t.id)).length;
+    $('message').textContent = opened ? `移开这一枚，${opened} 枚棋子的路通了。` : result.steps.length > 3 ? '沿着轨道绕出去了。' : '出去了。';
+    playSound('exit');
+  } else {
+    taps.clear();
+    if (result.travelPoints) animation = { route: result, start: performance.now(), duration: reduced ? 150 : MOTION.collisionMs };
+    $('message').textContent = result.status === 'loop' ? '这条路线绕回原处。转一下底盘换条路。' : '前方有棋子挡住。它在等另一个朝向。';
+    playSound('hit');
+  }
+  draw();
+}
+function rotate(direction) {
+  if (animation || turning || game.won) return;
+  taps.clear();
+  const before = new Set(available(game.level, game.tiles).map(t => t.id));
+  game.rotate(direction); hint = null; path = null;
+  const opened = available(game.level, game.tiles).filter(t => !before.has(t.id)).length;
+  turning = { direction, start: performance.now(), duration: reduced ? 100 : MOTION.rotationMs };
+  $('message').textContent = opened ? `这一转松开了 ${opened} 枚。` : '这个朝向什么都没松开。再转，或转回去。';
+  playSound('rotate'); draw();
+}
+canvas.addEventListener('pointerup', event => {
+  const rect = canvas.getBoundingClientRect(), cell = hitCell(game.level.cells, view, event.clientX - rect.left, event.clientY - rect.top);
+  const tile = cell && game.tiles.find(t => t.q === cell.q && t.r === cell.r);
+  if (tile) tap(tile);
+});
+$('left').onclick = () => rotate(-1);
+$('right').onclick = () => rotate(1);
+$('undo').onclick = () => { if (!animation && !turning && game.undo()) { clearEffects(); $('message').textContent = '回到上一步。'; draw(); } };
+$('reset').onclick = () => load(Number($('level').value));
+$('hint').onclick = () => {
+  const action = solveRotations({ ...game.level, tiles: game.tiles, moveLimit: game.moves }).actions[0];
+  if (!action) return;
+  if (action.type === 'rotate') { $('message').textContent = `向${action.direction === 1 ? '右' : '左'}转一次。`; }
+  else { hint = action.id; path = trace(game.level, game.tiles.find(t => t.id === hint), game.tiles); $('message').textContent = '这一枚现在可以走。'; }
+  draw();
+};
+$('level').onchange = () => load(Number($('level').value));
+document.addEventListener('pointerdown', unlockAudio, { passive: true });
+const atlas = new Image(); atlas.onload = () => { painter.atlas = atlas; draw(); }; atlas.src = '../../' + TILE_ATLAS;
+new ResizeObserver(resize).observe(canvas);
+
+const response = await fetch('../../levels/prototypes/d5.json');
+levels = (await response.json()).levels;
+$('level').innerHTML = levels.map((level, i) => `<option value="${i}">${String(i + 1).padStart(2, '0')} · ${level.prototype.family} r${level.prototype.radius} · ${level.tiles.length} 枚 · 锁住 ${pct(level.prototype.stats.lockedShare)} · 释放 ${level.prototype.stats.releasePerTurn.join('/')}</option>`).join('');
+load(0);