What qwen3.8-27b did

First, let's start by exploring the directory to understand the current state of the game.

Let's take a look at the three files.

Let me analyze the bugs:

**Bug 1: Sinking into platforms.**
Landing logic: `feetInside = player.y + player.h > p.y && player.y + player.h < p.y + p.h`. This only checks whether the feet (bottom edge) are within the platform's vertical range. It doesn't check that the player was above the platform (i.e., `player.y + player.h - player.vy <= p.y`, meaning they were above before the move). So if the player is inside the platform (feet inside the platform), it snaps `vy = 0` but doesn't reposition `player.y` to sit on top of the platform. So the player slowly sinks: gravity adds vy each frame, player.y increases, feet go deeper into the platform, `feetInside` stays true (until feet cross the bottom of the platform), vy is reset to 0 each frame, but y keeps growing by vy each frame... Actually, let me trace it:

Frame N: player lands with feet slightly below p.y. feetInside is true → vy=0, onGround=true.
Frame N+1: vy += GRAVITY → vy=0.9. y += 0.9 → feet go 0.9 deeper. feetInside still true (feet < p.y + p.h as long as not too deep) → vy=0 again. So the player sinks 0.9px per frame until feet reach p.y + p.h, at which point feetInside becomes false and the player falls through the bottom.

Fix: when landing, snap `player.y = p.y - player.h` (place on top). Also, only land if the player was above the platform before this frame's move (one-way platform behavior for thin ledges) — or, for the wall, handle horizontal collision.

**Bug 2: Falling through platforms at high speed.**
Classic tunneling: with high vy (falling fast), the feet jump from above the platform to below the bottom of the platform in one frame, and `feetInside` becomes false. Fix: use swept collision / previous position check: if `prevFeet <= p.y` and `newFeet >= p.y` (and X overlaps), land on it. This handles arbitrary fall speeds.

**Bug 3: Wall isn't solid.**
The wall is the platform at `{x: 300, y: 230, w: 20, h: 210}`. The collision code only handles landing on top (feet inside). There's no horizontal collision, so the player walks straight through. Fix: add horizontal collision resolution — resolve X first, then Y (separated axis). For the wall, if the player overlaps horizontally and vertically, push them out to the side they came from.

But careful: thin ledges should be one-way platforms (jumping from below should pass through them), while the wall should be solid on all sides. Hmm. How to distinguish? The wall is 20 wide × 210 tall. The ledges are 130/120 wide × 16 tall. The ground is 800×40.

Options:
- Add an explicit `solid: true` flag to the wall (and ground), and leave the ledges one-way. This is a physics fix, not a redesign — the level layout/art/controls stay the same. Adding a property to the wall is fine.
- Or infer: if platform height > threshold, treat as solid.

I think adding a `solid` flag is cleanest. Actually, let me think about what makes the level completable and feel right:

Level layout:
- Ground: y=440, full width.
- Ledge A: x=150, y=370, w=130, h=16 (top of ledge at 370).
- Wall: x=300, y=230, w=20, h=210 (top at 230, bottom at 440 — sits on the ground).
- Ledge B: x=360, y=300, w=130, h=16.
- Ledge C: x=545, y=235, w=120, h=16.
- Ledge D: x=680, y=165, w=120, h=16.
- Goal flag: x=730, y=125, w=20, h=40. Flag bottom is at 165, sitting on top of ledge D.

Spawn: (40, 380), player h=36 → feet at 416. Ground top is at 440. So the player falls 24px at spawn.

Path: jump from ground onto ledge A (top 370, 70 above ground top 440). Then jump from A over the wall? Wall top is at 230. From ledge A (top 370), the player's feet are at 370. Wall top is 230, which is 140 above ledge A's top. Jump velocity -13, gravity 0.9: jump height = v²/(2g) = 169/1.8 ≈ 93.9px. Not enough to clear a 140px wall from ledge A. Hmm.

Wait — the wall spans x=300..320, and ledge A spans x=150..280. So the player can't stand on top of ledge A adjacent to the wall. The gap between ledge A's right edge (280) and the wall's left edge (300) is 20px.

How do you get past the wall? Wall top is 230, ground top is 440. Wall height is 210. Jump height from the ground is about 94px. So you can't jump over the wall from the ground either.

Hmm, wait. Let me reconsider. Maybe you're supposed to go under the wall? The wall's bottom is at 440 (440 = 230+210), which is exactly the ground top. So no gap under the wall.

Hmm, so how do you get past the wall? Let me re-check: wall y=230, h=210 → bottom = 440. Ground top = 440. So the wall sits right on the ground. No gap.

So the only way over is to jump from somewhere. Jump height 94px. To land on top of the wall (top 230), the feet need to reach 230, i.e., feet need to rise 210px from the ground. Max jump from the ground: feet rise about 94px. Not enough.

Wait, maybe I miscalculated. JUMP_VELOCITY = -13, GRAVITY = 0.9. Rise distance = v²/(2g) = 169/1.8 = 93.9. Yeah, about 94px.

Hmm, so with the current physics, the player can't get over the wall at all? Let me check the ledges:

- Ledge B: x=360..490, top 300. To reach B from the ground: feet need to rise from 440 to 300 = 140px. Not possible with a 94px jump.
- From ledge A (top 370) to ledge B (top 300): 70px rise, horizontal distance from 280 to 360 = 80px gap. Possible! But wait, the wall at x=300..320, y=230..440 is between A and B. When jumping from A to B, the player has to pass through x=300..320 at a height above... The wall occupies y 230..440 in that x range. The player jumping from A (feet 370) to B (feet 300) passes through the wall's x range at feet between 370 and 300, which is inside the wall's y range 230..440. So the wall blocks it.

Hmm, so how is this level even completable? Let me think again...

Maybe the intended path is: jump from the ground to ledge A, then jump from A onto the top of the wall? Wall top 230, from A's top 370: rise needed 140 > 94. Not possible.

Hmm, wait. Maybe I should reconsider: the intended path is to jump from the ground over... no, the wall is 210 tall.

Hold on, maybe the intended design is that the wall is jumpable from the ground if you start from ledge A... no, that's not right.

Let me reconsider. Actually, maybe the original broken game was completable in some way, and my job is just to fix the physics so the level becomes completable. Let me think about what path is possible with jump height 94px:

Positions (foot positions when standing):
- Ground: y=440
- A: y=370 (70 above ground) ✓ reachable from ground (70 < 94)
- Wall top: y=230 (210 above ground, 140 above A) ✗
- B: y=300 (140 above ground, 70 above A) — reachable from A, but the wall blocks the horizontal path... unless you can jump over the wall from A. Wall top 230 is 140 above A's top. 140 > 94. ✗.
- C: y=235 (205 above ground, 65 above B) ✓ reachable from B.
- D: y=165 (275 above ground, 70 above C) ✓ reachable from C.
- Flag on D: flag at x=730, y=125..165.

So the path is: ground → A → B → C → D → flag. The only obstacle is the wall between A and B.

To get from A to B, the player has to jump over the wall (x 300..320). The wall top is 230. From A (feet 370), the feet need to reach above 230 while crossing x 300..320, i.e., rise 140px. Max rise is 94px. So with the current jump physics, this is impossible.

Hmm, wait, unless... the player can jump from the ground to A, then walk on A... A spans 150..280. The wall starts at 300.

Hmm, so with the current numbers, the level is not completable even with perfect physics? Let me double-check the jump height. Actually, maybe I should reconsider: is the jump velocity applied as an impulse and then gravity? vy = -13, then each frame vy += 0.9. Position update: y += vy (after gravity? in the code, `player.vy += GRAVITY; player.x += player.vx; player.y += player.y;` — wait, the code does vy += GRAVITY then y += vy. So the first frame y moves -13+0.9 = -12.1. Total rise = sum over frames until vy ≥ 0. Number of frames until vy=0: 13/0.9 ≈ 14.4 frames. Rise ≈ v²/(2g) ≈ 93.9px (with the discrete version slightly different, ~92-94).

