Maze generator & solver · hy4

We need build single index.html self-contained. Need use browser tools check initial, progress, New Maze active, clean replacement, solver steps open passages. Need implement robust.

Need think design, code, state cancellation. Need likely canvas app with controls. Need 25x15 cells, randomized recursive backtracking, perfect maze. Animate carving progress visible. After generation finishes animate BFS or A*, highlight complete path. Need Start upper-left, finish lower-right. Need legend styles. New Maze cancels previous animation and fresh maze; Replay Solver uses existing maze without changing walls. Need perhaps speed/responsive.

Need write file, run browser inspect DOM/console/screenshots, maybe instrument via JS global state to verify through browser perhaps browser inspect action returns DOM? Need understand available tool behavior. We can use browser actions. We can maybe use bash node? Need just file. Browser tool can screenshot, inspect DOM/console, clicks. We can expose `window.__mazeDebug` to make verification possible. Need perhaps use browser inspect with text? Tool likely returns snapshot including console, DOM perhaps. We'll explore.

Implementation plan:

Canvas dimensions based on CSS, internal high-DPI. Maze cols 25 rows 15. Cell data: walls top/right/bottom/left booleans; visited generation; path/exploration states. Randomized recursive backtracking using explicit stack. To animate carving step by step, each frame perform N carve steps (perhaps 2 or 3 per frame) based on speed. For each step: current stack top; unvisited neighbors; pick random; remove shared walls; mark visited; push; else pop. Progress visible through current cell highlight and recently carved cells; visited cells tinted. Need draw walls clearly on grid with all walls initially? We can draw only walls around visited cells? Requirement generate 25x15 rectangular maze and animate carving progress visible. If drawing all grid walls including unvisited area, removed wall updates visible but subtle. Better display unvisited cells dark solid/blank, carved cells light with wall removal. Need perhaps draw all cell outlines and can show carved area. Draw:
- background outside.
- For each visited cell: lightly tinted fill (#f7fbff), maybe generation visited (#e3eef8).
- For unvisited: dark navy (#111e30) perhaps.
- For each cell, draw walls:
   - For visited cells: draw actual wall lines (boundary and walls to neighbors). But walls toward unvisited should be drawn. Walls between two unvisited cells perhaps draw subtle grid? If all grid lines from unvisited region, then after carving clear but contrast nice.
   - Could draw walls for all cells, deduplicate by only top/left + bottom/right boundary. Yet wall is in both cells initially synchronized. For visited cells, draw top/left wall if walls true; plus right/bottom if boundary (or perhaps all right/bottom with dedup handled). Standard: iterate cells and draw top if wall, left if wall, bottom if row last or walls.bottom, right if col last or walls.right; but shared wall drawn from whichever cell bottom/right; since removed walls synchronized, fine. Could draw each wall once using top/left and boundaries. For every cell: if walls.top line; if walls.left line; if last row bottom; if last col right. This uses cells' own top/left; shared walls between row-1 and row are stored bottom of upper and top of lower. To draw bottom of upper need perhaps draw all right/bottom walls but dedup? If draw all walls per cell, overlapping lines just thicker same width no issue if same color. Better iterate walls: each cell draw top and left, plus right boundary and bottom boundary. Shared horizontal wall represented in lower cell's top, so fine. Shared vertical wall represented in right cell's left, fine. So always draw top/left walls of every cell and bottom/right outer boundaries. This gives full lattice. Walls color cream/white. Fill visited cell with light. Unvisited dark with perhaps subtle grid. Removed wall simply absent, but fill of both adjacent visited makes a continuous corridor. Need style clear.

Could draw passages via cell interiors connected across removed walls; walls line width maybe 2.5, cell size around 30-40. Canvas CSS width maybe 100%, max 1000, aspect ratio 25/15 = 5/3. We can set internal dimensions to 1000x600 plus padding 20 perhaps. Need responsive scaling via CSS width:100%, height:auto; set canvas width maybe e.g. 1100 height 680. Use device pixel ratio? We can set logical WORLD width=1000, height=600, cellSize=40, margin=0; canvas width/height via DPR and context.scale. CSS aspect-ratio 5/3. Simpler set canvas width=1000 height=600 and CSS width:100%; max-width:1000; aspect-ratio:5/3; image-rendering maybe. If high DPI not necessary but could use resizeCanvas with DPR and transform. Need avoid complexity.

Maybe margins around maze to clearly show border. Set CELL=36? 25*36=900, 15*36=540. canvas logical width = 900+40 = 940, height=540+40=580, origin 20,20. Aspect 940/580 ~1.62. Use responsive canvas with fixed intrinsic dimensions then CSS width 100%, height auto. Fine. Or 1000x620 with cell 38, origin 20 => width 990, height 610. Choose CELL=36 and canvas 940x580. On 1200x800 browser, perhaps width 1000? Actually app max-width 1040, canvas rendered ~1000 wide, scaled up from intrinsic 940, fine.

Need controls status:
- New Maze button
- Replay Solver button
- Maybe speed slider (optional) useful to slow animation for inspection; not required but can help test. Could include "Speed" select or range and "Pause"? We can include speed range, maybe initial speed around 8 cells/step? Need generation visible enough. 375 cells plus backtracking many steps => 750 steps. If one operation per frame at 60 fps => 12.5 sec. Solver BFS up to 375 cells ~6 sec. Could select "Slow/Medium/Fast", maybe default medium: generation 3 steps per 24ms or frame ~5 sec, solver 2 cells per frame ~3 sec. Need browser inspection and New Maze while active. If generation too fast, tough. Could make default slower ~2 steps per 35ms = 13 sec. Need likely check via browser snapshots and click. We can also expose debug APIs to pause/inspect. But UI controls perhaps speed slider. Let's include a "Speed" range (Slow to Fast), with values controlling timer intervals. Use requestAnimationFrame with time accumulator and steps based on speed. E.g. speed label and range 1..5 default 3. `stepInterval = [90,55,32,18,8][speed-1]`; `genStepsPerTick=[1,1,2,3,6]`; `solveStepsPerTick=[1,1,2,3,5]`. At medium ~375*2? Actually generation requires 2*375-ish? DFS steps each edge carve = 374 pushes + 374 pops = 748, at 32ms*2 operations per tick ~12 sec; okay. Solver 375 at 32ms*2 ~6 sec. Could default speed 4 => ~4 sec gen. For user-requested inspect progress, likely need enough. Browser tool actions may take some time. Perhaps default speed 2 (1 op per 55ms = ~41 sec generation) too long. Need avoid excessively long. We can make generation animation show one DFS "carving edge" per tick including auto backtracking as needed? We can define step that always carves a new cell (if possible), popping as many stack entries as required to find a candidate. Then exactly 374 carving steps. Each frame/tick carve 1 or more. This is a valid randomized recursive backtracking implementation. Need track stack and visited. At each `carveStep`: while stack nonempty, look at top, gather unvisited neighbors, if one pick and carve/push; else pop. This could pop multiple in one logical step but we can animate only carved edges; progress visible. Then 374 steps. At speed default maybe 18ms with 1 cell per tick => ~6.7 sec. Good. Could use requestAnimationFrame and every 24ms one carve. Need maybe user sees ~6 sec. Set speed 1..5 intervals [90,50,28,14,5], steps per tick [1,1,1,2,4]. Default 3 => 28ms => ~10.5 sec generation. Solver maybe increments queue expansions and can do 1 per tick => up to 10 sec too. Entire ~20 sec; browser test can click during generation. Fine. But waiting till solver starts in browser maybe 10+ sec; can use debug method or speed slider to fast. Need perhaps add "Skip to solver"? Not required. Debug global could offer `__mazeDebug.finishGeneration()` but that might be seen as tampering; for test, could use exposed state and call `generateInstantly`? Better to use speed controls in UI: choose fast with mouse via click perhaps. Browser tool can click at slider coordinate. Or we can use keyboard? Need finer. Could expose debug methods to verify invariants. But requirements focus runtime visual behavior. We can use browser's inspect output over time.

Alternative generation step can carve 2 cells/tick at 30ms => 5.6 sec; solver 2 expansions/tick => 5 sec. Good. Default speed medium maybe 2. Need enough to click New Maze during active; 5 sec likely. Browser actions have latency maybe ~0.5 sec. Could do initial `reload` then `inspect` then `click` New Maze within active. Need confirm creation timestamp changes and visited count resets. We can expose status in DOM attr or global. `data-phase`, `data-run-id`, `data-carved`, `data-maze-id`. Browser inspect likely shows DOM snapshot. We can put status text and perhaps a progress meter. Also add `<div id="debug" hidden>`? Not needed.

Need design robust cancellation:
- Use a single `runToken` or `generationToken` increment for any New Maze. All animation loops check token. Use requestAnimationFrame with scheduled handle; cancelAnimationFrame on New Maze. Need perhaps separate solver token? simplest `epoch` increment on newMaze/replaySolver? New Maze increments and cancels RAF; Replay Solver increments? Replay solver should cancel previous solver animation while same maze. To avoid overlapping loops, use one `animationId` and one `epoch`. `cancelAnimation()` cancels RAF and increments epoch. Then start loop captures epoch. On New Maze: cancel then initialize walls and generation state, increment `mazeId`, reset solver states, set phase generating, start `loop` with epoch. Replay: cancel then ensure generation must be complete? Requirement "Replay Solver uses existing maze without changing its walls." Could allow clicking during generation? Ideally disable Replay until maze complete. But user might click while generating; perhaps button disabled until generation done. We can set `replayBtn.disabled = phase==='generating'`. Then when generation complete enable. On replay, no wall changes. Need maybe expose checksum of walls before/after to verify. We can compute `wallsSignature()` and set `window.__mazeDebug.mazeSignature`; or global object with methods. Could make debug API:
```
window.__mazeDebug = {
 get state() { return { phase, mazeId, carved, visited..., wallsSignature(), ... }; },
 getCells() { return cells.map(... walls...) },
 openBetween(a,b), checkPerfectMaze() ...
}
```
No network. This is useful for browser tool inspect? `browser inspect` may not execute arbitrary JS. Maybe we can use browser's `click` or `type` only. There may be a tool to evaluate JS? Tool schema only actions reload, inspect, screenshot, motion, click, drag, key, type, scroll. `inspect` perhaps returns page DOM and console, maybe can inspect only. No evaluate. But we can add an on-page "Diagnostics" panel with text including invariants updated each step. Could use browser inspect to read DOM. Could also have the app console.log important milestones; browser inspect likely returns console. We can log at creation, finish, solver start, path found. Need route invariants to console; can then verify via inspect. We can add visible status with phase and counts.

Need expose debug via DOM hidden maybe a `<pre id="diagnostics">` and update as JSON. Could style as small monospace info panel. Maybe no need to hide; can show metrics:
- Status message "Carving maze — 42 / 375 cells"
- progress bar
- `Maze #2 • visited 42/375 • frontier ...`
- legend.
Need maybe annotations/legend with colored swatches:
  Start green, Finish gold, Exploration amber/purple, Solution magenta/red, Current blue, Carved pale blue, Unvisited dark. Need distinguish start/finish/exploration/solution. Ensure styles:
  - Start: emerald filled circle with "S"
  - Finish: orange/gold square or circle with "F"
  - Exploration: translucent cyan/teal fill with small dot
  - Solution: bright coral/red line drawn through cell centers and coral cell fill maybe.
  - Walls: off-white.
  - unvisited: dark navy.
  - carved: light slate / blue-gray.
  - current carving cell: bright blue outline/fill.
  - solution path as thick line with rounded joins; maybe glow.
  - Start/finish labels on top of path.

Need ensure path crosses only open passages. BFS:
- cells with walls booleans. `openBetween(c1,c2)` based on direction indices.
- Queue from start, visited set, parent map. Need animate exploration. At each tick expand one node, mark as explored, inspect neighbors in fixed/random? BFS deterministic direction order. If neighbor open and not visited, mark visited and enqueue, set parent; if neighbor target, can continue until dequeue target or stop immediately when discovered. To animate complete exploration, typical BFS mark discovered. We can stop when current===finish (dequeued) or when discovered. If stop on discovery, parent chain valid. Need show exploration. Use `discovered` perhaps. Steps:
```
function solverStep() {
 if queue.length===0 -> no path
 const current=queue.shift();
 explored.add(current);
 if current===finish { buildPath; phase='solved'; render; return false; }
 for neighbors:
   if open && !seen[n] { seen[n]=true; parent[n]=current; queue.push(n); discovered.add(n); }
 return true;
}
```
Draw discovered (frontier) maybe purple, explored cyan, path coral. Need "exploration" style clearly distinguish; perhaps explored cells filled translucent blue with dot, frontier violet outline. Legend "Explored" and "Frontier" maybe. Requirement mark exploration. Use one style for explored cells. Start/finish should remain visible even under exploration.

Need ensure "exactly one simple path between any pair". Perfect maze via spanning tree. Need check invariants maybe implement `validateMaze()` at generation completion:
- all 375 cells visited
- passage edges count = 374
- connectivity via DFS count=375
- no cycles (connected + edges N-1 implies tree)
- each wall reciprocal.
Then set status and console.log. Could include `data-valid` attribute. This is robust and can be surfaced. Need maybe not overcomplicate but good.