So max jump height is about 94px. The wall is 210 above the ground. From A it's 140.

So the level as designed is not completable with the current jump strength?! Unless... the player is supposed to jump from the ground to A, then from A to... hmm.

Wait, wait. Let me re-read the wall: `{ x: 300, y: 230, w: 20, h: 210 }`. y+h = 440. Ground top = 440. Yes.

Hmm, but maybe the intended path is: ground → A → (jump over the wall from A)... no.

Or: maybe the player can jump from the ground to B directly? B's top is 300, 140 above the ground. 140 > 94. No.

Hmm, so the level is not completable with the current physics. But the task says "fix those 5 bugs so the level is completable: jump the ledges, be stopped by the wall, reach the flag." And "tune the numbers until it feels right."

Hmm, "tune the numbers" — maybe I need to increase the jump velocity so the wall can be cleared? But the constraints say "keep the level layout, art, colors, and controls exactly as they are. This is a physics repair, not a redesign."

Tuning the jump velocity is a physics parameter, not a level layout. The bug report says "tune the numbers until it feels right rather than just implementing the words" — that's about the feel of the jump (variable height, coyote, buffer). But if the level is not completable with jump velocity -13, I need to bump it up.

Let me calculate what's needed: from A (feet 370) to clear the wall top (230) with some margin, and land on B (top 300, x 360..490).

Actually, to land on B, the feet need to be at 300 or below at x ≥ 360, and during the crossing of x 300..320, the feet need to be above 230 (i.e., y_feet < 230).

From A's right edge (x=280, feet 370), jump with velocity v. Time to rise from 370 to 230 is 140px: 140 = v*t - 0.45t² (discrete approximation). With v=15: solving 0.45t² - 15t + 140 = 0 → t = [15 ± sqrt(225 - 252)]/0.9 → discriminant negative. Hmm, that formula: y(t) = v t - (g/2) t² = 15t - 0.45t². Setting = 140: 0.45t² - 15t + 140 = 0 → discriminant = 225 - 4*0.45*140 = 225 - 252 = -27 < 0. So v=15 can't reach 140px. Max height with v=15: 225/1.8 = 125. Not enough.

v=17: max height = 289/1.8 = 160.6. Reaches 140: 0.45t² - 17t + 140 = 0 → discriminant = 289 - 252 = 37 → sqrt = 6.08 → t = (17-6.08)/0.9 = 12.13 frames (first crossing). Horizontal distance in 12.13 frames at speed 4: 48.5px. From x=280 (player's right edge is 280? no, wait, the player's position x is the left edge).

Hmm, let me be careful. Player w=24. Standing on A (x 150..280), player's left x can be at most 280-24 = 256, right edge at 280. Jumping from the right edge: player's left x=256, right edge 280. Wall at 300..320. Player's right edge needs to clear 320, i.e., left x ≥ 296... no wait, the player needs to fully pass: left x ≥ 320 to be past the wall. Distance from 256 to 320 = 64px = 16 frames at speed 4. During those 16 frames, the feet must stay above 230 (at least until the left x passes 320).

With v=17: feet y(t) = 370 - (17t - 0.45t²). Feet need to be < 230, i.e., rise > 140, during t ∈ [t1, t2], where 17t - 0.45t² = 140 → t1 = 12.13, t2 = (17+6.08)/0.9 = 25.6. So the feet are above the wall top from frame 12.1 to 25.6, a window of 13.5 frames. The player's right edge (left x + 24) crosses the wall region: the player overlaps the wall's x when left x ∈ (276, 320) (left x + 24 > 300 → left x > 276; left x < 320). At speed 4 from 256: left x = 256 + 4t. Left x > 276 → t > 5. Left x ≥ 320 → t ≥ 16. So during t ∈ (5, 16), the player overlaps the wall's x range. During that time, feet must be above 230 → rise > 140 → t > 12.13. But at t=5..12, the player overlaps the wall's x range while the feet are below the wall top → collision with the wall's side!

So even with v=17, jumping from A's right edge, the player hits the wall's side. Unless the player is pushed back (solid wall) — then they can't cross. Hmm.

So maybe the intended path isn't A → B. Let me reconsider.

What if the wall is meant to be jumped from the ground? Wall top 230, ground 440: rise 210. v needed: v²/(2g) > 210 + margin → v² > 2*0.9*220 = 396 → v > 19.9. That's a very high jump. And then B (top 300, x 360..490) is below the wall top — landing on B from the wall top is fine (falling).

Hmm, wait, actually, is the wall even blocking the A→B path in the intended design? Maybe the intended design is that the wall is solid and the path is ground → A → wall top → B → C → D. To stand on the wall top (230) from A (370): rise 140. v=17 gives max rise 160 — possible if you jump from A near the wall. Jump from A's right edge (left x=256): at apex (t = 17/0.9 ≈ 18.9 frames), horizontal movement = 75.5px → left x = 331.5, past the wall (320). Feet at apex: 370 - 160.6 = 209.4 < 230 ✓ above the wall top. But to land on the wall top, the player needs to be descending with feet at 230 while overlapping the wall's x (left x ∈ (276, 320)).

Descending: feet y(t) = 370 - 17t + 0.45t² = 230 → 0.45t² - 17t + 140 = 0 → t2 = 25.6. At t=25.6, left x = 256 + 102.4 = 358.4 — past the wall (wall ends at 320, player's left x needs to be < 320 to overlap; 358 > 320, no overlap). So the player passes over the wall and lands... where? At t=25.6, feet=230, left x=358. B spans 360..490, top 300. Player's feet 230, left x 358: player's right edge = 382, overlapping B's x (360..490)? Right edge 382 > 360 ✓. But feet 230 is above B's top 300 — still in the air, descending. Continues falling until feet reach 300: 370 - 17t + 0.45t² = 300 → 0.45t² -17t + 70 = 0 → t = [17 ± sqrt(289 - 126)]/0.9 = [17 ± sqrt(163)]/0.9 = [17 ± 12.77]/0.9 → t = 33.1 (descending). At t=33.1, left x = 256 + 132.4 = 388.4. On B (360..490) ✓.

So with v=17, jumping from A's right edge clears the wall and lands on B. But this requires the jump to start right at A's edge (left x=256, i.e., right at the edge) — actually, let me check with a slightly earlier start. If the player starts the jump at left x=250 (6px from the edge): at t=12.13 (feet reach 230), left x = 250 + 48.5 = 298.5 — overlapping the wall's x (276..320)! Feet at 230 = wall top. Hmm, exactly at the wall top at t=12.13, and before that the feet are below the top while overlapping → side collision.

So the jump needs to start within about 6px of the edge. That's a tight jump. Hmm, but with variable jump height (full hold), it's doable but finicky. Not great.

Alternatively, maybe the intended path is: ground → A → jump over the wall from A to B, and the wall is actually not in the way because... hmm.

Wait, actually, let me reconsider. Maybe I'm wrong about the wall blocking A→B. Wall x: 300..320. A: 150..280. B: 360..490. Yes, the wall is between them, spanning y 230..440. A→B jump at feet height 370→300 passes through y range 300..370 (feet), which is within 230..440. Blocked.

Hmm, OK, another thought: what if the wall is meant to be jumped from the ground? Wall top 230, ground 440: rise 210. v needed: v²/(2g) > 210 + margin → v² > 2*0.9*220 = 396 → v > 19.9. That's a very high jump. And then B (top 300, x 360..490) is below the wall top — landing on B from the wall top is fine (falling).

Hmm, wait, actually, is the wall even blocking the A→B path in the intended design? Maybe the intended design is that the wall is solid and the path is ground → A → wall top → B → C → D. To stand on the wall top (230) from A (370): rise 140. v=17 gives max rise 160 — possible if you jump from A near the wall. [same analysis as above]

Hmm, OK, yet another thought: what if the wall is not meant to be jumped over at all, and instead... the ground is under the wall? Wall bottom = 230+210 = 440 = ground top. No gap.

So the wall must be jumped over. From where? The only ledge before the wall is A (top 370). Required rise: 140 + margin. So the jump velocity needs to be at least about 17 (v²/(2g) ≥ 140+margin). With v=17, max rise 160.6, margin only 20px, and the jump needs to start near A's edge. Tight.

Or — wait. Maybe I should reconsider the approach: what if the wall is meant to be jumped from the ground? Wall top 230, ground 440: rise 210. v needed: v²/(2g) > 210 + margin → v > 19.9. Very high jump, and then B is below the wall top — landing on B from the wall top is fine (falling). But a 210px jump on a 480px canvas is huge (nearly half the screen). And the "stiff" jump at -13... the task says "tune the numbers until it feels right."

Hmm, wait a moment. Let me re-read the bug report: "3. The wall isn't solid. The tall block in the middle of the level can be walked straight through." — so the wall should be solid, and the player should be stopped by it. "Fix those 5 bugs so the level is completable: jump the ledges, be stopped by the wall, reach the flag."

"Be stopped by the wall" — so the wall stops horizontal movement. And the level must be completable. Given the geometry, the only way over the wall is from A (rise 140) or from the ground (rise 210).

Hmm, wait, actually — hold on. What about jumping from A to the wall top, standing on the wall, then jumping to B? Wall top 230, B top 300: falling, easy. So the path: ground → A → wall top → B → C → D → flag. From A to wall top: rise 140, horizontal distance from A's right edge (280) to the wall (300..320): the player can land on the wall top with left x ∈ (276, 344) (left x + 24 > 300 and left x < 320... wait, to stand on the wall top, the player needs to overlap the wall's x: left x < 320 and left x + 24 > 300 → left x ∈ (276, 320)).

From A's right edge (left x=256, feet 370) with jump v: feet reach 230 (rise 140) at t1, and land on the wall top when descending with feet=230 and left x ∈ (276, 320): left x = 256 + 4t ∈ (276, 320) → t ∈ (5, 21). Descending crossing of feet=230 is at t2. With v=17: t2 = 25.6 > 21. Miss — at t=21, left x=340, past the wall, feet at t=21: 370 - 357 + 198.45 = 211.45... wait, let me recompute: 17*21 = 357, 0.45*441 = 198.45, feet = 370 - 357 + 198.45 = 211.45. That's above 230 (211 < 230). So at t=21, the player is at left x=340 (right edge 364), feet 211 — past the wall (left x > 320) and above B's top (300). Then lands on B as computed (t=33.1, left x=388). So with v=17, jumping from A's edge, the player clears the wall entirely and lands on B.

With a slightly earlier start (left x=250): t2=25.6, left x = 250+102.4 = 352.4 — still past 320? 352 > 320 ✓. Feet at t=25.6 = 230. Then descends to B: feet=300 at t=33.1, left x = 250 + 132.4 = 382.4 ✓ on B. But wait — during the ascent, does the player hit the wall's side? The player overlaps the wall's x when left x ∈ (276, 320) → t ∈ ((276-250)/4, (320-250)/4) = (6.5, 17.5). During that time, the feet must be above 230: feet < 230 when t > t1 = 12.13. So during t ∈ (6.5, 12.13), the player overlaps the wall's x with feet below the wall top → side collision! The player hits the wall.

So with v=17, the jump must start at left x ≥ about 256 (right at the edge). Window: starting at left x=256: wall x overlap t ∈ (5, 16), feet above top from t=12.13 → collision during (5, 12.13)?? Wait, that's also a collision!

Hold on, I think I messed up. If the player starts at left x=256 (right at A's edge, right edge at 280), the player's right edge is at 280, wall starts at 300. The player overlaps the wall's x when left x + 24 > 300 → left x > 276 → t > (276-256)/4 = 5. And the player is past the wall when left x > 320 → t > 16. So during t ∈ (5, 16), the player's body overlaps the wall's x range. The wall's y range is 230..440. The player's body is from feet-36 to feet. For no collision, the player's bottom (feet) must be above 230 (feet < 230), or the player's top must be below 440 (always true). So feet < 230 is required during t ∈ (5, 16). Feet < 230 (rise > 140) only during t ∈ (12.13, 25.6). So during t ∈ (5, 12.13), the player overlaps the wall's x with feet ≥ 230 → collision.

So even jumping from the very edge with v=17, the player hits the wall's side! The rise is too slow. The player needs to rise 140px in 5 frames (to clear the wall's x before the body reaches it)... no wait, the body reaches the wall's x at t=5 (right edge touches 300). At t=5, the rise must already be ≥ 140? No — at t=5, the right edge just touches the wall's left face. As long as the feet are above 230 (or the right edge is past 320), there's no overlap. At t=5, rise = 17*5 - 0.45*25 = 85 - 11.25 = 73.75 < 140. Collision.

So v=17 doesn't work for A→(over wall)→B at all. The player needs to be higher when crossing the wall. Let me solve: the player starts at left x = 256 - d (d ≤ 0 from the edge... actually, the player can start at any left x ≤ 256 on A). The player's right edge reaches the wall's left face (300) at time t_a = (300 - (256-d) - 24)/4 = (20+d)/4. At that time, the rise must be ≥ 140 (feet at or above 230): v*t_a - 0.45t_a² ≥ 140.

Also, the player's left edge must be past... no wait, actually, once the feet are above 230 and rising, the player can cross the wall's x range freely. The constraint is: at t_a (right edge touching the wall), rise ≥ 140. And the player keeps rising until the apex. After the apex, the feet descend; the player's left edge must be past 320 (left x > 320, i.e., fully past) before the feet drop below 230 again. Left edge past 320 at t_b = (320 - (256-d))/4 = (64+d)/4. Feet back to 230 (descending) at t_c, where v*t - 0.45t² = 140 → t_c = (v + sqrt(v² - 252))/0.9. Need t_b < t_c.

To maximize the window, start from the edge d=0: t_a = 5, t_b = 16. Need v*5 - 11.25 ≥ 140 → v ≥ 30.5?? That's a huge jump. Max rise = v²/1.8 = 30.5²/1.8 ≈ 518px. That's off-screen (canvas is 480 tall).

Hmm, that can't be the intended design. Let me reconsider.

Wait... maybe I have the wall's position wrong. Let me re-read: `{ x: 300, y: 230, w: 20, h: 210 }`. Hmm, w=20, h=210. So it's 20 wide, 210 tall. x 300..320, y 230..440.

And ledge A: x 150..280, top 370. Gap between A and the wall: 20px (280..300).

Hmm, OK, wait, maybe the intended path doesn't involve jumping over the wall from A. What if the path is: ground → A → back to ground

The .session file is just a log of my own session. Let's continue the analysis.

Key geometry:
- Canvas: 800×480
- Ground: x 0..800, y 440..480 (top edge 440)
- Ledge A: x 150..280, y 370..386 (top edge 370)
- Wall: x 300..320, y 230..440 (top edge 230, bottom edge 440 = sits on the ground)
- Ledge B: x 360..490, y 300..316 (top edge 300)
- Ledge C: x 545..665, y 235..251 (top edge 235)
- Ledge D: x 680..800, y 165..181 (top edge 165)
- Goal: x 730..750, y 125..165 (flag sits on top of D, flag bottom = 165 = D's top edge)
- Spawn: (40, 380), player 24×36, feet at 416

Current physics: gravity 0.9, jump velocity -13 → max jump height ≈ 94px.

Required path: ground → A → (clear the wall) → B → C → D → flag.

Wall clearance from A: need to rise 140px while crossing x 300..320.

Hmm, wait. Let me reconsider. Maybe the intended path is ground → A → wall top → B. No wait, I showed that landing on the wall top from A also doesn't work with v=17 (the descending crossing happens past the wall's x range).

Hmm, let me think about what jump velocity would make this level comfortably clearable.

For A → B over the wall:
- Start from A's right edge: left x = 256, feet = 370.
- Constraint 1: when the player's right edge first enters the wall's x range (left x = 276, t = 5), feet must already be above 230 (rise ≥ 140).
  - rise(5) = 5v - 0.45·25 = 5v - 11.25 ≥ 140 → v ≥ 30.5. Way too big.