New Maze cancellation:
```
let rafId=null, epoch=0, mazeId=0, phase='idle';
function stopAnimation() {
  if (rafId!==null) cancelAnimationFrame(rafId);
  rafId=null;
  epoch++;
}
function newMaze() {
  stopAnimation();
  mazeId++;
  initialize();
  phase='generating';
  replayBtn.disabled=true;
  runEpoch=epoch;
  last=0; accum=0;
  rafId=requestAnimationFrame(frame);
}
function frame(ts) {
 if (myEpoch!==epoch) return;
 ...
 if phase generating loop gen ...
 else if solving ...
 if still active rafId=requestAnimationFrame(frame)
 else rafId=null;
}
```
Potential issue stopAnimation increments epoch, then start with current epoch. Fine.
- `lastTime=0, accumulator=0`.
- If phase transition generation -> solving, we can reset accumulator and perhaps have brief transition delay ~400ms to let completed maze view show. Use `phase='generated'`, `phaseUntil=ts+400`, then startSolver automatically at frame after delay. But solver should start after generation finishes. Could implement immediate but with a short pause. Need phase state. Simpler in `frame`:
```
if phase==='generating' and carved===N:
  completeGeneration(ts) sets phase='pause'; phaseEnd=ts+500;
else if phase==='pause' && ts>=phaseEnd: startSolverWithoutCancel(); phase='solving';
```
But replay must remain disabled until solving perhaps. Need keep walls unchanged. If button enabled during pause, replay could cancel and start solver; okay. But requirement replay uses existing maze, fine. Need ensure no generation cleanup repeats. Could set `phase = 'generated'; phaseEnd = ts+500` during frame. Need not cancel animation. Then when time passes, call `initializeSolver()` (clears solver-only states) and phase='solving'. `replayBtn.disabled=false` after generation. If user clicks Replay during the pause, `stopAnimation()` cancels RAF, then initializeSolver and start loop; no walls changed. Fine.
- But if user clicks New Maze while solver active or solved, cancel and reset.

Replay Solver:
```
function replaySolver() {
 if (!mazeComplete) return;
 const before = wallsSignature();
 stopAnimation();
 resetSolverState();
 // perhaps assert after === before
 phase='solving';
 startLoop();
 console.log(`... walls unchanged ${before===...}`);
}
```
`stopAnimation` should not alter maze states. `initializeSolver` must clear `seen`, `frontier`, etc only.
- Need avoid race if clicked while generation: button disabled; could still call via JS but guard.
- New Maze must cancel previous animation and replace previous view cleanly: on New Maze, reset all cells/walls and solver/generation state; render immediate clears previous view; then start. Need use `render()` after reset. It should show unvisited dark grid and new ID. Must ensure RAF old callback doesn't run: cancel + epoch check.
- Need perhaps track `mazeId` in status and console; visible "Maze #2". New Maze checks `carved` resets to 1 and path/exploration cleared. status should update. Could set DOM data attributes for inspect:
```
app.dataset.phase=phase;
app.dataset.mazeId=mazeId;
app.dataset.carved=carved;
...
```
Then browser inspect can read.

Need UI:
```
<header>
<h1>Maze Lab</h1>
<p>Randomized recursive backtracking → breadth-first search</p>
<div class="controls">
<button id=new>New Maze</button>
<button id=replay disabled>Replay Solver</button>
<label>Speed <input id=speed type=range min=1 max=5 value=3></label><span>Normal</span>
</div>
</header>
<section class=stage>
<canvas id=maze width=940 height=580 aria-label=...></canvas>
<div class=statusbar> ... progress ...
</section>
<aside or footer legend with swatches>
...
<footer>Facts: 25 × 15 = 375 cells / 374 passages ... maybe validation message.</footer>
```
Need fit 1200x800 viewport. Canvas rendered width maybe 940 (max). CSS body width. Need top header ~110, canvas ~580 plus border/padding, status ~50, legend ~60 = 800+ perhaps scroll. Browser viewport 1200x800; screenshot may show partial legend. Could choose smaller CELL=32 -> maze 800x480, canvas 840x520, fits with header 100 + stage padding 20 + status 45 + legend 70 = 755. Great. At 1200 screen width, max-width maybe 1080, canvas rendered 840? Could set max-width 900 and canvas width 100% -> maybe 900? Let's use logical cell=32, margin=16 => canvas 832x512. CSS width:min(100%, 832px); so no upscaling perhaps. Center. At viewport 1200, canvas 832x512. Header ~100, stage ~570, legend ~80 -> total 750. Fits. Wall line 2.6 logical px; at 832 actual, clear. Cell 32 enough for labels. Could use canvas 1000x620 with CSS scaled down to 900; but sharpness maybe okay. Better high DPI responsive:
```
const BASE_W = 25*CELL+2*PAD = 832
const BASE_H = 15*CELL+2*PAD = 512
canvas.style.width='100%'; canvas.style.aspectRatio='832 / 512';
function resizeCanvas() {
 const rect = canvas.getBoundingClientRect();
 const dpr = window.devicePixelRatio || 1;
 canvas.width = Math.round(rect.width*dpr);
 canvas.height = Math.round(rect.height*dpr);
 ctx.setTransform(canvas.width/BASE_W,0,0,canvas.height/BASE_H,0,0);
 render();
}
```
Need CSS `width:100%; max-width:832px; aspect-ratio:832/512; height:auto; display:block;` and initial width/height attributes maybe 832x512. Using resize to DPR makes internal coordinate scaling correct. `ctx.setTransform(sx,0,0,sy,0,0)` but line widths scale too; if same ratio, fine. Need call on resize; if resizing during animation, render uses current transform. But if `render()` starts with `ctx.setTransform(...)`, avoid cumulative transforms. Could just set canvas width/height attributes fixed to logical 832x512 and CSS scale; no need DPR. Simplicity and reliable. But high quality? CSS scaling is okay. Use `canvas.width=1000?` Let's choose 1000x620 with cells 38.4? integer coordinates no issue. Could set CELL=36, PAD=18 => 936x576. CSS max 936; on 1200x800 maybe total 800 and some scroll. 832x512 better.

High DPI implementation:
```
function fitCanvas() {
 const rect = canvas.getBoundingClientRect();
 const dpr = Math.min(window.devicePixelRatio||1,2);
 const pixelW=Math.round(rect.width*dpr), pixelH=Math.round(rect.height*dpr);
 if(canvas.width!==pixelW || canvas.height!==pixelH){ ...}
 const sx = pixelW / WORLD_W, sy = pixelH / WORLD_H;
 ctx.setTransform(sx,0,0,sy,0,0);
 render();
}
```
`render` assumes transform already set; but browser may reset transform when canvas dimensions changed only. We call fitCanvas on resize. We can have `render` call `ctx.setTransform(canvas.width/W,0,0,canvas.height/H,0,0); ctx.clearRect(0,0,W,H);` so robust. Then `fitCanvas` sets dimensions and calls render. Because canvas width/height set to CSS*dpr, and world mapped accordingly. `ctx.clearRect(0,0,W,H)` under scaled transform clears world area exactly. Good. `lineWidth=2` in world units yields 2*dpr*scale pixels; okay.

Need render order:
1. clear/background.
2. For each cell fill:
   - base unvisited `#10192b`, visited `#dce9f3` maybe.
   - generation visited `#d8e7f5`; current `#69b7ff`; maybe recent edge cells `#b9dcf7`.
   - exploration overlays after walls? Need fills before walls, then wall lines. Path line perhaps after walls? If line at cell centers and cross passages, should be under wall lines to show respecting walls; draw path after cell fills but before walls to make walls cover path at any wall crossing. But if path valid, no crossings. Drawing after walls could hide walls at corridors if path width ~10 and wall line along edge; not cross. Start/finish markers after walls maybe. Need decide:
```
drawCellFills();
drawExploration();
drawSolutionPath();
drawWalls();
drawCurrentCarve();
drawStartFinish();
draw maybe finish flag.
```
Walls on top ensure crisp. Solution line under walls. Start/finish circles on top. Exploration cell fills under walls. Current highlight maybe a rectangle inset 3 and border, under walls? could draw after walls with inset avoids covering walls.
- Outer border perhaps strong line around maze.
- Grid walls: for each cell:
```
ctx.strokeStyle = '#9fb3c8'? 
ctx.lineWidth = 2.2; ctx.lineCap='square';
ctx.beginPath();
for each cell:
 x=PAD+c*CELL, y=PAD+r*CELL;
 if(cell.walls[0]) move x,y line x+CELL,y
 if(cell.walls[3]) move x,y line x,y+CELL
 if(r===ROWS-1 && cell.walls[2]) ... bottom
 if(c===COLS-1 && cell.walls[1]) ... right
ctx.stroke();
```
Since all cells initialized with walls true and we remove reciprocal, top/left of lower/right cells represent shared walls. But need check: Suppose wall between (r,c) and (r,c+1) removed. We set `right` of left false and `left` of right false. We draw top/left of right -> no wall. We never draw right of left (except boundary), so no line. Good. Suppose wall between (r,c) and (r+1,c) removed: top of bottom false, no line. We never draw bottom of top (except boundary), so none. Good. Outer border: top of row0 and left of col0 and bottom of row14 and right of col24. all true. Draw perhaps thicker border separately `strokeRect(PAD,PAD,COLS*CELL,ROWS*CELL)` with lineWidth 3.5.
- For unvisited region, top/left walls drawn for all cells; grid lines visible. Need wall color perhaps `#6c88aa` over dark background; visited region walls dark navy `#263b56` over light fill? One uniform wall color maybe dark `#1b2f4b` won't show on dark unvisited. Need perhaps draw wall lines in two passes: unvisited wall segments in blue-gray, carved walls in dark navy. But shared boundary between visited/unvisited? top/left based on target cell; could color based on cell. Simpler draw fill dark unvisited with subtle grid using one wall color lighten. Then draw walls for all cells in light `(#8aa4c3)` and visited walls perhaps dark? Could draw all walls with a light color and shadow, but over light visited fill might be low contrast. We can base wall color on cell visited:
   - For each cell, draw its top/left walls with `visited ? '#24344e' : '#354a67'` and boundary same. But shared boundary between visited/unvisited represented by top/left of one cell only (e.g., if lower/right cell visited vs its upper/left neighbor unvisited). If the wall exists, color based on lower/right cell. Fine.
   - Have two path batches: `darkWalls` and `unvisitedWalls` or just loop and stroke individually. 375*2 lines per render ~750; fine. Could group by color into Path2D? Need compatibility. Use beginPath for each color with conditions.
```
for each cell:
 add top/left plus boundaries to path based on cell.visited
ctx.strokeStyle='#263b56'; ctx.lineWidth=2.5; ctx.stroke(visitedPath);
ctx.strokeStyle='#47617f'; ctx.lineWidth=1.6; ctx.stroke(unvisitedPath);
```
Need the wall to be clear in visited area. Since visited cells light and walls dark, yes.
- To show carving, maybe draw passage "bridge" fill for removed walls? Since cells connected by adjacent fills and no wall, enough.

Cell style:
- unvisited: `#111a2c`.
- visited generation: `#eaf2fb` maybe. Could use slight color based on DFS order/index? `carveOrder` array. To show progress visually, shade visited cells based on recency: older light gray-blue, newer mint/blue. Could set each cell's `carveIndex`; fill by age:
```
const age = carved - cell.carveIndex;
if age < 12 interpolate from '#8bd3ff' to '#e9f3fb'
else '#e9f3fb'
```
This makes carving progress visible. Current stack top bright yellow maybe.
- stack cells maybe highlighted with subtle blue outline? Could render DFS stack as a faint trail? Could be nice but not necessary. "carving progress visible" via cells lightening and moving head. Could draw stack path as thin blue line through centers to show backtracking. But maybe clutter. Could draw current cell fill cyan with a small pulsing outline. Also `carved count`.
- `recentCells` maybe last 8 with brighter blue gradient.

Generation algorithm with randomized neighbor:
```
function initMaze() {
 cells = Array.from({length:N}, (_,i)=>({r:...,c:...,walls:[true,true,true,true],visited:false,carveIndex:-1}));
 start.visited=true; carveIndex=0; carved=1; stack=[0]; generationDone=false; ...
}
function carveOne() {
 while(stack.length) {
   const idx=stack[stack.length-1];
   const candidates = neighborOffsets.map...filter(!visited)
   if(candidates.length) {
     const pick=candidates[Math.floor(Math.random()*...)]
     removeWalls(idx,next,direction)
     cells[next].visited=true; cells[next].carveIndex=carved++;
     stack.push(next);
     return true;
   }
   stack.pop();
 }
 generationDone=true;
 return false;
}
```
This performs all backtracking instantly once no frontier; at final return false. Visual still 374 carved steps. Need maybe show backtracking? Requirement recursive backtracking; not necessarily show pops. Could animate pops as steps too; then stronger. But our carveOne collapses multiple pops; still algorithm. Need maybe progress visible with current stack path. To be faithful to animation, perhaps define each frame as one backtracking step including either carve or pop; so all 748 steps visible. But would take longer. Could do 2 steps/tick. At default 2 and 28ms => 10.5 sec; okay. Let's implement one algorithm operation per logical step and 2 per tick if speed >=3? Need default speed 3: `genOperationsPerTick=2`, `solverExpansionsPerTick=2`, interval 24ms => ~9 sec generation, ~4.5 sec solver. Good. But at each pop there may be no visual change unless we render stack trail. We can show current cell and stack highlight. Need use `currentIndex=stack[stack.length-1]`; on pop, current moves back. Draw stack cells with a faint blue tint or line. That makes backtracking visible. Need initial generation finish when stack empties. At each logical step:
```
if stack empty -> finish
const current=...
const candidates...
if any: remove wall, mark visited, push, carved++; current=...
else { stack.pop(); backtracks++; current=stack top; }
```
At end, all cells visited (since tree). Number operations ~748. Default 2/tick=>374 ticks*24ms=9 sec. Fine. Maybe speed 4 =>4/tick*14ms=2.6 sec. We can set speed slider to 5 for quick checks. Need browser tool no arbitrary evaluate; can click slider at right. Could also add keyboard shortcuts? Not necessary.

Alternative use one carve + any pops hidden for 374 steps; simpler and enough. But a stack trail drawn during generation highlights progress. Faithfulness likely okay. I'd choose one algorithm op/tick at varying speed:
Speed settings:
```
[
 {label:'Slow', interval:90, carve:1, solve:1},
 {label:'Steady', interval:50, carve:1, solve:1},
 {label:'Normal', interval:26, carve:2, solve:2},
 {label:'Fast', interval:14, carve:3, solve:3},
 {label:'Turbo', interval:6, carve:6, solve:6}
]
```
At normal ~9.7 sec gen, ~5 sec BFS. Good. At slow 67 sec, maybe too slow but user can choose. "Slow" optional. Could use `slider value=3`, labels.

Need solver state:
```
let solver = { queue:[0], seen:Uint8Array(N), explored:Uint8Array(N), parent:Int32Array(N).fill(-1), solution:[], done:false};
```
Need typed arrays reset each replay. Could use Sets for simplicity; 375 cells. `Set` and Map. But to render, use sets.
```
solver = {
 seen: new Set([START]),
 frontier: new Set([START]),
 explored: new Set(),
 queue:[START],
 head:0,
 parent:new Map(),
 solution:[],
 expansions:0
};
```
Use queue head pointer, no shift. At step:
```
const idx=solver.queue[solver.head++];
solver.frontier.delete(idx);
solver.explored.add(idx);
solver.expansions++;
if idx===FINISH { buildSolution(); phase='solved'; ...; return false; }
for dirs:
 if open and !seen:
   seen.add(n); frontier.add(n); parent.set(n,idx); queue.push(n);
return true;
```
Draw `explored` cells with e.g. translucent aqua; frontier maybe purple with border/center dot. Could color both as exploration shades. Need legend includes "Exploration" maybe one swatch with blue/purple gradient. Requirement short legend; 4 or 5 items okay.
- `START` and `FINISH` remain distinct. If solver explored includes them, fill may override base; draw markers at end.
- Path: from finish back via parent. If solved, draw thick coral line. Could animate path tracing after BFS? Requirement "then highlight the complete path". Could reveal solution progressively along path for polish. Need maybe immediate highlight after BFS. Could add phase `'tracing'` with `solutionProgress` increments and animation; then phase `'solved'`. But "highlight complete path" eventually. Replay Solver should animate exploration then highlight. Could implement path reveal animation at same tick speed, with one cell per maybe 15ms. This adds visual. Need manage. Maybe simpler: at BFS finish, set `solution` full and phase='solved'; render. But requirement "then highlight complete path" can be immediate. Yet "animate either BFS or A-star exploring ... then highlight" okay. Could still trace path with animation for nicer. Let's implement path tracing:
```
function finishSearch(ts) {
 solution = buildPath();
 solutionProgress=1; phase='tracing'; phaseEnd=ts+...;
 log...
}
```
Then frame if `phase==='tracing'` increment progress based on tick; when >=solution.length, phase='solved'. Need choose path reveal speed maybe one cell per `interval` (or 2 per tick). This extends ~path length (could 50-150) * 26ms = 1-4 sec. Fine. But if BFS stops at finish on dequeue, explored count may be all cells (in tree, unique path; BFS from start visits cells in increasing tree depth; finish may be discovered late but not necessarily last; okay). Need avoid complexity with pause. Could define separate `traceAccumulator`. Use same loop interval.
- Path line drawn through centers from start to `solutionProgress` points, with partial segment? We can just draw integer prefix; likely fine. Animate highlight cell by cell. Need "complete path" at solved state. Need maybe label status "Tracing solution — 34 / 73 cells" then "Solved — path length 73".
- `replayBtn.disabled` could stay enabled during solving and tracing, so replay can restart. That's fine; stopAnimation cancels.
- New Maze always active.

Need app state phases: `'generating'`, `'mazeReady'`, `'solving'`, `'tracing'`, `'solved'`, maybe `'idle'`.
- `mazeReady` is a short pause before solver. During this phase, replay button enabled.
- `completeGeneration(ts)`:
```
generationComplete=true;
const validation=validateMaze();
console.log(...)
phase='mazeReady';
phaseUntil=ts+480;
updateUI();
```
- `frame(ts)`:
```
if (phase==='mazeReady') { if(ts>=phaseUntil) { resetSolver(); phase='solving'; } else { render maybe; schedule; return; } }
```
Need no huge accumulator from last generation; reset accumulator.
- For solving/tracing/generating use accumulator:
```
if (!lastTime) lastTime=ts;
let elapsed=ts-lastTime; lastTime=ts;
accumulator=Math.min(accumulator+elapsed, 250); // avoid catchup
while(accumulator>=interval && active && iterations<max?) { accumulator-=interval; performBatch(); }
render();
```
Need preserve timing after phase change. When changing from mazeReady, set accumulator=0 maybe. When new start, `lastTime=0; accumulator=0`.
- Each tick batch can perform e.g. `opsPerTick` steps. Need check phase inside loop to stop on generation finish/search finish. For solving, stop when finish dequeued. For tracing, increment path reveal by e.g. 2. Need call `updateUI` after batch and render maybe each frame. Could update UI only when counts change or phase; DOM updates 60fps fine, but we can call each frame.
- Need ensure generation animation current stack trail visible. We can draw stack line:
```
if phase==='generating' && stack.length>1:
 ctx.beginPath(); for stack centers lineTo; stroke rgba(56,165,248,.35), lineWidth=5; ctx.stroke();
```
Draw after cell fills before walls. When backtracking, stack line shrink. Could add tiny dot at each stack cell. This shows backtracking. Maybe too much but nice.
- Current cell: bright blue fill with inset circle or border. Need not overlap start/finish. Draw after walls:
```
ctx.fillStyle='rgba(14,165,233,.28)'; fill rect inset 3
ctx.strokeStyle='#0284c7'; lineWidth=2; strokeRect inset 4
ctx.beginPath arc center radius 4 fill...
```
- Start marker: green circle radius 10, white "S". Finish: orange rounded square or circle radius 10, "F" white/dark. Need distinct shape maybe start circle, finish diamond/square. Draw start as circle emerald with `S`; finish as rounded square amber with `F`. Legend swatches correspond.
- Solution: draw line through centers with width 8, rounded; perhaps outer glow width 14 rgba. Draw path cell fill perhaps light coral? Need avoid hiding exploration. Use line only. Ensure line under walls; path crosses open passages (centers along adjacent cells). Could perhaps add small circles at start/end. Markers on top.
- Exploration cells: fill with `rgba(14, 165, 233, 0.22)` for explored, frontier `rgba(139,92,246,.2)` with small square/dot. Need distinguish solution (coral line) clearly. Legend:
```
<span class=swatch start></span> Start
<span class=swatch finish></span> Finish
<span class=swatch explore></span> Explored / frontier
<span class=swatch path></span> Solution path
<span class=swatch carve></span> Current carve
```
Short legend perhaps 5 items.
- Unvisited not necessary, but "unvisited" may be in legend to explain dark cells. Could include 6 items. Requirement short legend; 5-6 okay. Use CSS swatches.

Status and metrics:
```
<div id=status class=status role=status>
 <span class=indicator></span>
 <strong id=phaseLabel>Generating…</strong>
 <span id=detail>...</span>
</div>
<div class=progress><div id=progressFill></div></div>
<div id=validation>Perfect maze check: pending</div>
```
Need maybe show "Batch #1" etc. Use:
- `phaseLabel`: "Carving maze #1"
- `detail`: "Recursive backtracking · 124 / 375 cells carved · stack 32"
- progress value carved/N for generation; explored/N for solving; solutionProgress/path length for tracing; 100% solved.
- `validation`: "Perfect maze: pending walls" during gen, "Perfect maze ✓ 375 reachable cells, 374 passages, no cycles" after. This directly signals invariant. Could compute validation at completion and set dataset. Need `validateMaze()` exact.
- Console logs:
```
console.log(`[maze] New maze #${mazeId}; previous animation cancelled`);
console.log(`[maze] #${id} complete: ${result...}`);
console.log(`[solver] BFS start on maze #${id}, wall signature ${sig}`);
console.log(`[solver] #${id} path found: ${solution.length} cells; all adjacent pairs open=true`);
console.log(`[replay] wall signature unchanged: ${before===after}`);
```
Need avoid too many logs; initial reload maybe console. Good.
- Maybe set `document.body.dataset...` and `app.dataset` for browser inspect. Need use status DOM. `updateUI` sets:
```
stage.dataset.phase=phase;
stage.dataset.mazeId=mazeId;
stage.dataset.carved=carved;
stage.dataset.generationComplete=...
stage.dataset.wallSignature=wallsSignature() maybe expensive each frame; compute only on replay/completion and store.
stage.dataset.explored=solver.explored.size;
stage.dataset.solutionLength=solution.length;
stage.dataset.pathOpen=... maybe after solution.
```
Could include a hidden `<output id="diagnostics">` with structured text visible maybe a small "Diagnostics" line. Let's make a small footer with `<span id=runInfo>Maze #1 · ...</span>` and maybe update. Hidden attributes with data might show in DOM snapshot? likely. Use markup:
```
<main id="app" data-phase="idle" ...>
...
<pre id="diagnostics" aria-hidden="true"></pre>
```
Could visually hide `display:none` but browser inspect maybe DOM text still. We can update with JSON:
```
diagnostics.textContent = JSON.stringify({phase,mazeId,carved, ...});
```
Could also expose `window.mazeAppDebug = ...`. Browser inspect might not show global. But console logging can be read.
Need potential evaluation via browser tool: `browser inspect` maybe returns arbitrary expression? Tool description says "Run index.html, inspect DOM/console, interact, and see screenshots or motion frames." `inspect` action likely no parameters except x/y? It may take text? Schema has `text` perhaps can pass JS? Need check. Could try `browser action=inspect text="..."` maybe perhaps not. But we can use `browser` tool's generic `text` for `type` only likely. Maybe inspect returns DOM including data attributes. We can also create on-page diagnostic text.

Need likely use `motion` action to inspect animation frames. Need perhaps read its output. We can test.

Need implement file with no external resources. Use system fonts (`ui-sans-serif`) and CSS gradients. All self-contained.

Need maybe check all walls removed correspond: direction constants `[0,-1]?` Let's define directions array:
```
const DIRS = [
 {dr:-1, dc:0, wall:0, opposite:2, bit:1},
 {dr:0, dc:1, wall:1, opposite:3, bit:2},
 {dr:0, dc:1?}
]
```
Let's carefully define `walls` as `[top,right,bottom,left]`.
```
const DIRS = [
 {dr:-1,dc:0,wall:0,opp:2}, // top
 {dr:0,dc:1,wall:1,opp:3}, // right
 {dr:1,dc:0,wall:2,opp:0}, // bottom
 {dr:0,dc:-1,wall:3,opp:1} // left
];
```
`neighborIndex(idx,dir)` computes `r=Math.floor(idx/COLS), c=idx%COLS`; in bounds.
`removeWall(a,nb,d)` set `cells[a].walls[d.wall]=false; cells[nb].walls[d.opp]=false;`.
`openBetween(a,b,d)` require adjacent and `!cells[a].walls[d]` and `!cells[b].walls[d.opp]`. Could simply check `!walls[d]`. For reciprocal consistency, validate both.
- Validate edge count: iterate right and bottom neighbors to avoid duplication.
```
for r,c:
 if c<COLS-1 && !walls[1] edges++;
 if r<ROWS-1 && !walls[2] edges++;
```
Check reciprocal for each internal wall:
```
if cells[i].walls[1] !== cells[i+1].walls[3] -> error
if cells[i].walls[2] !== cells[i+COLS].walls[0] -> error
```
Connectivity via BFS using openings; count all. Need also all cells `visited`. edges should N-1. If connected and edges=N-1, acyclic. "exactly one simple path between any pair" follows from connected tree. Could maybe explicitly check no cycles via union-find:
```
parent DSU; for each open edge, if find same cycle => false; union.
```
Do both. Need compute `allOpenAdjacent`: iterate right/down. `validateMaze` returns `{ok, reached, edges, cycles, reciprocal, visited}`.
- Might expose `window.__maze` object:
```
window.mazeDebug = {
 getSnapshot() { ... },
 wallsSignature() { ... },
 validate: () => validateMaze(),
 areOpen(a,b) ...
}
```
This helps if browser tool supports JS eval; otherwise just there. Need maybe a button that opens diagnostics? Not required but could include a "Run checks" button that prints diagnostics to visible panel. But no need. Could add a tiny details `<details><summary>Verification data</summary><pre id=...>` that shows JSON. Then browser inspect can read it; user perhaps sees current checks. But final app might look cluttered. Could use `details` collapsed but still DOM text. Nice:
```
<details class="checks">
 <summary>Verification data</summary>
 <pre id="diagnostics">{}</pre>
</details>
```
Collapsed by default, does not take much space. Browser inspect might include text. Could include after legend; a user can expand. Update diagnostics each UI update. This also demonstrates invariants. But perhaps `details` text in DOM snapshot even collapsed likely yes. We can style small. Need keep no network.

Need path verification:
- Build path from parent. Check:
```
function validateSolution(path) {
 path[0]===START, path.at(-1)===FINISH;
 for each pair:
   determine dr/dc; ensure adjacency, find DIRS index, !wall and reciprocal
}
```
Set `pathOpen` true in diagnostics/console. Need maybe visually show "Path crossings: open passages only ✓". Good.
- BFS exploration must "visible steps follow open passages." Each discovered neighbor checked via `isOpen(idx,n,d)`. We should maybe log first few? Could keep a `solverSteps` array record of `{from,to}` and verify all. diagnostics could count invalid transitions. Need ensure drawing of frontier only displays cells reached via open passages. Add `invalidSolverSteps=0`; in solver step if check false no enqueue. Could expose. Maybe use a thin animated line from parent to newly discovered? To visually demonstrate steps follow openings, draw "explorer" edges? Requirement asks check visible steps follow open passages. We can draw exploration tree edges (parent links) as thin blue lines between centers; because parent links are open passages. Then any visible exploration step line can be seen crossing only openings. Draw lines under walls:
```
for each seen cell with parent:
  line from parent center to cell center, stroke rgba(56,189,248,.28), lineWidth=3
```
This makes visible exploration paths. Need perhaps differentiate from solution. Use cyan for exploration tree, coral for solution. Then if walls drawn on top, any line crossing a wall would be hidden? Actually line under wall still visible until wall line; but since valid, no issue. Could add `ctx.strokeStyle='rgba(20,184,166,.25)'`. Maybe subtle.
- Animate current BFS node with a cyan ring. Then visible step from current to neighbors through open passages. Need perhaps draw line from current to frontier children specifically. We can draw `solver.lastEdges` from current to newly discovered neighbors in bright cyan for one tick. This clearly follows corridors. But rendering walls on top will mask if invalid. Need implement:
```
solver.lastEdges=[]
on expansion:
 for each discovered n: lastEdges.push([idx,n])
```
Draw after fills before walls with `strokeStyle='rgba(6,182,212,.85)'`, width 4, rounded; and a small dot at current. Then next frame moves. This is a visual step. Need if multiple expansions per tick, lastEdges only last expansion; okay at normal 2. Could perhaps keep edges from all batch but not needed.
- Need also distinguish "exploration" by fill. Good.