That's impossible. So A→B in a single jump over the wall is geometrically impossible with reasonable physics, because the wall's x range is only 40px from A's edge and the player has to rise 140px before the right edge reaches x=300 (5 frames at speed 4).

Wait, is that really so? The player's right edge reaches 300 at t=5 (from left x=256: 256+24=280, 300-280=20px, 20/4=5 frames). Yes.

Hmm, but what if the player jumps from further back on A and approaches slower? No, speed is fixed at 4.

What if the player jumps from the ground? Ground → wall top: rise 210. From left x=276 (right edge 300, touching the wall): t=0. rise(t) = vt - 0.45t². Need to be above 230 (rise ≥ 210) from t=0 (right edge at wall face) until left edge passes 320 (left x = 320 → t = 44/4 = 11). rise(0) = 0 < 210 → immediate collision. So a ground jump toward the wall also collides unless you jump much earlier: right edge reaches 300 at t_a, need rise(t_a) ≥ 210, and left edge passes 320 at t_b = t_a + 11 (player width 24 + wall width 20 = 44px = 11 frames), need feet still ≥ 210 at t_b... no wait, need feet above 230 (rise ≥ 210) throughout [t_a, t_b].

rise(t) = vt - 0.45t² ≥ 210 for t ∈ [t_a, t_a+11]. Max rise = v²/1.8 ≥ 210 + margin. v = 22: max rise = 484/1.8 = 269. rise(t) = 210 → 0.45t² - 22t + 210 = 0 → t = [22 ± sqrt(484 - 378)]/0.9 = [22 ± 10.3]/0.9 → t1 = 13, t2 = 35.9. So feet above 230 during t ∈ (13, 35.9), a window of 23 frames. Need t_a ≥ 13 and t_a + 11 ≤ 35.9 → t_a ∈ [13, 24.9]. t_a = time from jump start until right edge reaches 300. If the player jumps at left x = x0 (feet 440), t_a = (300 - x0 - 24)/4. t_a = 13 → x0 = 300 - 24 - 52 = 224. t_a = 24.9 → x0 = 300-24-99.6 = 176.4. So jumping from anywhere on the ground with left x ∈ [176, 224] (a 48px window) clears the wall with v=22! Then the player lands on... wall top (230) or B (300)?

Descending crossing of feet=230 (wall top) at t2 = 35.9: left x = x0 + 4·35.9 = x0 + 143.6. For x0 ∈ [176, 224]: left x ∈ [319.6, 367.6]. Wall x range for standing: left x ∈ (276, 320). So for x0 ≈ 176 (left x ≈ 319.6 at t2), the player lands on the wall top (barely). For larger x0, the player passes over the wall and lands on B (top 300, x 360..490): feet=300 crossing: 0.45t² - 22t + 140 = 0 → t = [22 ± sqrt(484-252)]/0.9 = [22 ± 15.23]/0.9 → t = 39.2 (descending). left x = x0 + 156.8 ∈ [332.8, 380.8]. B's x range: left x ∈ (336, 490) (left x + 24 > 360 → left x > 336; left x < 490). So for x0 ≥ about 180, lands on B.

So with v=22 (max jump 269px — 56% of canvas height!), the player can jump over the wall from the ground. But a 269px jump on a 480px canvas is enormous — the player nearly doubles in screen height. Feels floaty/huge. Hmm.

Wait, wait. Let me step back and reconsider the level. Maybe I'm misreading which ledges connect. Let me re-list:

```
{ x: 0, y: 440, w: 800, h: 40 },     // ground: top edge 440
{ x: 150, y: 370, w: 130, h: 16 },   // A: top edge 370, x 150..280
{ x: 300, y: 230, w: 20, h: 210 },   // wall: top edge 230, x 300..320, bottom edge 440
{ x: 360, y: 300, w: 130, h: 16 },   // B: top edge 300, x 360..490
{ x: 545, y: 235, w: 120, h: 16 },   // C: top edge 235, x 545..665
{ x: 680, y: 165, w: 120, h: 16 },   // D: top edge 165, x 680..800
```

B → C: B top edge 300, C top edge 235: rise 65. Horizontal: B's right edge 490, C's left edge 545: gap 55px. No problem.
C → D: C top edge 235, D top edge 165: rise 70. C's right edge 665, D's left edge 680: gap 15px. No problem.
A → B: rise 70, but the wall in between (top edge 230, 140 above A).
Ground → A: rise 70. No problem.

So the wall is the only problem. To cross the wall, you must clear its top edge (230). The only places to jump from are A (feet 370, need rise 140) or the ground (feet 440, need rise 210).

Hmm, wait — can you jump from A and land on the wall top? Wall top 230, from A's feet 370: rise 140. To land on the wall top, the player must be descending with feet = 230 while overlapping the wall's x (left x ∈ (276, 320)). From A's right edge (left x=256): left x = 256 + 4t ∈ (276, 320) → t ∈ (5, 21). Descending crossing of feet=230 at t2 = (v + sqrt(v² - 2·0.9·140))/0.9 = (v + sqrt(v² - 252))/0.9. Need t2 ∈ (5, 21), plus ascent constraint: while left x ∈ (276, 320) (t ∈ (5, 21)), feet must be ≥ 230 (no side collision) — that is, feet must not be below 230 during t ∈ (5, t2). Feet below 230 during ascent until t1 = (v - sqrt(v²-252))/0.9. Need t1 ≤ 5.

t1 ≤ 5: (v - sqrt(v²-252))/0.9 ≤ 5 → v - sqrt(v²-252) ≤ 4.5 → sqrt(v²-252) ≥ v - 4.5 → v² - 252 ≥ v² - 9v + 20.25 → 9v ≥ 272.25 → v ≥ 30.25. Again v ≈ 30. Max rise = 900/1.8 = 500px. Completely unreasonable.

So: with this level geometry, the wall can only be cleared by a huge jump from the ground (v ≥ about 22, rise ≥ about 270px), or an unreasonable jump from A (v ≥ 30).

Hmm, wait, that doesn't seem right for a "very small platformer." Let me re-check the wall dimensions. `{ x: 300, y: 230, w: 20, h: 210 }`. Hmm, what if I misread and it's actually w: 200? No, it's `w: 20, h: 210`. The comment says "the tall wall."

Hmm, hold on. Let me reconsider. What if the intended path is to jump from A to B, and the wall is... hmm, the wall spans y 230..440. A's top edge is 370, B's top edge is 300. A→B jump trajectory: feet go from 370 up to at most 370-94 = 276 (with v=13) and back down to 300. The feet's maximum height is 276, which is below the wall top 230 (276 > 230 means lower on screen). So an A→B jump with v=13 passes through the wall region at feet height 276..370 — inside the wall's y range 230..440. Collision.

So with v=13, the level is not clearable, period. The bug report says "fix those 5 bugs and the level becomes clearable: jump the ledges, be stopped by the wall, reach the flag." So the implication is that fixing the 5 bugs makes it clearable. But mathematically, with JUMP_VELOCITY=-13 and GRAVITY=0.9, the wall (210 tall from the ground, 140 above A) cannot be cleared.

Unless... the intended interaction with the wall is different. What if the wall is not meant to be jumped over, and instead the player is supposed to... hmm, "be stopped by the wall" — the wall stops you. So you bounce off it. Then how do you get past?

Wait. What if the intended path is: ground → A → jump from A and hit the wall (get stopped, slide down), then... no.

Hmm, let me look at the geometry from another angle. What if the player jumps from A, and the wall blocks, and the player is supposed to jump higher...

Actually, you know what — let me reconsider. Maybe the intended design is that the wall top is a stepping stone: ground → A → wall top → B → C → D. And the "tuning" includes raising the jump velocity so that A → wall top works. From A to wall top: rise 140, need t1 ≤ 5 (no side collision) → v ≥ 30.25. No good.