Potential issue: randomized recursive backtracking with 25x15 cells and DFS could produce a very long winding path (hundreds). Fine.

Responsive:
```
body { min-height:100vh; margin:0; background radial-gradient...; color:#e8eff9; font-family:...; display:flex; justify-content:center; padding:22px; }
.shell { width:min(100%, 1000px); }
header ... 
```
Maybe all in 800px. Need top header + canvas + legend. Use CSS grid desktop header maybe controls right, but at 1200 width ~1000. On mobile stack. Fine.
Canvas wrapper `.canvas-card { background:#0b1221; border...; padding:12px; border-radius:18px; }`. Canvas itself width:100%; max-width:832px; margin:auto; aspect-ratio...; background...; border-radius:8px;.
At 1200x800, shell width 1000; canvas max 832; header 90; stage padding 12x2 + 512 + status/progress 60 = 596; legend 60; footer ~30; total ~776 plus body padding 32 = 808 maybe slight scroll. Fine. Could reduce body padding to 14 => 792. Or canvas max-width 760 to fit. CSS width: min(100%, 832px) but shell width 1000; centered. Height 512. Need perhaps use `max-height`? Could set `.canvas-frame { width:min(100%, 790px); }` and canvas scales to 790x486, saving 26px. But walls still clear. Let's choose logical 900x560? Hmm.

Let's calculate: body padding top/bottom 16*2=32. header maybe 88 (h1 30 + p 16 + controls 40 + gaps 10) = 96. stage: card padding 12*2=24 + canvas 512 + status row 36 + progress 8 + gaps 12 = 592. legend 54 + margin 12 =66. checks collapsed summary 28 + margin 10 =38. total 824. Need maybe scroll. Browser initial screenshot 800 tall may show legend partially. Could use canvas logical 832x512 but CSS max-width 760 (scales to 468 height), saving 44 -> total 780. Good. Set `.canvas-wrap { max-width: 780px; margin:auto; }`, canvas width 100%, height auto. That fits. At 1200 viewport, shell width 1000, canvas 780x480. Clear enough. Or 800x492. Use max-width:800px. Total ~798. Good.
Could make header compact and legend inline. Fine.

Need perhaps screenshot initial output after reload; generation active so dark lattice with small carved region. Need browser initial screenshot maybe after load delay? Browser tool likely loads and screenshot some time. We can maybe use `reload`, then `screenshot`. Need inspect console. Use browser tool. Need possibly use actions with coordinates. Need know button positions; can inspect DOM first. Browser inspect output likely includes bounding boxes etc. We can use screenshot visually determine.

Need maybe use a lightweight test harness? Could run Node with jsdom? likely not installed. Could use browser tool. Need perhaps write custom JS to run validation and log. Could include an internal self-test that runs after generation complete. Need all app code has no syntax errors. We can use `node --check` by extracting script? Could use bash with Python regex to extract and node --check. Need no external deps. We can run a quick syntax check after writing:
```
python - <<'PY'
... extract script ...
PY
node --check /tmp/app.js
```
Allowed since file operations. Need maybe use jsdom absent. Could maybe parse with Node's `vm` but DOM references fail. We can use `node --check`.

Need perhaps ensure no network requests. No external URLs, no fetch.

Let's draft code fully. Need be careful with `ctx.roundRect` compatibility; could avoid. Use custom `roundedRect` helper or use `ctx.fillRect`. For buttons CSS only. Canvas use `arc`, `fillRect`, `strokeRect`. For finish marker rounded square perhaps use custom `roundRectPath` with quadratic curves. Good.

Color scheme:
```
:root {
 --bg:#07111f; --panel:#0d1a2d; --ink:#eaf2ff; --muted:#9badc4; --line:#29405e; --accent:#38bdf8; --start:#22c55e; --finish:#f59e0b; --solution:#fb7185;
}
```
Canvas:
- `BACK='#0b1424'`
- unvisited `#111e33`
- carved `#e9f2fb`
- recent gradient from `#93c5fd` to etc. Need compute colors perhaps use HSL:
```
if (cell.carveIndex>=0 && phase==='generating') {
 const age=carved-cell.carveIndex;
 if(age<10) ctx.fillStyle=`hsl(${205 - age*2} 90% ${72 - age*1.5}%)`; else '#e8f1fa';
}
```
But after generation, need reset base to carved light. Use generation phase only. During solving, visited cells all `#e8f1fa` with exploration overlays.
- For unvisited, perhaps draw subtle all walls. `ctx.fillStyle = '#101d31'`.
- Draw stack trail perhaps blue/mint. Need avoid interfering with unvisited region: stack only visited cells.
- Draw generation current marker maybe neon blue.
- Walls path for visited/unvisited:
```
const visitedPath = new Path2D(); const unvisitedPath = new Path2D();
...
const active = cell.carveIndex>=0; const target=active?visitedPath:unvisitedPath;
if(walls[0]) ...
if(walls[3]) ...
if(r===ROWS-1 && walls[2]) ...
if(c===COLS-1 && walls[1]) ...
```
`Path2D` is standard. Could avoid to be safe with `ctx.beginPath()` groups:
```
function strokeWalls(filterColor, visited) {
 ctx.beginPath();
 for cells where cell.carveIndex>=0===visited ... add segments
 ctx.strokeStyle=...; ctx.lineWidth=...
 ctx.stroke();
}
```
Need call twice, loops through all cells each time. Fine.
Actually if cell has carveIndex >=0 after generation; yes.
- For unvisited walls color `#425b7a`, lineWidth 1.4; visited walls `#23364f`, lineWidth 2.4. Outer border separate white-ish/blue.
- To ensure removed wall boundaries between visited/unvisited don't get accidentally drawn: top/left condition based on target cell's wall. If target unvisited, wall true; if visited and removed with previous cell, false. Fine.
- Need maybe draw all wall segments with lineCap='square'; outer border lineWidth=3.0. Shared walls with lineWidth 2.4.
- Path drawing:
```
function drawSolutionPath() {
 if (!solution.length||solutionProgress<1) return;
 const count=Math.min(solution.length, Math.floor(solutionProgress)); // solutionProgress integer
 ctx.lineCap='round'; ctx.lineJoin='round';
 ctx.beginPath(); centers...
 ctx.strokeStyle='rgba(251,113,133,.25)'; ctx.lineWidth=14; stroke();
 ctx.strokeStyle='#fb7185'; ctx.lineWidth=6; stroke();
 // maybe little circle at end of partial path
}
```
Need if solutionProgress=1, line with one point doesn't show; draw small circle. Fine.
- Exploration tree:
```
if (solver.parent.size) {
 ctx.strokeStyle='rgba(14,165,233,.22)'; lineWidth=4;
 for ([child,parent] of solver.parent) line...
}
if (solver.lastEdges.length) bright lines...
```
Need visually no wall crossings; drawing walls after.
- Exploration cell fills:
```
for idx of solver.explored: fillStyle='rgba(14,165,233,.25)'; fillRect(x+2,y+2,CELL-4,CELL-4)
for idx of solver.frontier: fillStyle='rgba(139,92,246,.25)'; ...; maybe dot
```
- Start/finish markers:
```
ctx.save(); ctx.translate(cx,cy);
ctx.shadowColor ...; ctx.shadowBlur=10;
circle start...
ctx.fillText('S'...); 
```
Need set text baseline etc. Finish:
```
roundRectPath(ctx,-10,-10,20,20,5); fill.
```
- If current carve equals start/finish, marker draws over. Fine.
- Need maybe draw "Start / Finish" text outside? Legend enough. Markers S and F.
- Could draw small flags? no.

Progress and status:
```
function updateUI() {
 let label, detail, pct;
 switch...
 root.dataset.phase=phase; root.dataset.mazeId=...
 ...
 diagnostic.textContent = JSON.stringify({...}, null, 2);
}
```
Need avoid `wallsSignature()` every frame perhaps signature = computed when maze complete. But can compute for diagnostic each time maybe 375*4 bits => simple. Could cache:
```
let wallSignature='';
function signature() { ... bits ... return hash string maybe simple FNV hex }
```
At New Maze, signature initial; after each wall removal could update? No need until complete/replay. For diagnostic, store `wallSignature = computeWallSignature()` at completion. Replay sets `replaySignatureMatch`.
Need data attributes:
```
root.dataset.wallSignature=wallSignature;
root.dataset.pathOpen=String(pathOpen);
root.dataset.invalidSolverSteps=String(invalidSteps);
root.dataset.generationComplete=String(generationComplete);
```
Need snapshot diagnostic include:
```
{
 phase, mazeId, carved, total:N, generationComplete,
 validation, wallSignature,
 explored: solver.explored.size, frontier:solver.frontier.size,
 solutionLength:solution.length, pathRevealed:..., pathOpen,
 invalidSolverEdges:solver.invalidEdges,
 replayWallsUnchanged:...
}
```
Could update every frame; fine. Need avoid including Sets directly in JSON.

Need `validateMaze` potentially use DSU. Let's implement robust:
```
function validateMaze() {
 const parent = Array.from({length:N},(_,i)=>i);
 function find(x){...}
 let cycles=0, edges=0, reciprocal=true;
 for i:
  if c+1<COLS:
    const j=i+1; const aOpen=!cells[i].walls[1]; const bOpen=!cells[j].walls[3];
    if(aOpen!==bOpen) reciprocal=false;
    if(aOpen && bOpen){ edges++; if(find(i)===find(j)) cycles++; else union; }
  ...
 connectivity via stack from START using openDirection helper; seen...
 return {ok:...}
}
```
Need ensure walls indices. `openInDirection(i,d)` checks both cells? For traversal:
```
function passageOpen(i,d) {
 const n=neighborIndex(i,d); if(n<0) return false;
 return !cells[i].walls[d.wall] && !cells[n].walls[d.opp];
}
```
Use this in BFS too.
`allVisited = cells.every(c=>c.carveIndex>=0)`.
`ok = reached===N && edges===N-1 && cycles===0 && reciprocal && allVisited && carved===N`.
- Because DFS can finish stack empty before all cells visited only if bug; but should. Need if `stack.length===0 && carved<N` maybe fallback? Could run generation until all visited? Since graph connected grid, DFS from start visits all. Fine.
- Need path validation with `directionBetween(a,b)`:
```
const dr=Math.floor(b/COLS)-Math.floor(a/COLS), dc=...
return DIRS.find(d=>d.dr===dr && d.dc===dc)
```
`passageOpen(a,d)`.
- `solution` build:
```
const path=[]; let at=FINISH; while(at!==-1){path.push(at); if(at===START) break; at=solver.parent.get(at)??-1;}
path.reverse();
if(path[0]!==START) { ... }
pathOpen=validate...
```
Need if parent missing impossible.
- `invalidSolverEdges` count: BFS only checks `passageOpen` before enqueue. If false no enqueue. Could increment if attempted? We don't attempt walls; filtered. Need maybe `lastEdges` all valid by construction. We can count invalid ones if `passageOpen` false but walls state erroneously. Not needed. Could set `invalidSolverEdges=0` and verify each parent edge via path validation. Need maybe diagnostics says "solverEdgesOpen": every parent edge open. Compute:
```
function allParentEdgesOpen() {
 for (const [child,parent] of solver.parent) {
   const d=directionBetween(parent,child);
   if(d<0 || !passageOpen(parent,d)) return false;
 }
 return true;
}
```
Set diagnostic `solverEdgesOpen`. This directly checks visible exploration steps. Could update every UI refresh; map <=375, cheap.
- Need maybe store `lastEdges` from current expansion; drawn via center lines. All checked.

Animation cancellation nuance with `requestAnimationFrame`:
- At initialization, call `newMaze()` which calls `stopAnimation()` -> `epoch++` from 0 to1; cancel null; setup; `startLoop()` captures `myEpoch=epoch`; calls `rafId=requestAnimationFrame(tick)`. `tick` closure calls `tick(ts, epoch)`? We can define:
```
function startLoop() {
 const token=epoch;
 lastTime=0; accumulator=0;
 function frame(ts) {
   if (token !== epoch) return;
   ...
   if (isAnimating()) rafId=requestAnimationFrame(frame);
   else rafId=null;
 }
 rafId=requestAnimationFrame(frame);
}
```
The frame closure captures token. `stopAnimation` increments epoch and cancels current scheduled RAF. If a frame is currently executing and calls New Maze synchronously? Event handler doesn't overlap with RAF in JS single thread. Fine.
- `stopAnimation()`:
```
if(rafId!==null) cancelAnimationFrame(rafId);
rafId=null;
epoch++;
lastTime=0; accumulator=0;
```
But startLoop captures new epoch. Good.
- Need `isAnimating()` maybe phases generating/mazeReady/solving/tracing; `'solved'` stops loop. If phase `'solved'`, no more RAF. But Replay button still works; New Maze works.
- If replay during mazeReady, `stopAnimation()` increments and calls `beginSolver()` which might call `startLoop()`, okay.
- At generation completion, we don't want `stopAnimation`; we just set phase and phaseUntil. Need render and schedule continues. We can at end of batch:
```
if (phase==='generating' && stack.length===0) {
 finishGeneration(ts);
 break; // maybe no solver until delay
}
```
`finishGeneration(ts)` sets `phase='mazeReady'; phaseUntil=ts+450; accumulator=0; validation=...; console.log`.
- In frame:
```
if (phase==='mazeReady' && ts>=phaseUntil) {
 resetSolver();
 phase='solving';
 accumulator=0;
 console.log...
}
```
Then process time loop in same frame perhaps. Need `lastTime` update logic. Could structure:
```
function frame(ts){
 if(token!==epoch)return;
 if(!lastTime) lastTime=ts;
 let dt=Math.min(ts-lastTime,200); lastTime=ts;

 if(phase==='mazeReady' && ts>=phaseUntil){ beginSolver(); accumulator=0; }
 if(phase==='mazeReady') { render(); updateUI(); rafId=requestAnimationFrame(frame); return; }

 accumulator+=dt;
 const config=...
 let guard=0;
 while(accumulator>=interval && guard++<20){
   accumulator-=interval;
   performSteps(config, ts);
   if(!isAnimating()) break;
 }
 render(); updateUI();
 if(isAnimating()) rafId=... else rafId=null;
}
```
`performSteps` for generating:
```
for i<config.genOps:
 if(!carveStep()) { finishGeneration(ts); break; }
```
Need `carveStep` returns false when stack empty. At final pop, stack becomes empty and return false. Actually if it pops last cell, stack empty; should return false. Need check:
```
else {
 stack.pop();
 if(stack.length===0) return false;
 return true;
}
```
All cells already carved. Fine.
- solving:
```
for i<config.solveOps:
 if(!bfsStep()) { beginTrace(ts); break; }
```
`bfsStep` returns false when finish dequeued or queue exhausted. Need if queue exhausted with no path (shouldn't) set phase failed; maybe status.
- tracing:
```
for i<config.traceOps:
 solutionProgress++;
 if(solutionProgress>=solution.length) { phase='solved'; ...; break; }
```
At beginTrace, `solutionProgress=1`; need if path length=1 (impossible) solved.
- `isAnimating` returns phase in generating, mazeReady, solving, tracing.
- On `phase='solved'`, update UI and render; loop ends. But maybe `status` needs final; frame does.
- Need initial render before first frame on New Maze; call `render(); updateUI();` inside newMaze before startLoop.
- Need maybe `New Maze` button click while generation active: call stopAnimation increments epoch; reset; render; startLoop. Old `frame` callback canceled, and even if executes checks token. clean.
- Need `Replay Solver` click while solving/tracing: stopAnimation; reset solver; no wall changes; render; startLoop. Need store `signatureBefore` and `signatureAfter` and log.
- `Replay Solver` button disabled while `!generationComplete` (i.e. during generation). On generation complete, enable. Could style disabled. Need updateUI set disabled accordingly. But if replay button disabled and user clicks via browser, no event. Fine.
- Speed slider: input event updates config/label. No need cancel loop. Need maybe `speedLabel.textContent = SPEEDS[value-1].name`. To inspect step pace, user can drag. Browser click slider maybe. Need perhaps use keyboard with focused slider? Could use browser `click` at x then `key` ArrowRight etc. But likely not needed.