Or: ground → wall top directly (rise 210): v ≥ 22 or so. Then wall top → B (falling 70, horizontal from wall (300..320) to B (360..490): gap from wall right edge 320 to B left edge 360 = 40px = 10 frames; falling 70px takes sqrt(2·70/0.9) ≈ 12.5 frames — no problem).

Hmm, so the "intended" path might be: ground → A (resting spot) → big jump from the ground near the wall to clear it → B → C → D. But a 270px jump is huge.

Hmm, wait a moment. Let me reconsider whether the wall is really at y=230 with h=210. What if the wall was intended to be shorter, e.g., h=110 (top edge 330)? Then from A (370) the wall top is 40 above — easy. But the file says 210. I can't change the level layout ("keep the level layout exactly as-is").

OK, so the constraints are: keep the level layout (platform positions/sizes), art, colors, controls. Physics tuning is allowed (that's the whole point: "tune the numbers until it feels right"). So I need to pick GRAVITY and JUMP_VELOCITY such that:
1. The level is clearable with comfortable margins.
2. The jump "feels right" — not too floaty, not too stiff.
3. Variable jump, coyote, buffer.

Let me think about what jump height is needed:
- Ground → A: rise 70.
- A → over wall → B: need to clear 140 while crossing the wall's x range... this is the hard one. As shown, a single A→B jump requires v ≥ 30 (rise 500px). Unreasonable.
- Ground → over wall → B/wall top: need about 210+ clearance while crossing 44px of wall x range (11 frames). v=22 gives a 23-frame window above 230, with a 48px (12-frame) jump-start window. Workable but a huge jump (269px).

Hmm, hmm. A 269px jump on a 480px canvas... the player (36px tall) rises 7.5 times its own height. That's Mario-level high (Mario's small jump is about 4× his height, big jump about 6×). Actually, SMB's big jump: 36px-tall Mario jumps about 100px ≈ 2.8×. 7.5× is way too floaty.

Let me reconsider. Maybe I'm wrong that A→B must clear the wall top in one jump. What if the player can land on the wall top? From A: rise 140, and I showed that requires v ≥ 30 to avoid side collision. From the ground: rise 210, v ≥ 22.

Hmm, OK, wait wait wait. Let me recompute the A→wall-top case more carefully. I might have been too strict. The side collision constraint is: while the player's x range overlaps the wall's x range (300..320), the player's y range must not overlap the wall's y range (230..440). The player's y range is [feet-36, feet]. No overlap when feet ≤ 230 (player's bottom at or above wall top) — i.e., feet < 230 strictly, or feet = 230 exactly (touching, no overlap with strict inequality).

Start from A's right edge: left x0 = 256, feet0 = 370. Jump at t=0 with velocity v (upward).
- Player's right edge = 280 + 4t. Reaches 300 at t = 5.
- Player's left edge = 256 + 4t. Reaches 320 at t = 16.
- So x overlap during t ∈ (5, 16).
- feet(t) = 370 - (v·t - 0.45t²) (discrete, close enough).
- Need feet(t) ≤ 230 for all t ∈ (5, 16) → v·t - 0.45t² ≥ 140 for all t ∈ (5,16).
- Minimum of rise on [5,16]: the rise function is concave (parabola opening downward), so the minimum on the interval is at an endpoint. rise(5) = 5v - 11.25; rise(16) = 16v - 115.2. For v ≈ 17: rise(5) = 73.75, rise(16) = 156.8. So the binding constraint is t=5: v ≥ 30.5. Confirmed.

So A→B in one jump is impossible with reasonable physics. The wall is simply too close to A (20px gap) and too tall (140 above A).

Therefore the only clearable route is from the ground: jump from the ground, clear the wall top (230, 210 above the ground), and land on the wall top or B.

Required: rise ≥ 210 during x overlap with the wall. From the ground, player's right edge reaches 300 at t_a, left edge passes 320 at t_a + 11. Need feet ≤ 230 during [t_a, t_a+11].

With jump velocity v (upward) and g=0.9: rise(t) = vt - 0.45t².
Need rise ≥ 210 during [t_a, t_a+11]. The window where rise ≥ 210 is (t1, t2), where t1 = (v - sqrt(v²-378))/0.9, t2 = (v + sqrt(v²-378))/0.9. Need t_a ≥ t1 and t_a + 11 ≤ t2, i.e., t2 - t1 ≥ 11 → 2·sqrt(v²-378)/0.9 ≥ 11 → sqrt(v²-378) ≥ 4.95 → v² ≥ 378 + 24.5 = 402.5 → v ≥ 20.06.

And the jump-start window: t_a = (300 - x0 - 24)/4, where x0 is the player's left x at jump start (on the ground, x0 < 300-24=276... must also be ≥ 0, and the player must be on the ground, not under anything — the ground is fine). t_a ∈ [t1, t2 - 11].

v = 21: sqrt(441-378) = sqrt(63) = 7.94. t1 = (21-7.94)/0.9 = 14.5, t2 = (21+7.94)/0.9 = 32.2. Window length 17.6 ≥ 11 ✓. t_a ∈ [14.5, 21.2] → x0 = 276 - 4t_a ∈ [276-84.8, 276-58] = [191.2, 218]. So jumping from ground x0 ∈ [191, 218] (a 27px window) clears the wall with v=21. Max rise = 441/1.8 = 245px.

v = 22: max rise 269. Window t_a ∈ [13, 24.9] → x0 ∈ [176.4, 224]. 48px window.

v = 24: sqrt(576-378)=sqrt(198)=14.07. t1 = (24-14.07)/0.9 = 11.0, t2 = 37.9. t_a ∈ [11, 26.9] → x0 ∈ [168.4, 232]. 64px window. Max rise 320px. Whoa.

So the smaller v is (closer to 20), the smaller the jump but the tighter the start window. v=21: 27px window (about 7 frames of positioning at speed 4). Hmm, that's a bit tight, but with coyote time and careful play, OK. Actually, the player can also jump from a standstill (vx=0): t_a is then... if the player stands at x0 and jumps straight up, the player doesn't move horizontally — x overlap with the wall requires the player to be at x0 ∈ (276-24... wait, if standing still: player's x range [x0, x0+24] must overlap [300,320] → x0 ∈ (276, 320). But x0 > 276 means the player is already horizontally overlapping the wall while on the ground — impossible, the wall occupies that space down to the ground. So the player must be at x0 ≤ 276 on the ground. Jumping straight up from x0 ≤ 276: no x overlap with the wall ever (player's right edge = x0+24 ≤ 300). So a straight-up jump from the ground can't clear the wall. You have to move right while jumping.

Hmm, OK. So the intended gameplay is: run right from the ground, jump near the wall (within a window of about 27-48px before the wall), clear the 210px wall, and land on the wall top or B.

But wait — what about ledge A? If the wall can be cleared from the ground, what's A for? A is at x 150..280, top edge 370. The jump window on the ground is x0 ∈ [191, 224] (v=22) — that's above A's x range (150..280)! So the player can stand on A (feet 370) and jump from there... but from A the wall is only 140 above the feet, and the gap to the wall is 20px — as computed, A→wall clearance requires v ≥ 30.

Hmm, wait, no! If the player stands on A at left x0 = 256 (right edge 280) and jumps with v=22: feet0 = 370, need feet ≤ 230 during x overlap t ∈ (5, 16) → rise ≥ 140 during (5,16). rise(5) = 110 - 11.25 = 98.75 < 140. Collision at t=5. So a jump from A's edge still hits the wall even with v=22.

So A is a dead end for wall clearance. A is just... a decorative ledge? Or a rest spot? Hmm. Or maybe A is for the return journey (B → A → ground)? From B (feet 300) to A (top edge 370): falling 70, horizontal gap from B's left edge 360 to A's right edge 280 = 80px. Easy.

Hmm, wait, actually, let me reconsider. Maybe I should re-verify: is it possible that the intended path is ground → A → wall top, and the wall top is reachable from A with the right velocity? I computed v ≥ 30.25. Max rise 500px — the player would go off the top of the screen (feet 370 - 500 = -130 < 0). The player can't leave the canvas (constraint: "must not be able to leave the canvas"). So no.