Need perhaps add "Skip to solver" button? Not required. Avoid.

Need internal diagnostics panel maybe useful. Let's add a details with `id=diagnosticsBox` collapsed:
```
<details class="diagnostics">
 <summary>Live verification</summary>
 <pre id="diagnostics"></pre>
</details>
```
If collapsed, height ~30. Need update its content.
- Include explanatory line in summary? "Live verification (perfect maze + passage checks)" perhaps.
- `status` perhaps show validation pill:
```
<span id=validationBadge class=badge>pending</span>
```
Need short. Could include in status. 
Maybe:
```
<div class="status-line">
 <div class=status-left><span class=pulse></span><strong id=phaseLabel>...</strong><span id=phaseDetail>...</span></div>
 <span id=badge class=badge>...</span>
</div>
<div class=progress><div id=progressFill></div></div>
```
`badge`: "Tree check pending" / "Perfect maze ✓" / "Path valid ✓".
- Controls at header:
```
<button class=primary id=newMaze>↻ New Maze</button>
<button id=replay disabled>▶ Replay Solver</button>
<div class=speed> ... </div>
```
Unicode icons okay; no external assets. Maybe use plain text to avoid font issues. Use `⟳` etc. fine.
- Legend below stage:
```
<div class=legend aria-label="Legend">
 <span><i class="swatch start"></i>Start (S)</span>
 ...
</div>
```
CSS swatches. Need short.
- Header text mentions "25 × 15 • randomized recursive backtracking • breadth-first search". Good.
- Canvas `<canvas id=maze width=832 height=512 role=img aria-label=...>`. Need fallback text.

Potential issue with browser initial console: some CSS `color-mix` might not be supported; avoid. Use standard gradients. Use `accent-color`. Fine.

Need generate file. Let's write carefully. Could use write tool. Let's draft full HTML ~600 lines maybe. Need concise but thorough.

Let's build code:

```
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8">
<meta name="viewport"...>
<title>Maze Generator & Solver</title>
<style>
...
</style>
</head>
<body>
<main id="app" data-phase="idle"...>
<header>...
</header>
<section class=card>
 <div class=canvas-wrap><canvas ...>...</canvas></div>
 <div class=status...>
 ...
</section>
<section class=legend...>
...
</section>
<details class=diagnostics>
<summary>Live verification data</summary>
<pre id=diagnostics></pre>
</details>
</main>
<script>
(() => {
 'use strict';
 const COLS=25...
 ...
})();
</script>
</body>
</html>
```
Need if app dataset initial maybe set. Good.

Detailed JS:
```
const canvas=...
const ctx=canvas.getContext('2d');
const app=...
...
const DIRS=...
const START=0, FINISH=N-1;
const SPEEDS = ...
let cells=[], stack=[], mazeId=0, carved=0, generationComplete=false, stackTop=-1;
let solver = emptySolver();
let solution=[], solutionProgress=0, pathOpen=null, solverEdgesOpen=null;
let phase='idle', phaseUntil=0, validation=null, wallSignature='';
let replayWallsUnchanged=null;
let rafId=null, epoch=0, lastTime=0, accumulator=0;
let speedIndex=3;
```
`emptySolver()` returns object with sets etc:
```
function freshSolver() {
 return {seen:new Set([START]), frontier:new Set([START]), explored:new Set(), parent:new Map(), queue:[START], head:0, current:START, lastEdges:[], expansions:0};
}
let solver=freshSolver(); 
```
Need call after constants. Fine.

`cellIndex`, `cellRow`, `cellCol`, `centerX/Y`.
`neighbor(idx,d)`:
```
const r=Math.floor(idx/COLS), c=idx%COLS, nr=r+DIRS[d].dr...
return {idx:nr*COLS+nc, dir: d}
```
Could optimize by function `neighborInDirection(idx,d)` returns index or -1.
```
function neighborIndex(idx,dIndex) {...}
function passageOpen(idx,dIndex) {...}
```
`directionBetween` returns index or -1.
`shuffle` not needed; candidates built with random selection. Need randomize order? Pick random candidate suffices, but deterministic neighbor list order with random pick is standard randomized. Could also shuffle candidate list using Fisher-Yates; no need.

`initCells()`:
```
cells=Array.from({length:N},(_,i)=>({walls:[true,true,true,true],carveIndex:-1}));
```
Need maybe avoid shared array reference; yes.

`resetMaze()`:
```
stack=[START]; cells[START].carveIndex=0; carved=1; generationComplete=false; solver=freshSolver(); solution=[]; ...
validation=null; wallSignature=''; pathOpen=null; ...
```
Need `freshSolver` may override current marker even during generation; no issue.

`removeWall`.
`carveStep()`:
```
if(stack.length===0) return false;
const current=stack[stack.length-1];
const candidates=[];
for d 0..3 { n=neighborIndex(current,d); if(n>=0 && cells[n].carveIndex<0) candidates.push(...)}
if(candidates.length) {
 const pick=...
 removeWall...
 cells[pick.n].carveIndex=carved++;
 stack.push(pick.n);
 return true;
}
stack.pop();
return stack.length>0;
```
Need when stack length becomes0, return false; UI frame calls finishGeneration. Good.
`carved` increments to N exactly.
`generationComplete` set in finish.

`finishGeneration(ts)`:
```
generationComplete=true;
validation=validateMaze();
wallSignature=computeWallSignature();
phase='mazeReady';
phaseUntil=ts+450;
accumulator=0;
console.log('[maze] ...', validation);
```
Need if validation not ok, console.error but still solver; maybe fail. Could set badge. Can't log object with browser inspect perhaps. Fine.
`validateMaze` uses `passageOpen` which checks reciprocal. Connectivity.
Implementation DSU:
```
const dsu = Array.from({length:N},(_,i)=>i);
function find(x){ while(dsu[x]!==x){ dsu[x]=dsu[dsu[x]]; x=dsu[x];} return x;}
...
if(find(i)===find(j)) cycles++; else dsu[find(i)]=find(j); // careful call find twice after assignment; store roots.
```
Need open passage count and reciprocal. Loop for all cells:
```
if(c<COLS-1){ const right=i+1; const openA=!cells[i].walls[1], openB=!cells[right].walls[3]; if(openA!==openB) reciprocal=false; if(openA&&openB){...}}
if(r<ROWS-1){...}
```
Connectivity BFS:
```
const seen=new Uint8Array(N); const q=[START]; seen[START]=1; let reached=0, head=0;
while(head<q.length){ const at=q[head++]; reached++; for d... if(passageOpen(at,d)){...}}
```
All outer walls true check? Could include:
```
let borderIntact=true;
for c: if(!cells[c].walls[0]...)...
```
Need check top row etc. Good.
`ok=... && borderIntact`.
`computeWallSignature`: maybe string of 0/1 for right/bottom plus boundaries. Need simple hash:
```
let bits='';
for cell walls four bits? Could create chars `cells[i].walls.map...`; 1500 chars; signature hash via FNV:
let h=2166136261;
for each wall bit:
 h ^= bit; h=Math.imul(h,16777619);
return (h>>>0).toString(16).padStart(8,'0');
```
Could include mazeId? no, pure walls. Need signature stable. Use all 4 walls bits. Fine.
`validateParentEdges`:
```
let all=true;
for(const [child,parent] of solver.parent){ const d=directionBetween(parent,child); if(d<0||!passageOpen(parent,d)){all=false;break;}}
return all;
```
Need `directionBetween` based on row/col difference. If parent-child adjacent; okay.
`validatePath(path)`:
```
if(path[0]!==START||path[path.length-1]!==FINISH) return false;
for i... {const d=directionBetween(...); if(d<0||!passageOpen(...)) return false;}
return true;
```
`beginSolver(replay=false)`:
```
solver=freshSolver(); solution=[]; ...; phase='solving'; phaseUntil=0; accumulator=0; replayBtn.disabled=false;
const before=computeWallSignature(); maybe assign wallSignature if not set.
console.log(`[solver] ...`);
```
Need replay walls unchanged assertion:
```
function replaySolver(){
 if(!generationComplete)return;
 const before=computeWallSignature();
 stopAnimation();
 const after=computeWallSignature();
 replayWallsUnchanged = before===after && before===wallSignature;
 beginSolver(true); // doesn't modify walls
 console.log(`[replay] wall signature...`);
}
```
But `stopAnimation` doesn't modify walls. `beginSolver` doesn't. Could call `stopAnimation(); resetSolver...`; need not call `beginSolver` that sets `wallSignature` perhaps. Keep `wallSignature` from generation. Need track `replayWallsUnchanged` after `beginSolver`.
```
function replaySolver() {
 if (!generationComplete) return;
 const before=computeWallSignature();
 stopAnimation();
 resetSolverState();
 phase='solving';...
 const after=computeWallSignature();
 replayWallsUnchanged=(before===after && after===wallSignature);
 console.log(...)
 render(); updateUI(); startLoop();
}
```
Need maybe restart loop from start with proper lastTime. `startLoop()` sets lastTime=0.
- During mazeReady auto-solver, call `resetSolverState()` and phase solving; don't call stopAnimation. Need maybe `console.log` and reset accumulator.
```
function startBFS(replay) {...}
```
Can unify:
```
function prepareSolver(replay) {
 solver=freshSolver(); solution=[]; ...; phase='solving'; ...
}
```
Then both call.

`bfsStep()`:
```
if(solver.head>=solver.queue.length) { phase='failed'; ...; return false; }
const current=solver.queue[solver.head++];
solver.frontier.delete(current);
solver.explored.add(current);
solver.current=current;
solver.lastEdges=[];
if(current===FINISH) { buildSolution(); return false; }
for d=0..3:
 const n=neighborIndex(current,d);
 if(n<0 || solver.seen.has(n)) continue;
 if(!passageOpen(current,d)) continue;
 solver.seen.add(n); solver.frontier.add(n); solver.parent.set(n,current); solver.queue.push(n); solver.lastEdges.push([current,n]);
return true;
```
Need if no new edges, lastEdges empty and current ring still moves. Fine.
`buildSolution()`:
```
const path=[]; let at=FINISH; let guard=0;
while(at!==-1 && guard++<=N) { path.push(at); if(at===START) break; at=solver.parent.has(at)?solver.parent.get(at):-1;}
path.reverse();
if(path[0]===START){solution=path;} else {solution=[];}
pathOpen=validatePath(solution);
solutionProgress=Math.min(1,solution.length);
phase = solution.length>1 ? 'tracing':'solved';
if(phase==='solved') ...
console.log(...);
```
Need when finish dequeued, parent chain to start exists. Good.
`beginTrace()` perhaps just set phase in buildSolution. Need `lastTime` not reset. Fine.
Need if replay can click during tracing; works.

`stepBatch(config, ts)`:
```
if(phase==='generating') {
 for... if(!carveStep()){finishGeneration(ts);break;}
} else if(phase==='solving') {
 for... if(!bfsStep()) break;
} else if(phase==='tracing') {
 for... {
  solutionProgress=Math.min(solution.length, solutionProgress+1);
  if(solutionProgress>=solution.length) { phase='solved'; console.log; break; }
 }
}
```
`bfsStep` on finish sets phase tracing, so loop should break:
```
if(phase!=='solving') break;
```
Need return active.
```
function performBatch(cfg,ts){
...
}
```
If generation completes, `finishGeneration(ts)` sets phase mazeReady. Need break.
`frame`:
```
function frame(ts){
 if(token!==epoch)return;
 if(!lastTime)lastTime=ts;
 const dt=Math.min(200,ts-lastTime); lastTime=ts;
 if(phase==='mazeReady' && ts>=phaseUntil){
   prepareSolver(false);
   accumulator=0;
 }
 if(phase==='mazeReady'){
   render(); updateUI(); rafId=requestAnimationFrame(frame); return;
 }
 const cfg=SPEEDS[speedIndex-1];
 accumulator+=dt;
 let guard=0;
 while(accumulator>=cfg.interval && guard++<16 && isAnimating()){
    accumulator-=cfg.interval;
    performBatch(cfg,ts);
    if(phase==='mazeReady') {accumulator=0; break;}
 }
 render(); updateUI();
 if(isAnimating()) rafId=requestAnimationFrame(frame); else {rafId=null;}
}
```
Potential issue when `phase` transitions from `solving` to `tracing` inside performBatch, while loop continues with same config and perhaps calls trace increments in same batch if loop iterations remain. Fine. When `phase` becomes solved, `isAnimating` false and loop ends.
`isAnimating` includes mazeReady. In while condition, if phase mazeReady after generation, could continue condition? We explicitly break on phase==='mazeReady'. Good.
`guard<16` avoids catchup. If dt huge and interval small, 16 batches max. Fine.
`accumulator` after phase changes from solving to tracing not reset; okay.
- Need maybe render during mazeReady pause every frame; fine.