So: the wall must be cleared from the ground with a big jump. The level's A is a rest spot / optional.

Hmm, wait. Actually, hold on. Let me reconsider the problem. Let me re-read the bug report: "3. The wall isn't solid. The tall block in the middle of the level can be walked straight through." — "walked straight through" — at ground level! The player walks on the ground (y 440) and the wall occupies 230..440, so walking right at ground level hits the wall at x=300. In the broken game, the player walks through. Fix: make the wall solid so the player is stopped.

And "the level becomes clearable: jump the ledges, be stopped by the wall, reach the flag."

So the intended experience: walk right, get stopped by the wall, jump over it (from the ground), land on B (or the wall top), then B → C → D → flag. Ledge A: jump up from the ground (rise 70), rest, jump down. A is a "ledge" you can jump onto — "jump the ledges" is plural, including A.

OK, so I'm now pretty confident in the design:
- A: optional rest ledge (reachable: rise 70).
- Wall: must be jumped over from the ground with a big jump.
- B, C, D: the main staircase to the flag.

Now, what jump velocity? The wall requires v ≥ 20.06 (g=0.9). Let me think about feel:
- Max jump height = v²/(2g). v=21, g=0.9: 245px. v=22: 269. v=20.5: 233.
- Jump duration (full): 2v/g. v=21: 46.7 frames ≈ 0.78s at 60fps. That's a long jump (Mario's big jump is about 0.6-0.7s). Hmm, a bit floaty but OK for a casual game.
- Horizontal distance at speed 4: 46.7 × 4 = 187px.

Alternatively, I could raise gravity to make the jump snappier: e.g., g=1.4, v=?: need v ≥ sqrt(2·g·210·margin)... let me parameterize: need window t2-t1 ≥ 11 frames, where t2-t1 = 2·sqrt(v²-2·g·210)/g. And max rise = v²/(2g).

Actually, the constraint "rise ≥ 210 during 11 frames" is about the time the player spends above the wall top. Higher gravity → faster jump → less time above 210 → need higher v for the same window. The product that matters: the player must be above 230 (feet) for 11 consecutive frames.

Let me think in terms of the trajectory: the player's feet follow a parabola. Time above height h: t_above = 2·sqrt(v² - 2·g·h)/g. Need t_above(210) ≥ 11 (frames, at 60fps).

g=0.9: v ≥ 20.06 (computed). t_above at v=21: 2·sqrt(441-378)/0.9 = 2·7.94/0.9 = 17.6 frames.
g=1.2: need 2·sqrt(v²-504)/1.2 ≥ 11 → sqrt(v²-504) ≥ 6.6 → v² ≥ 504+43.6 = 547.6 → v ≥ 23.4. Max rise = 547/2.4 ≈ 228 (at v=23.4: 547.6/2.4 = 228). t_above at v=24: 2·sqrt(576-504)/1.2 = 2·8.49/1.2 = 14.1.
g=1.5: need sqrt(v²-630) ≥ 8.25 → v² ≥ 630+68 = 698 → v ≥ 26.4. Max rise = 698/3 = 233.

Interesting — max rise stays around 230-270 regardless. Because the constraint is essentially "be 210px up for 11 frames," which forces a certain trajectory shape.

Hmm, OK, wait, actually, let me reconsider. Is it really necessary to be above the wall top for the full 11 frames? The player's x overlap with the wall is 44px (player width 24 + wall width 20) = 11 frames at speed 4. Yes, the feet must be above 230 (or the player's bottom above the wall top) for the entire time the player's body crosses the wall's x range. Yes, 11 frames.

Unless the player jumps over the wall while moving... no, horizontal speed is fixed at 4.

OK, so the physics must support a jump that is above 210px for at least 11 frames. That's a big jump. Let me also check the landing: after clearing the wall, the player lands on the wall top (230) or B (300). From the apex (about 245px rise → feet at 440-245 = 195), falling to 230: no problem.

But hmm, one more consideration: when the player clears the wall and lands on the wall top — the wall top is only 20px wide (x 300..320). The player is 24 wide. To stand on the wall top, the player's x range must overlap [300,320]: left x ∈ (276, 320) — a 44px window. Landing on the wall top is possible but a narrow perch; the player can then jump from the wall top to B (falling 70, gap 40) — easy. Or land directly on B (top edge 300, x 360..490): left x ∈ (336, 490) — a wide target.

Let me also check B → C and C → D with the chosen physics:
- B → C: rise 65, gap 55 (B's right edge 490 → C's left edge 545). Max rise 245 ≫ 65. Horizontal: need to cover 55px while rising 65. Time above 65px: 2·sqrt(v²-2·g·65)/g... at v=21, g=0.9: sqrt(441-117)=sqrt(324)=18, t_above = 40 frames = 160px. Plenty.
- C → D: rise 70, gap 15. Easy.
- D → flag: the flag is at x 730..750, y 125..165, sitting on D (top edge 165). The win condition (to be fixed) should trigger when the player is at the flag. The player stands on D with feet 165, and the flag occupies y 125..165, x 730..750. The player's x range [x, x+24] overlaps [730,750] when x ∈ (706, 750). D spans 680..800, so the player can stand at x 706..750 with feet 165, overlapping the flag's x range. The flag's y range 125..165 overlaps the player's y range [129, 165] (player

Confirmed my analysis:
- The wall (top edge 230) is 210px above the ground and 140px above ledge A.
- With the current jump (max rise 94px), you can't clear the wall from anywhere.
- The only feasible route: jump over the wall from the ground (need to rise 210px while crossing the 44px-wide x-range of the wall = 11 frames at speed 4), then land on the wall top or B, then B→C→D→flag.
- The win condition `player.x > goal.x + goal.w && feet < goal.y` is geometrically impossible (the player can't be to the right of the flag while being above it — the flag is 50px from the right wall, and the player is 24 wide). It needs to be an overlap test.

So the physics parameters need to be tuned so that the wall can be cleared. Let me simulate candidate physics and measure the jump start window on the ground for clearing the wall. I'll write a headless simulation of the exact collision code I plan to implement, and do the following:

1. Verify that the wall can be cleared with a comfortable window.
2. Verify all ledges are reachable.
3. Verify no tunneling at max fall speed.
4. Verify the player doesn't get stuck or go out of bounds.
5. Verify the full route to the flag is completable.

Let me design the physics:

Fixed timestep 60Hz (1/60 sec), accumulator in rAF.

Parameters to try:
- MOVE_SPEED = 4 (keep — controls/layout unchanged; this is fine)
- GRAVITY = 0.9 (keep? or tune)
- JUMP_VELOCITY: needs to be about -21 or more for g=0.9.

Let me think about feel. With g=0.9, v=21:
- Max rise: 245px (feet go from 440 to 195). Player head at 195-36=159 > 0. OK, stays within canvas.
- Full jump time: 2·21/0.9 = 46.7 frames = 0.78 sec. A bit floaty.
- Horizontal distance: 187px.

With g=1.2, v=23.5:
- Max rise: 23.5²/2.4 = 230px. Feet at 210, head at 174.
- Full jump time: 2·23.5/1.2 = 39.2 frames = 0.65 sec. Snappier.
- Horizontal distance: 157px.

Time above 210px (needed ≥11 frames):
- g=0.9, v=21: 2·sqrt(441-378)/0.9 = 17.6 frames ✓ (window is comfortable)
- g=1.2, v=23.5: 2·sqrt(552.25-504)/1.2 = 2·sqrt(48.25)/1.2 = 2·6.95/1.2 = 11.6 frames — barely 11! Too tight. v=24.5: 2·sqrt(600.25-504)/1.2 = 2·9.81/1.2 = 16.3 ✓. Max rise 600.25/2.4 = 250.

Hmm. Let me think about which feels better. Actually, for a casual small platformer, a slightly floaty, high jump is fine — the level demands a big jump. But 0.78 sec airtime is quite floaty. Let me consider g=1.0, v=21.5:
- Max rise: 462.25/2 = 231px. Feet at 209, head at 173.
- Airtime: 43 frames = 0.72 sec.
- Time above 210: 2·sqrt(462.25-420)/1 = 2·6.5 = 13 frames ✓ (2 frames of margin over the required 11).
- Horizontal distance: 172px.

g=1.0, v=22:
- Max rise 242, airtime 44 frames, time above 210: 2·sqrt(484-420) = 2·8 = 16 ✓.

Let me also consider the jump start window on the ground for clearing the wall (the actual gameplay constraint). Simulate it exactly. Actually, let me write the full game code first, then write a headless test harness that imports the same physics (structure game.js so the physics can be tested: e.g., guard the DOM parts, or duplicate the core in the test). Simpler: write a standalone simulation in the test file that mirrors the update logic exactly, and run the scenarios. Risk of divergence… better: structure game.js so `update` is pure enough, and in the test stub out `document`/`canvas` minimally and load game.js in node. game.js uses `document.getElementById`, `addEventListener`, `requestAnimationFrame` at the top level. I can stub these in node before `require`-ing game.js. But game.js isn't a module… I can read the file and eval it in a context with stubs. That way I test the actual code.

Plan:
1. Write the new game.js.
2. Write a test harness (temp file, delete later — "keep it to the existing 3 files" refers to the deliverable; I can create a temp test file and delete it. Or place it outside the directory. Let me put it in /tmp to keep the directory clean).
3. Run the tests:
   - Scenario A: full route with a scripted "player" — actually, I can just directly simulate key inputs: hold right, jump at the right timing, etc. Better: write an auto-player: move right, and when within the jump window for the next target, jump. Hmm, that's complex. Alternative: test the physics primitives directly:
     a. Landing: drop the player from above each platform, verify it lands exactly on top, doesn't sink, doesn't tunnel even at high speed (e.g., vy=30).
     b. Wall: verify that walking right on the ground stops at x=276 (player's left edge, right edge at 300), and the player can't pass through.
     c. Wall clearance: from the ground, with right held, jump at various start positions; find the window where the player clears the wall and lands on the wall top or B. Verify the window is comfortably wide (≥ ~15px, ideally more).
     d. One-way ledges: verify that jumping from below passes through B/C/D (e.g., jump from the ground under B… B is at x 360..490, top 300; jumping from the ground under B: the player's head reaches at most 440-242=198 < 300 so the player's body overlaps B's y-range while ascending? B's y-range is 300..316. Player's feet pass through 316..300 while ascending under B — with one-way, no collision, passes through. Then lands on B while descending. Good test.
     e. Coyote: walk off an edge, jump 5 frames later, verify the jump fires.
     f. Buffer: jump 6 frames before landing, verify the jump fires on landing.
     g. Variable height: tap (release after 2 frames) vs hold: measure the rise.
     h. Out of bounds: verify the player never goes outside the canvas in any scenario; verify no reset from falling (shouldn't happen since the ground covers the full width).
     i. Win: stand on D at the flag position, verify won=true.
   - Also, verify the full route with a scripted sequence of key inputs (approximating human play): e.g., a sequence of (hold right, jump at x=..., release at x=...) that reaches the flag. I can write a simple bot: at each step, if the next platform is reachable, decide when to jump… simpler: use the computed jump windows to hardcode the route with specific jump timings, and verify that won=true at the end.

Let me first decide the physics parameters, then verify with the simulation.

Actually, let me reconsider whether to keep GRAVITY=0.9. The bug report says "tune the numbers until it feels right." The original feel: v=13, g=0.9 → rise 94px, airtime 28.9 frames (0.48 sec). For the new physics, the wall requires a big jump. Let me pick g=1.0, v=22 (rise 242, airtime 0.73 sec, horizontal 173px). Or keep g=0.9, v=21.

Hmm, one more consideration: falling. Max fall speed: cap at about 16-18 (terminal velocity). Falling from the top of the canvas (480px): v = sqrt(2·g·480) = sqrt(960) ≈ 31 (g=1). Capping at 18 makes falls snappier; 18px/frame = 1080px/sec. With one-way swept collision, tunneling is handled anyway. Cap at 18.

Also, variable jump: on release during ascent, vy *= 0.45 (cutoff). Tap height: if released at frame k during ascent… let me compute: rise with cutoff at velocity v_c: the player rises until vy reaches the cutoff point. If released when vy = -r (r < v), then vy becomes -0.45r, and the player continues to rise until vy=0: additional rise = (0.45r)²/(2g). Total rise ≈ (v² - r²)/(2g) + (0.45r)²/(2g)… approximately (v² - r² + 0.2·r²)/(2g) = (v² - 0.8r²)/(2g).

If released at frame 3 (vy ≈ -22+3 = -19, g=1): total ≈ (484 - 0.8·361)/2 = (484-289)/2 = 97px. A tap gives about 97px rise vs 242 for a full jump. Nice ratio (about 40%).

If released at frame 1 (vy=-21): (484 - 0.8·441)/2 = (484-353)/2 = 65px. A very short tap gives 65px — can it still clear ledge A (70px)? Just barely not. Hmm, a 1-frame tap is about 65px. A 2-frame tap (vy=-20): (484-320)/2 = 82px ✓ clears A. OK, good — a deliberate short tap (2+ frames) reaches A; a full hold clears the wall. That's a nice skill gradient.

Coyote time: 0.1 sec = 6 frames. Buffer: 0.12 sec ≈ 7 frames.

Now, the wall clearance window. Let me simulate exactly with g=1.0, v=22, speed 4.

Actually, let me write the code and then the simulation. Let me write the new game.js now.

Structure:

```js
const canvas = document.getElementById("game");
const ctx = canvas.getContext("2d");

const platforms = [ ... unchanged ... ];
const goal = { ... unchanged ... };
const spawn = { ... unchanged ... };

const player = { x, y, w, h, vx, vy, onGround: false, coyote: 0, buffer: 0 };

// Physics tuning (60Hz fixed step)
const STEP = 1/60;
const GRAVITY = 1.0;
const MOVE_SPEED = 4;
const JUMP_VELOCITY = -22;
const JUMP_CUTOFF = 0.45;      // vy multiplier on early release
const MAX_FALL = 18;
const COYOTE_TIME = 0.1;       // seconds
const BUFFER_TIME = 0.12;      // seconds

let won = false;
const keys = {};
let jumpHeld = false; // derived

addEventListener("keydown", (e) => {
  if (e.repeat) { ... } // handle buffer: set buffer on fresh press only
  keys[e.code] = true;
  if (e.code === "KeyR") reset();
  if (jump keys) { e.preventDefault(); if (!e.repeat) player.buffer = BUFFER_TIME; }
});
addEventListener("keyup", (e) => {
  keys[e.code] = false;
  if (jump key && player.vy < 0) player.vy *= JUMP_CUTOFF;  // variable jump
});
```

Hmm, wait, about variable jump: the cutoff should only apply if the jump was actually initiated by a held key and the player is ascending. If the player is ascending and the key is released → vy *= 0.45. That's the standard. But note: if the player is ascending from a jump and the key is released, the cutoff applies. If the player is ascending… that's the only case vy<0. OK.

But a subtle point: the keyup handler runs asynchronously between frames; the cutoff applies immediately — that's fine, it's a one-shot.

Jump initiation in update:
```js
const wantJump = keys.Space || keys.ArrowUp || keys.KeyW;
// buffer is set on keydown (fresh press)
if (player.buffer > 0 && (player.onGround || player.coyote > 0)) {
  player.vy = JUMP_VELOCITY;
  player.onGround = false;
  player.coyote = 0;
  player.buffer = 0;
}
player.coyote = Math.max(0, player.coyote - STEP);
player.buffer = Math.max(0, player.buffer - STEP);
```

Wait, but if the player is on the ground and holds the key (no fresh press, buffer already consumed), no re-jump. Good — no auto-bounce. But hmm: if the player is on the ground and holds jump from before landing (buffered), the jump fires on landing — that's the buffer feature. Good.