`startLoop`:
```
function startLoop(){
 const token=epoch;
 lastTime=0; accumulator=0;
 function frame(ts){... frame...}
 rafId=requestAnimationFrame(frame);
}
```
Need name conflict with outer `frame` if define inside; okay.
`stopAnimation`:
```
if(rafId!==null) cancelAnimationFrame(rafId);
rafId=null; epoch+=1; lastTime=0; accumulator=0;
```
`newMaze`:
```
function newMaze(){
 stopAnimation();
 mazeId++;
 resetMazeState();
 phase='generating';
 console.log(`[maze] ...`);
 render(); updateUI(); startLoop();
}
```
Important: `resetMazeState()` calls `solver=freshSolver()`, which uses START constant. Fine. It should set `replayWallsUnchanged=null`, `pathOpen=null`, etc.
- `wallSignature` compute initial? Set `''` until complete. Fine.
- `updateUI()` calls `replayBtn.disabled=!generationComplete`. During phase generating false. On solved true. Fine.
- `status` initial after reset. Need `validation` null.
- Need `phaseUntil=0`.

`replaySolver`:
```
function replaySolver(){
 if(!generationComplete) return;
 const before=computeWallSignature();
 stopAnimation();
 prepareSolver(true);
 const after=computeWallSignature();
 replayWallsUnchanged = before===after && after===wallSignature;
 wallSignature=after; // maybe keep
 console.log(`[replay] maze #... walls unchanged=${...} signature=${after}`);
 render(); updateUI(); startLoop();
}
```
`prepareSolver(true)` should not change wallSignature. Need perhaps set phase solving and log. It resets `replayWallsUnchanged`? no.
```
function prepareSolver(isReplay){
 solver=freshSolver();...
 phase='solving'; phaseUntil=0; accumulator=0;
 console.log(`[solver] ...`);
}
```
Need if auto begins during frame, setting accumulator=0 then frame adds dt after? In frame we currently calculate dt before phase transition, then `accumulator=0`, then skip mazeReady and then accumulator += dt (but code architecture maybe yes). We can structure to avoid. Let's lay out:
```
function frame(ts) {
 if token...
 if(lastTime===0) lastTime=ts;
 let dt=...; lastTime=ts;

 if(phase==='mazeReady' && ts>=phaseUntil){ prepareSolver(false); dt=0; accumulator=0; }
 if(phase==='mazeReady') { ...; return; }

 accumulator += dt;
 ...
}
```
Set dt=0. Fine.
- `prepareSolver` sets `accumulator=0` but frame then adds dt; dt=0.
- `startLoop` after New Maze sets lastTime=0; first frame dt=0. Good.
- In replay, `prepareSolver` sets `accumulator=0`; then `startLoop` resets. Fine.

`fitCanvas`:
```
function fitCanvas(){
 const rect=canvas.getBoundingClientRect();
 const dpr=Math.min(window.devicePixelRatio||1,2);
 const w=Math.max(1,Math.round(rect.width*dpr));
 const h=Math.max(1,Math.round(rect.height*dpr));
 if(canvas.width!==w||canvas.height!==h){canvas.width=w;canvas.height=h;}
 render();
}
```
But CSS canvas has `height:auto` and width/height attributes initially 832/512; if we change width/height attributes to CSS*dpr, CSS `height:auto` will use intrinsic aspect ratio w/h. If w/h ratio matches CSS width rect / rect.height (which uses aspect-ratio CSS), okay. We should set CSS explicitly `aspect-ratio: 832 / 512; height: auto;` and width 100%. When `canvas.width/height` set to dpr-scaled rect, intrinsic ratio still same, so rect remains. But if width attr changed, CSS width 100% still, height auto uses intrinsic ratio; yes.
Need `render()` sets transform based on `canvas.width/WORLD_W`, `canvas.height/WORLD_H`; if canvas CSS width smaller than WORLD_W, scale <1*dpr perhaps. Fine.
```
function render(){
 const sx=canvas.width/WORLD_W, sy=canvas.height/WORLD_H;
 ctx.setTransform(sx,0,0,sy,0,0);
 ctx.clearRect(0,0,WORLD_W,WORLD_H);
 ...
}
```
Need if `canvas.width` initially 832 and `canvas.height` 512, transform 1. Good.
- `window.addEventListener('resize', fitCanvas);` But `fitCanvas` calls render; if called during a frame, transform setup is correct.
- Could use ResizeObserver to handle container. DevicePixelRatio only. `ResizeObserver` standard. Use:
```
new ResizeObserver(fitCanvas).observe(canvas);
```
But changing canvas width/height may trigger resize? CSS rect unchanged, so no. Add fallback window resize.
- Need avoid render before cells initialized? At script bottom, `newMaze()` will call render; then fitCanvas maybe. We can call `fitCanvas()` before `newMaze()`? If render uses cells empty, fine maybe all loops skip. Better:
```
init event listeners();
fitCanvas(); // cells empty; render background only
newMaze();
```
But fitCanvas can use `cells` empty in render; need render guards. Simpler call `newMaze()` first (render with intrinsic dims), then `fitCanvas()`. The canvas rect is available after DOM loaded since script at bottom. Good.
- `ResizeObserver` callback can call fitCanvas repeatedly. Fine.

`render` details:
```
function render(){
 ctx.setTransform(...);
 ctx.clearRect...
 ctx.fillStyle=BACKGROUND; ctx.fillRect(0,0,W,H);
 // maybe subtle outer glow
 ctx.fillStyle='#0d192b'; roundRect? no
 // cell fills
 for i...
 // stack trail
 // exploration overlays
 // exploration parent edges and last edges
 // solution path
 // wall strokes
 // current markers
 // start/finish
}
```
Need `roundRectPath` helper maybe for finish marker only. Could also use for stage? no.
Cell fill:
```
for (let i=0;i<N;i++){
 const cell=cells[i]; const x=PAD+(i%COLS)*CELL, y=PAD+Math.floor(i/COLS)*CELL;
 if(cell.carveIndex<0) {
   ctx.fillStyle='#111d31'; ctx.fillRect(x+0.5,y+0.5,CELL-1,CELL-1);
 } else {
   let fill='#e9f2fb';
   if(phase==='generating'){
      const age=carved-cell.carveIndex;
      if(age<=12) fill=`hsl(${202+Math.min(age,12)*2} 90% ${78-Math.min(age,12)*2.2}%)`;
      else fill='#e9f2fb';
   }
   ctx.fillStyle=fill; ctx.fillRect(x,y,CELL,CELL);
 }
}
```
Need boundary line widths and fill seams. fillRect x,y,CELL,CELL adjacent; no gaps. For unvisited use full cell; then unvisited wall grid drawn. Fine.
- perhaps grid dots in unvisited: no.
- stack trail:
```
if(phase==='generating' && stack.length>1){
 ctx.beginPath();
 stack.forEach((idx,k)=>...);
 ctx.strokeStyle='rgba(37,99,235,.28)';
 ctx.lineWidth=7; ctx.lineJoin='round'; ctx.lineCap='round'; ctx.stroke();
 ctx.strokeStyle='rgba(14,165,233,.45)'; ctx.lineWidth=2; ctx.stroke();
}
```
Need this line crosses only open passages by construction (stack path consists of carved edges). Walls drawn on top. Good.
- exploration overlays:
```
if(solver.explored.size){ ... fillRect(x+2,y+2,CELL-4,CELL-4); }
```
Need after generation only but sets empty initially. Fine.
- frontier fill with violet and small center dot:
```
for idx of solver.frontier... fillRect; ctx.beginPath arc center radius 3...
```
Potential start/finish marker overlays.
- parent edges:
```
if(solver.parent.size){
 ctx.beginPath();
 for (const [child,parent] of solver.parent){ move center parent, line center child; }
 ctx.strokeStyle='rgba(8,145,178,.28)'; ctx.lineWidth=4; ...
}
```
Need line from parent to child same as open passage. Good.
- lastEdges:
```
if(phase==='solving' && solver.lastEdges.length) { ... bright cyan width 5 ...; }
```
- solution path: as above.
- walls:
```
drawWallPass(true); drawWallPass(false); outer border.
```
Need draw line segments for unvisited cell walls with `cell.carveIndex<0`; for visited cell walls with `>=0`.
```
function addSegments(path predicate)... 
```
Use `ctx.beginPath()` inside pass. Need maybe in unvisited pass include top/left boundaries; in visited pass include top/left and outer bottom/right. fine.
```
function strokeWallSet(visited, color,width){
 ctx.beginPath();
 for i... if ((cells[i].carveIndex>=0)!==visited) continue;
 ...
 ctx.strokeStyle=color; ctx.lineWidth=width; ctx.lineCap='square'; ctx.stroke();
}
```
- Outer border:
```
ctx.strokeStyle='#dce9f7'; ctx.lineWidth=3; ctx.strokeRect(PAD+1.5,PAD+1.5,COLS*CELL-3,ROWS*CELL-3);
```
Could maybe too bright; use `#bcd0e8`. Need border clearly.
- current carve:
```
if(phase==='generating'&&stack.length){ const idx=stack.at(-1); ... fill rect inset; stroke rect; arc ... }
```
Need `Array.prototype.at` maybe supported; use `stack[stack.length-1]`.
- current solver node:
```
if((phase==='solving'||phase==='tracing')&&solver.current>=0){
 ctx.beginPath(); arc center radius CELL*.31; strokeStyle '#0891b2'; lineWidth=2.5; stroke();
}
```
- start/finish markers. Need perhaps marker rendering correct with scaling and shadows. Use `ctx.save()` and `ctx.restore()`. `shadowBlur=8`.
```
drawStartMarker() {
 const [x,y]...
 ctx.save(); ctx.shadow...; ctx.fillStyle='#22c55e'; ctx.beginPath(); ctx.arc(x,y,10,0,2π); fill(); ctx.shadowBlur=0; ctx.strokeStyle='#eafff1'; lineWidth=2; stroke(); ctx.fillStyle='#052e16'; ctx.font='bold 11px system-ui'; ctx.textAlign='center'; ctx.textBaseline='middle'; ctx.fillText('S',x,y+0.5); ctx.restore();
}
```
Finish:
```
roundRectPath(ctx,x-10,y-10,20,20,5); fill '#f59e0b'; stroke...
text 'F' dark.
```
Need if solution line underneath marker; okay.
- Maybe draw tiny arrows? no.

`roundRectPath`:
```
function roundRectPath(ctx,x,y,w,h,r){
 ctx.beginPath(); ctx.moveTo(x+r,y); ctx.lineTo(x+w-r,y); ctx.quadraticCurveTo(...); ...; ctx.closePath();
}
```

`updateUI`:
```
const cfg=SPEEDS[speedIndex-1]; speedValue.textContent=cfg.name;
let label,detail,pct,badgeText,badgeClass;
...
phase generating:
 label=`Carving maze #${mazeId}`;
 detail=`${carved} / ${N} cells • stack ${stack.length} • randomized recursive backtracking`;
 pct=carved/N*100;
 badge='Tree check pending'; ...
mazeReady: "Maze complete — solver starting"; ...
solving: "BFS exploring" ...
tracing: "Tracing shortest route" ...
solved: "Solved" ...
```
BFS on tree gives shortest number of cells. Need say "BFS solution".
`badge`: if `validation?.ok` "Perfect maze ✓"; plus path. Could set:
- gen: "checking…"
- mazeReady/solving: validation.ok ? "Perfect maze ✓" : "Check failed"
- tracing/solved: pathOpen ? "Path uses open passages ✓" : "Path check failed"
Need classes success/error/neutral.
`progressFill.style.width=...`.
`app.dataset...`:
```
app.dataset.phase=phase;
app.dataset.mazeId=String(mazeId);
app.dataset.carved=String(carved);
app.dataset.generationComplete=String(generationComplete);
app.dataset.explored=String(solver.explored.size);
app.dataset.solutionLength=String(solution.length);
app.dataset.pathOpen=pathOpen===null?'pending':String(pathOpen);
app.dataset.wallSignature=wallSignature;
app.dataset.replayWallsUnchanged=...
```
`diagnostics.textContent = JSON.stringify({...}, null, 2);` Need include `validation`, `solverEdgesOpen`, etc.
`replayBtn.disabled = !generationComplete;`
Need `phaseLabel.textContent`, etc.
Maybe detail too long on narrow screen; CSS wraps. Fine.
- `validation` object could include `ok`. Need JSON ready no Sets.
- `computeWallSignature()` each update? store cached. Need after each carve no update; wallSignature empty while gen. For replay, compute before/after. For diagnostics maybe wallSignature from completion. Good.
- `solverEdgesOpen=validateParentEdges()` computed in updateUI perhaps. Need set global variable from function:
```
const edgesOpen=validateParentEdges();
```
Call each updateUI; okay.
- Need `replayWallsUnchanged` false/null prior to replay. In diagnostics.
- Need `solver.lastEdges.length` etc. Fine.

`console.log` with object:
```
console.log(`[maze] #${mazeId} complete:`, validation);
```
Could browser console show object. Fine.
Initial log:
```
console.log(`[maze] New maze #${mazeId}; previous run cancelled; 25x15 target`);
```
Need perhaps "previous animation cancelled" even first run no previous. Could log `Cancelled run token ${epoch-1}; ...` but not necessary. To verify New Maze cancellation via console, on second New Maze log includes `stopped epoch`. Could have stopAnimation return old epoch:
```
function stopAnimation(){const canceled=rafId!==null;...; return canceled;}
```
Then newMaze logs `[maze] New maze #... (cancelled ${canceled?'active':'none'} animation)`. Need on click during generation, `rafId` non-null; clear. Add to diagnostics perhaps `lastCancellation`. Could set global `lastCancel`.
```
let lastCancellation='initial';
function newMaze(){
 const wasActive = stopAnimation();
 lastCancellation = wasActive ? `cancelled active ${phase}` : `no active frame`;
 ...
 console.log(`[maze] New maze #${mazeId}; ${lastCancellation}`);
}
```
Need `phase` still old when stopAnimation called; capture `oldPhase`.
```
const oldPhase=phase; const canceled=stopAnimation(); lastCancellation=`${canceled?'cancelled':'reset'} ${oldPhase} run`;
```
Then reset. This helps verify. Set `app.dataset.lastCancellation`.
Need `stopAnimation()` return boolean whether rafId non-null, but if phase solved rafId null. Fine.
- New Maze clean replacement: diagnostic `carved=1`, `solutionLength=0`, `explored=0`, phase generating, new mazeId. DOM status. Browser inspect after click can check. Need maybe ensure `render` clears canvas in same event; yes.
- Need perhaps color of animated carving enough visually. Screenshot check.

Potential browser tool limitations: Need perhaps use `browser action=inspect` and see output. Let's write file then check syntax and launch.

Let's now write.

Need check syntax. I noticed DIRS first object has `opposite: 3 - 1` =2 actually correct, placeholder comment says replaced below, and then set 2. Fine but weird. Could clean. Need use node --check extraction. Also potential bug: `prepareSolver(false)` inside frame sets `accumulator=0`, then frame sets delta=0, okay. `prepareSolver(true)` on replay then after compute wall signature; startLoop. Good.

Potential bug: `fitCanvas()` after `newMaze()` calls render. `ResizeObserver` constructor likely triggers callback soon. fine.

Potential bug: `stopAnimation()` increments epoch on initial newMaze, then `startLoop` token=epoch. good.

Potential bug: `render()` called from `newMaze()` before `fitCanvas()` with canvas.width=832, height=512; transform=1. fine.

Potential bug: `strokeWallsFor` false/true. Shared walls between unvisited cells drawn once as top/left of lower/right cell. Outer top row top walls and outer left col left walls; outer bottom/right boundaries. Good.

Potential bug: `validateMaze` DSU cycles: If connected tree, no cycles. Our wall removal always to unvisited, so no cycles. Fine.

Potential bug: `bfsStep` when finish is discovered but not dequeued, parent set; when dequeued build path. fine.

Potential bug: path tracing speed and `solutionProgress`: at buildSolution, phase='tracing', progress=1. performBatch returns after bfsStep false; then while loop `isAnimating()` true and may continue remaining accumulator, calling tracing increments in same frame. Fine. Could reveal a few initial path cells instantly; not issue.

Potential bug: `isAnimating()` false on failed, but replay button still enabled; can replay. fine.

Potential bug: `validation` object from perfect maze check includes `ok`; okay.

Potential bug: `lastCancellation` "cancelled active generating run" on New Maze click during generation. good.

Potential bug: Replay Solver when clicked while generation is active is disabled, so no effect. requirement "Replay Solver uses existing maze without changing walls." That's okay; after generation done. Could maybe phrase disabled until maze ready. Fine.

Need run syntax check.

No python3. Use Node to extract directly. Need use bash with node script or perl. Use node -e reading file.

Need browser check. Use browser reload/inspect/screenshot. Need know tool outputs. Let's call reload then inspect maybe parallel? Need sequential because reload then inspect. Call reload first.

Interesting reload output DOM says 13/375 cells while screenshot says 3/375; perhaps reload frame 1 at +0ms then screenshot rendered later? Actually the tool result shows console and DOM text 13 cells, attached image 3 cells. Maybe screenshot captured at earlier frame or tool output composited multiple timing. Need okay. Initial output looks good. Note canvas drawing dark grid, carved cells top-left with wall removals, start/finish markers. Header controls, legend. Need inspect progress over time and New Maze while active. Browser `motion` perhaps captures frames. Need use `motion` maybe output multiple frames. Let's call `motion` likely captures 5 frames over duration. Need perhaps first use inspect to read current state. Also need click New Maze during active. Need know button x= maybe 692, y=50. Use browser click. But before click, we need perhaps capture progress and data attrs. Browser inspect output might include DOM text but not data attrs, perhaps can use details visible diagnostics via clicking summary. Could use browser click on details summary to expand and inspect. But `browser inspect` DOM includes `pre` text maybe even collapsed. It didn't show pre content in DOM output maybe because collapsed. Could click summary at x=180,y=694; then inspect. Need perhaps use browser action inspect with `text` maybe not. Let's try motion first.

Motion shows at nearly complete generation with stack trail. But note blue path stack trail crossing from current to start appears to pass through walls? It should not; drawn under walls but walls mask. It looks like it goes through corridors. Fine.

But I notice unvisited cells displayed as dark blocks with no grid walls maybe one dark cell behind start etc. Fine.

Need specifically inspect carving progress and request New Maze while animation active, clean replacement. Need perhaps reload to reset then click New Maze quickly. Since currently generation almost done; still active maybe likely done by now. Use reload then click New Maze within active. Need perhaps use `reload`, then `click` New Maze. Need capture data after. Maybe browser action click returns DOM/console with status. Need use coordinate from screenshot: New Maze button center ~691, 53. Need call `click` x=691 y=53. But after reload, maybe page stays at initial generation active around 10 sec. Need click soon. Let's do reload and click sequential. Could perhaps use multi_tool parallel? No, need sequential. First reload.

Now click New Maze at (691,53) while active.

Interesting screenshot after click shows canvas fully uncarved with only start cell outlined, status DOM says 5/375 but screenshot 1/375? Tool frame captured screenshot perhaps immediately at newMaze render (1 cell) before next frame; DOM text maybe after next frame (5 cells). Progress bar still at ~70% from previous maze! Wait screenshot shows progress bar blue to ~70% despite status 1/375. That indicates CSS transition on progress width, so it hasn't caught up yet; after click, updateUI sets width maybe 0.27%, but transition .12s linear and screenshot captured immediately at frame 1, so bar still animating down from ~70%. That's a visual issue: "new generation replaces previous view cleanly"; a lingering progress bar for 0.12 sec could be seen as not clean. Need fix clear problem: when New Maze, immediately disable transition or force progress bar to 0. Could set `progressFill.style.transition='none'; progressFill.style.width='0%';` then force reflow and restore transition. Or simply remove CSS transition entirely. Progress bar width updates each frame; no need CSS transition. Remove `transition: width .12s linear;` yields immediate replacement. That is a clear issue discovered. Need edit. Also screenshot status DOM mismatch not concerning; screenshot captured right at 1 cell. Need maybe after click wait/inspect to see clean view. We should remove transition. Also note Starting cell is highlighted with blue outline; fine.

Need check for solver starts during inspection and visible steps follow open passages. Need perhaps accelerate speed to Turbo to get to solver quickly; or wait. Could click speed slider at right end (x=1030?) in screenshot: slider from ~949 to1030, value 3 at 990. To set Turbo, click x=1030,y=53 or use drag from handle to right. Browser `click` on range maybe sets value to click position. Need do that. Could also use `drag`. After generation, auto solver starts; we need inspect. Use turbo now and then perhaps `motion` with multiple frames. Need first fix progress transition. Also potentially clean replacement of canvas: it is fully reset in screenshot, good. Progress bar lingering is minor but fix.

Need maybe fix DIRS placeholder weirdness? Not necessary but clean. Could simplify first object to `opposite:2` and remove `DIRS[0].opposite=2;`. Not a functional issue but maybe do. Use edit with exact replacements including CSS transition removal. Need one edit call with multiple entries. Let's do.

Need reload after edit. Need perhaps inspect initial output and console again. Then set speed turbo. Need also perhaps use details expansion to see diagnostics. Let's reload then click speed slider rightmost, then maybe use motion to wait through generation+solver. But speed turbo after load changes speedIndex via input event; need browser click on range at x maybe 1030, y=53. Need note `click` on range may not fire `input` event? likely yes. Need maybe use drag from handle x=990 to x=1032. Could use `browser action=drag x=990 y=53 toX=1035 toY=53`. Need perhaps click at x=1031 simpler. We can inspect DOM after click to see speedName Turbo. Let's reload first.

Now click slider rightmost. Need x maybe 1032, y=53. Use drag from handle at x=990 to x=1035. Need control range actual width perhaps from 949 to1032; screenshot handle at 990 (value 3). Drag from 990 to1035.

We set turbo and generation near complete. Need wait for solver. Use motion maybe captures frames. Need perhaps also expand diagnostics to get verification data. Could click summary at (180,694) after solver maybe. But tool inspect DOM doesn't show pre content if collapsed. We can expand and inspect. Need first get to solver. Use browser `motion` maybe 4 frames over 1.8sec; at turbo generation/solver should complete maybe entire run in <2 sec. Need capture solver frames. Let's call motion; perhaps frames from current state through solver.

Need note screenshot tool: motion frames all solved because at time of motion capture perhaps solver already done before motion? Console logs include entire sequence happened during preceding drag action perhaps and motion captures after. Need need inspect solver steps visible. Could use Replay Solver at slower speed and capture frames. Need perhaps set speed slider to Slow or Easy then click Replay Solver. Then motion frames show exploration. Need also verify walls unchanged and visible steps follow open passages. Need expand diagnostics maybe. Need maybe clicking Replay with current maze at Turbo; then set speed to Normal/Slow to capture. Need first set slider to Easy maybe drag handle from x=1027 to x=970? Need perhaps click x=970 (value 2). Then click Replay Solver x=818,y=53. Need perhaps console log replay walls unchanged. Then motion capture frames. Let's do. Need maybe after solution complete, `replayWallsUnchanged` true. Could expand diagnostics and inspect. Let's sequence.

But before that, maybe potential visual issue: solution path appears red and wall lines black. It crosses only corridors; screenshot seems path's thick line may visually cover wall lines? We draw walls after path, so wall lines black on top. In screenshot at many corners, red line appears to be near walls but not crossing. Need inspect closer maybe perhaps some red goes through black walls? Need zoom mentally. The path line width 6 (scaled 0.96), walls 2.4; at a wall crossing, black line would be drawn on top if crossing. In screenshot, red line stays within corridors. Good.

However exploration cells appear light cyan but mostly all left side, indicating BFS stops at finish after exploring 284 cells; right region unvisited by solver. That is expected. It may look like dark uncarved? Actually right region white with black walls, not explored, fine. Legend doesn't explicitly style unvisited by solver versus carved; dark swatch "Uncarved" refers generation. Could be okay. Need perhaps distinguish "Exploration / frontier" style; screenshot shows cyan and purple cross near center. Good.

Need maybe update user requested "If the solver starts during inspection, check that its visible steps follow open passages." We can use diagnostics `visibleSolverEdgesOpen` and console. Need inspect after replay. Need expand details. Let's set speed to Easy, click replay. Need perhaps use `drag` from current handle to x=970. Then click Replay. Let's do sequential.

Now click Replay Solver at x=818,y=53. Need capture immediate after click perhaps.

Replay clean: solver reset, walls intact, path removed, progress bar nearly zero. Great. Need motion capture to see BFS step progression. Need call motion now while Easy (~52ms per expansion, 284 expansions ~15 sec, plus path 213 ~11 sec; motion 1.8 sec shows first ~35 cells). Good. Need perhaps expand diagnostics first? Could click summary while solver active; then inspect DOM includes pre. Need maybe do motion first to capture visible steps. Let's call motion.

We see exploration lines clearly follow corridors. But I notice major visual issue: exploration tree lines drawn in light blue appear to cross walls? Need inspect. In first frame, cyan line to left region maybe overlays black walls? Actually from start, thick cyan lines navigate corridors. Need look carefully: At left top maze, black walls form grid; cyan line can be seen partly crossing vertical black wall? For example near top-left, cyan line from start goes right? start cell at (0,0), next cells maybe down? The cyan line seems at center of cells and follows open passages, but some Cyan segments appear to cross black wall lines due to being drawn under walls; black walls should show on top. In screenshot, black walls do show over cyan? Hard to tell. Need perhaps verify programmatically via `visibleSolverEdgesOpen` in diagnostics. Need expand diagnostics and inspect. Could click summary at x=175,y=694 during solver. It will expand and shift page maybe; canvas still visible? Need no issue. Browser inspect after click shows pre text. Let's do while solver active. Need use click at (170,694).

Great. Diagnostics confirms all. Note `lastCancellation` still "reset idle run" because replay doesn't update lastCancellation; diagnostics after replay still initial. That's fine, but perhaps New Maze cancellation check earlier showed "cancelled active generating run" from console. Could include lastCancellation updated on replay? Not needed. But maybe clean replacement verification via data not visible because expanded diagnostics after replay has lastCancellation initial. We did inspect earlier console and DOM. Fine.

Need check potential issue: in screenshot during tracing, light cyan exploration tree lines seem to cross black walls? Need scrutinize: e.g., top row near x=300? It appears blue horizontal line from start to right through a black wall at x=273? Let's analyze algorithm. parent lines are drawn center-to-center for adjacent cells where `passageOpen`. They should cross border where wall absent, so no black line at that border. However the screenshot's maze walls are dark thin lines at many cell edges. Cyan line overlays under walls, so if wall present, dark line should cover at border. At places where cyan line seems pass through a black wall, perhaps that black wall is perpendicular along adjacent cell edge but doesn't actually block? Need maybe due to drawing line under black line: black wall should be visible over cyan line, creating a break, but because line width 14 for glow and 6 for coral? For exploration tree, width 4; black walls 2.4. If crossing a wall, black line should cover a 2.4-wide vertical strip but cyan continues on both sides; visually could look like crossing. The code ensures no crossing anyway. Diagnostics `visibleSolverEdgesOpen: true`. Fine.

Need maybe verify path crossing only open passages visually in solution screenshot. Console diagnostics `solutionUsesOnlyOpenPassages:true`. Good.

Need maybe check New Maze clean replacement after progress transition fix. We should recheck affected behavior: reload, set speed maybe Normal default, click New Maze during generation, inspect screenshot to ensure progress bar resets and canvas clean. We did earlier before fix. Need recheck after fix. Also need maybe need verify New Maze while solver active? Requirement specifically while animation active; generation active enough. Could also click New Maze while solver/tracing active to ensure cancellation. Need perhaps test. We currently have details expanded; path tracing active. Could click New Maze at (691,53) while tracing active and inspect. That would check clear replacement and cancellation from solver. Then maybe click New Maze again while generation active to specifically recheck progress bar. Need not overdo but good.

Need perhaps use current state (tracing active) to click New Maze. Browser action click returns console and screenshot. Need likely details expanded causing page taller; New Maze still at same coordinates. Let's click New Maze while tracing.

Clean replacement: all walls reset, no solution/exploration, progress bar zero. Good. But note console says "reset solved run" not "cancelled active tracing run" because by time click happened solver had already completed. Fine. Need specifically recheck New Maze during active generation after transition fix. We can click New Maze again now while generation active (Easy, 1 cell/52ms ~40 sec). Call click again. Need inspect progress bar reset and console cancellation active generating. This is straightforward.

Progress bar reset immediately. Great. Need maybe initial output after reload with details collapsed and speed normal; already checked. Need maybe check full solver path final screenshot. We saw solved screenshot in motion frame 4 from turbo. It showed complete path. Need maybe maybe path line seems to pass through walls? Diagnostics says no. Fine.

Need perhaps test initial default speed generation progress and New Maze while animation active after transition fix specifically with default speed? We tested with Easy. Good. Need maybe need test "New Maze cancels previous animation" more robust: Could there still be old RAF loop running after New Maze? Console/diagnostics show no duplicate progress jumping; epoch cancel. Need perhaps check no old solver starts later after New Maze. We could wait a bit and see if phase remains generating, no log from old maze. Need perhaps use motion after clicking New Maze with Easy; generation will take ~37 sec; wait 1.8 sec and check no logs from old maze, status stays carving #3. We can call motion. This would also verify carving progress after reset. Need perhaps do that. Also need maybe set speed to normal/turbo to run full solver on new maze #3 and check auto solver starts. But we already did full solver on maze #1. Need perhaps not necessary. Yet requirement "After generation finishes, animate BFS ... then highlight complete path" we verified on maze #1. Good.

Potential hidden bug: `validateParentEdges()` called during generation when `solver.parent` empty; returns true. It uses `passageOpen` with cells reset but no parent entries, no issue.

Potential hidden bug: `fitCanvas()` with ResizeObserver could cause render using a transform based on canvas.width/height that changes to 1600x... and then `strokeRect` etc. fine.

Potential hidden bug: newMaze while `details` expanded; page height changes but canvas width unchanged. fine.

Potential hidden bug: `replaySolver` while generating disabled. fine.

Potential hidden bug: `startLoop` after `replaySolver`: `prepareSolver(true)` sets phase solving and accumulator=0; then `replayWallsUnchanged` computed; `render(); updateUI(); startLoop();` fine.
Potential hidden bug: `stopAnimation` in replay increments epoch, cancel current RAF; if phase solved rafId null but epoch increments, okay. No other loop.
Potential hidden bug: frame with `token !== epoch` return, no render. fine.

Potential hidden bug: `performBatch` generation loop when stack empty at final pop returns false and calls finishGeneration. But at that moment carved=N. Good. If all cells carved but stack length >1 due to backtracking, continue pops. Animation shows backtracking. Good.
Potential hidden bug: random DFS can get stack length large; stack trail drawn. fine.

Potential hidden bug: "exactly one simple path between any pair of cells" validated by connected tree: 375 reached, 374 edges, cycles 0, reciprocal. Good.

Potential hidden bug: "All cells must be reachable, with exactly one simple path between any pair". Outer walls intact and no cycles. yes.

Potential hidden bug: "path must cross only open passages". BFS only enqueues when `passageOpen` checks both cell walls, path validation checks both. yes.

Potential hidden bug: "Start upper-left and Finish lower-right." markers at index0 and N-1. yes.

Potential hidden bug: "Draw cell walls clearly" walls are dark lines on white and light blue on dark. yes.

Potential hidden bug: "animate generation so carving progress visible." cells lighten, stack trail, current head, counter. yes.

Potential hidden bug: "After generation finishes, animate either BFS or A-star exploring." auto BFS after 450ms. yes.

Potential hidden bug: "then highlight complete path." path traced and final solved. yes.

Potential hidden bug: "New Maze cancels previous animation and generates fresh maze." yes.

Potential hidden bug: "Replay Solver uses existing maze without changing its walls." wall signature hash before/after. yes.

Potential hidden bug: "short legend" six items but short. yes.

Need maybe perhaps fix weird `lastCancellation` phrase "reset solved run" rather than "cancelled active tracing run" when clicking New Maze after solved; not a requirement. Fine.
Need maybe perhaps ensure `New Maze` can cancel solving when animation active, we didn't explicitly click while solving after fix; the earlier click from tracing was after solver had completed. We could test by setting Turbo and clicking replay then New Maze while active, but solver at Turbo very short. At Easy we can start Replay then click New Maze within ~1 sec. But requirement says New Maze cancels previous animation; we tested while generating. That's enough. Could test while solving too to be thorough, but no need with limited time. Yet we have plenty. Need maybe verify no old BFS logs from canceled generation/solver. Could maybe call motion after New Maze #3. Let's do quick motion with Easy; should stay generation. Then maybe set speed to Turbo to let complete and solver start; could observe a different maze's perfect check. Need perhaps not necessary but good final check. Maybe need check console errors none. We can call `inspect` after motion. Need perhaps using `motion` frames from #3 with carved progress over 1.8 sec (about 34 cells). Need check no duplicate loops. Let's do.

Interesting frame sequence: carved count increments 239,244,245,254 while time spans 1.7 sec; Easy config should 1 op / 52ms = ~33 operations per sec; yes ~15 carves due to backtracking. Fine.

But visual issue: the stack trail seems to be drawn from start through all carved cells? Actually blue line highlights entire DFS stack, which is path from start to current, nice. But I notice recent cells shown as blue blocks and stack trail extends through dark uncarved region? Wait the trail line appears to go through dark cells that are not carved? Need analyze: In frame 1, dark region extends left-middle with blue lines around border. Some blue line appears inside dark region? The blue trail perhaps goes through carved cells which appear dark because we draw them dark? Wait carved cells should be light. But the dark region might be uncarved. The blue trail lines might overlay dark region because we draw stack trail after fills; stack consists only carved cells, so could draw over dark cells that have been carved? Actually carved cells always have `carveIndex>=0`, and fill light. So any blue line through dark region would be over uncarved cells, impossible if stack path includes only carved cells. But perhaps the line is exploration tree from previous solver? No, solver reset. Could be wall grid lines in dark uncarved region colored blue-ish. Our unvisited walls color `#486383`, which at scale appears blue-gray; not bright cyan. The thick light blue lines are stack trail. They form a long continuous path from start along carved region boundary. At frame 1, there is a light blue line from start to lower-right that goes through white cells only? It seems along white corridors. Dark region maybe carved? Wait dark region could be uncarved cells, but white cells around it are carved. The stack trail line goes around dark cells on white corridor. Fine.

Need maybe concern: status says carved 239/375 but large region dark ~40% uncarved; reasonable. Stack trail path from start to current uses all stack cells; many white cells. Fine.

Need perhaps check stack trail "backtracking" visible: frame 1 current head around center. frame 2 head moves up; frame 3 moves left; frame4 head down-left. Nice.

Need maybe consider that `stack` trail can pass through cells that are carveIndex>=0 but are no longer on current stack? It draws full stack path only; okay.

Need maybe check screenshot initial output at default speed with details collapsed; already good. Need perhaps after final state, does details panel expanded push legend beyond viewport? It does but page scroll; not a functional issue. On initial load details collapsed, fits. Fine.

Need perhaps check console no errors. The console output has only logs, no errors. Need perhaps use `inspect` action to check console maybe no warnings. Already. Need maybe check `browser action=inspect` after final file reload with no details expanded? Need perhaps final check on default speed and maybe one full run to solved state with Turbo. We already did full run on maze #1 after edit? Wait we edited CSS transition and DIRS after first run? Timeline:
- wrote file
- syntax check
- initial browser runs / new maze click (before edit)
- edited CSS transition and DIRS
- reloaded and ran full solver on maze #1 (after edit)
- replay etc
So full run after final edit. Good.

Need maybe check final file syntax after edits. Could run node check again. Also perhaps file exists with all inline and no external resources. Need grep for http/fetch, external src/href. Use bash.

Need perhaps maybe reload final file after syntax check? We already ran browser after edits; no further edits. Fine. Need maybe maybe we should collapse details in final file initial state; it's collapsed by default. Browser currently has details expanded due to user interaction, not file state. Fine.

Need perhaps perhaps verify New Maze cancellation from solver active specifically. Could set speed Turbo? But generation #3 at Easy currently 255/375; need maybe use speed slider to Turbo and wait for generation complete and solver, then click New Maze during BFS. But we have evidence New Maze cancels generation and full solver. Requirement says New Maze cancels previous animation; generation is animation. Not necessary. But we might want to be thorough near end. We have maybe 5+ minutes left. Could run one more check: set speed to Normal or Easy and click replay solver on solved maze, then quickly click New Maze during BFS. Need ensure no old solver logs after cancellation. But we have to wait for current maze #3 generation to complete and auto solve; at Easy ~ maybe 30 sec. Could set Turbo via drag handle x=970 to1035, which will complete quickly; then click Replay Solver at Fast? Need to click New Maze while BFS active. At Turbo BFS ~2 sec, can click quickly. Could set speed to Easy after generation? Hmm.

Alternative use current generation #3 and set speed to Turbo to finish in <1 sec; then while auto BFS starts (Turbo ~2 sec), click New Maze. The browser tool call to drag itself may capture console through solver; maybe by the time drag returns, solver could already done. Need perhaps set speed to Fast (14ms*4 ops ~1.3 sec BFS) or Normal (27ms*2 ~5 sec BFS) to have time. Current slider Easy; can drag to value3 Normal (x=990). Generation remaining 120 cells * maybe 2 ops per cell ~240 ops /2 per27ms =3.2 sec. The drag action itself perhaps returns immediate but page continues; we can then call inspect after ~4 sec? Tool calls have latency maybe. Then click New Maze while BFS active. Could do. But we've already verified via code and console. Might not need.

Need perhaps check one subtle issue: `newMaze()` logs "reset solved run" when rafId null even if phase `'failed'`; fine. `lastCancellation` not updated on replay; fine.

Need perhaps question: "Use HTML, CSS, and JavaScript as needed. Write it to index.html ... Inline your own CSS and JavaScript. Do not use external assets, CDNs, or network requests." done.

Need final response: concise, mention created file, what checked, what remains unverified. Must specifically mention brief browser pass: initial output and console, carving progress, New Maze while active, clean replacement, solver steps and path. Need mention "unverified behaviors" per addendum. Need identify what remains unverified. Could say "I did not exhaustively test every possible random maze or mobile viewport; no console errors observed." Need perhaps mention verified via diagnostics:
- 375 cells, 374 passages, cycles 0, reciprocal walls, all reachable.
- replay wall signature unchanged.
- visible solver edges open and solution uses only open passages.
- no console errors.
- New Maze cancellation of active generation and clean reset.
Need mention "I did not verify all randomized seeds / long-session resizing; broad behavior from one/two generated mazes." Need be honest: we did check full solver on one maze and replay; New Maze on two/three. Could say "Remaining unverified: exhaustive random seed coverage and mobile/narrow layouts." Need maybe initial output console checked. yes.

Need perhaps mention no external resources. Fine.

Before final, maybe perhaps check if we should leave browser in a nice final state (details expanded, generation active). Not relevant; file itself reloads collapsed. Could maybe reload final file to confirm initial output after our edit, which we did. But currently browser state details expanded. Addendum says "Run application in browser and inspect initial output and console." We did. Fine.

Need perhaps maybe use `browser action=reload` after final file to collapse details and ensure no console errors, then screenshot. We already reloaded after edit (before full solver). That's enough. But final state of browser not persisted to file. Fine.

Maybe there is a hidden issue with `DFS[0].opposite` edit: We set 2 direct. good.

Need perhaps maybe check that progress bar clean replacement after fix while New Maze active; yes screenshot from second click shows tiny progress bar matching 2/375. Good.

Need perhaps maybe check that New Maze button during active generation after first edit console says "cancelled active generating run"; yes.

Need perhaps maybe check solver's visible steps follow open passages: diagnostics true; motion frames show cyan exploration tree through corridors; path check true. yes.

Need maybe mention "BFS expands 284 cells; solution 213 cells, path check passed" from one run. Good.

Need perhaps mention "replay wall signature unchanged YES." Good.

Need perhaps mention "New Maze cancels prior animation and resets carved=1, solution=0, explored=0, no stale logs." We checked no stale logs after 1.7 sec motion; yes. Could mention.

Need perhaps mention "console only informational logs; no errors." Need ensure no warnings. Console output no errors. Good.

Need final answer maybe:

"Created `/tmp/job-3ZeqXj/index.html` as a single self-contained file."

Then bullet checks:
- Initial load: 25x15 maze carving, dark uncarved/light carved walls, legend/controls, no console errors.
- New Maze clicked during active generation: console `cancelled active generating run`; new maze ID, carved reset to 1/375, prior view/path/progress cleared; later frames advanced only new maze.
- Full generation: validation object 375 reached, 374 passages, 0 cycles, reciprocal walls, border intact; BFS exploration and traced path; diagnostics `visibleSolverEdgesOpen:true`, `solutionUsesOnlyOpenPassages:true`.
- Replay Solver: wall signature unchanged, solution reset and BFS restarted.
- Unverified: exhaustive random seeds, very narrow/mobile layout, long-running session/resize edge cases.

Need maybe say "No external requests." Good.

Need be concise. Ensure no claim "no external requests" via static check, yes.

Let's final.