Edge case: player on ground, presses jump → buffer set → jump fires next frame. If the key is held and the player walks off a ledge: coyote counts down from when onGround becomes false. If the player presses jump during coyote → fires. Good.

Movement and collision (per fixed step):

```js
// horizontal
player.vx = input;
player.x += player.vx;
// resolve horizontal against solid platforms (wall, ground)
for (const p of solids) {
  if (overlap(player, p)) {
    if (player.vx > 0) player.x = p.x - player.w;
    else if (player.vx < 0) player.x = p.x + p.w;
    else {
      // no horizontal movement but overlapping (e.g., landed on a corner?) push out to nearest side
      const leftPen = player.x + player.w - p.x;
      const rightPen = p.x + p.w - player.x;
      player.x += leftPen < rightPen ? -leftPen : rightPen;
    }
  }
}
// clamp to canvas
player.x = clamp(player.x, 0, canvas.width - player.w);
```

Hmm, wait, should the ground be "solid" horizontally? The ground spans the full width; its sides are at the canvas edges, which are clamped anyway. If I make the ground solid, the horizontal resolution against it is a no-op (the player can't get inside the ground from the side since the ground top is 440 and the player is always above… actually, can the player ever be at y > 440 (inside the ground)? Only if they tunnel through the ground — with swept one-way landing, no. So the ground being solid horizontally is harmless. But simpler: only the wall is solid. Let me mark the wall with `solid: true` in the platforms array. But wait — "keep the level layout exactly" — adding a `solid` property doesn't change the layout. Fine.

Hmm, actually, let me reconsider: should the ground also be solid for robustness? If for some reason the player's feet go below 440 (shouldn't happen), the one-way landing handles it. Let me keep only the wall solid — minimal.

Vertical:
```js
player.vy = Math.min(player.vy + GRAVITY, MAX_FALL);
const prevBottom = player.y + player.h;
player.y += player.vy;
player.onGround = false;
for (const p of platforms) {
  const overlapX = player.x + player.w > p.x && player.x < p.x + p.w;
  if (!overlapX) continue;
  const bottom = player.y + player.h;
  if (p.solid) {
    // full AABB resolution
    if (player.y + player.h > p.y && player.y < p.y + p.h) {
      if (prevBottom <= p.y + EPS && player.vy >= 0) { // was above, moving down
        player.y = p.y - player.h; player.vy = 0; player.onGround = true;
      } else if (prevBottom >= p.y + p.h && player.vy < 0) { // was below, moving up
        player.y = p.y + p.h; player.vy = 0;
      } else {
        // deep overlap: push out along the smaller axis (shouldn't happen)
        ...
      }
    }
  } else {
    // one-way: land only when crossing the top face downward
    if (player.vy >= 0 && prevBottom <= p.y && bottom >= p.y) {
      player.y = p.y - player.h; player.vy = 0; player.onGround = true;
    }
  }
}
```

Hmm, wait, there's a subtlety with one-way landing and the "grounded" state: if the player is standing on a ledge and the ledge is one-way, each frame: vy += g → vy = 1, prevBottom = p.y (exactly on top), y += 1 → bottom = p.y + 1. Check: vy ≥ 0 ✓, prevBottom ≤ p.y ✓ (equal), bottom ≥ p.y ✓ → snap back to p.y, vy=0, onGround. Good, stable, no sinking.

But what if the player walks off the edge? overlapX becomes false → no landing → onGround=false, coyote starts. Good.

What about standing on a ledge and jumping? vy = -22, y decreases. Next frame, prevBottom is above p.y… the one-way check requires vy ≥ 0, so no collision while ascending. Good — the player can jump out from under a ledge (pass through from below).

Now, the solid wall vertical resolution: the player can land on the wall top (prevBottom ≤ 230, vy ≥ 0 → snap to top). The player can't hit the wall's underside (the wall bottom is 440 = the ground top; the player can't be below 440). The side is handled by horizontal resolution.

Order of operations per step:
1. Read input, set vx.
2. Handle jump (buffer/coyote).
3. x += vx; resolve horizontal against solid; clamp x to canvas.
4. vy += g (cap); prevBottom = y+h; y += vy; resolve vertical (one-way + solid);
5. Coyote: if onGround → coyote = COYOTE_TIME, else coyote -= STEP. (Set after resolution.)
6. If y > canvas.height → reset (safety; shouldn't happen).
7. Check win: player AABB overlaps goal AABB → won = true.

Wait, one issue: horizontal resolution before vertical. Classic order. When the player walks into the wall on the ground: x += 4 → player's right edge 300+ → overlap with wall (player's y-range [404,440] vs wall [230,440]: overlap? player.y+h = 440 > 230 ✓, player.y = 404 < 440 ✓ → overlap). vx > 0 → x = 300 - 24 = 276. Right edge exactly at 300. Next frame: x += 4 → 280 → overlap → back to 276. Stable, player stands against the wall.

But hmm — what if the player is standing on the wall top and walks off? No problem, one-way… the wall top is solid but landing on top works via the solid branch.

Corner case: the player jumps and lands exactly on the wall's top-left corner while moving right: horizontal resolution first: during ascent/descent, if the player's x overlaps the wall's x and y overlaps the wall's y → pushed left. Hmm, that could cause a "corner catch": the player descends toward the wall top; at the moment the feet cross 230, the player's right edge is slightly past 300 (x-overlap with the wall). Vertical resolution would snap to the wall top, but horizontal resolution (which runs first that frame) sees the overlap (feet already below 230 from the previous frame? no —). Let me trace: frame N: feet at 229 (above 230), x-overlap with the wall (right edge 302). Horizontal: y-range [193, 229] vs wall [230,440]: 229 > 230? No, 229 < 230 → no y-overlap → no push. Vertical: feet 229 + vy(=say 10) = 239 ≥ 230, prevBottom 229 ≤ 230 → snap to wall top: y = 230-36 = 194, feet=230. onGround. Good — lands on the wall top with right edge at 302, overlapping the wall's x — that's fine, standing on top of it.

Frame N+1: on the wall top, moving right: x += 4 → right edge 306. Horizontal: y-range [194, 230] vs wall [230,440]: 230 > 230? No (strict) → no overlap → no push. Good, walks off the wall top.

If the feet are exactly at 230 (touching the top) and x overlaps: no y-overlap (strict inequality) → no horizontal push. Correct.

Now the tricky case: the player descends toward the wall top but is too low (feet cross 230 while the body is still to the left of the wall… no wait, that's a side hit). Trace: player on the ground at x=276 (right edge 300, touching the wall's left face), jumps: vy=-22. Ascent: y-range rises. At some point the feet go above 230 → can move right over the wall. If the jump is too weak (feet don't reach 230): the player ascends, x += 4 each frame; when the right edge passes 300 with feet below 230 → horizontal overlap → pushed back to 276, vx effectively zeroed (x clamped). The player slides down against the wall. That's "stopped by the wall" — correct behavior.

Now, the "stuck on the wall" concern: the player is pushed to x=276, gravity pulls down, lands on the ground. Not stuck. Good.

Now, the win check: overlap of player and goal:
```js
if (player.x < goal.x + goal.w && player.x + player.w > goal.x &&
    player.y < goal.y + goal.h && player.y + player.h > goal.y) won = true;
```
Standing on D at the flag: player's feet 165, y-range [129,165] vs flag [125,165]: overlap [129,165] ✓. x: player at x=730: [730,754] vs [730,750] ✓. Won.

Also: can the player hit the flag from the side while jumping (e.g., jumping from C to D and passing through the flag's x-range)? The flag's y-range is 125..165. Jumping from C (feet 235) to D: max feet 235-242 = -7?? Wait, that's off the top of the canvas! Hmm: C top 235, full jump rise 242 → feet reach 235-242 = -7 < 0. The player's head goes to -43. Off canvas!

The constraint: "the player must never be… able to leave the canvas." Hmm. Does that mean the player's body must always stay within the canvas? Strictly, a jump from C with a full hold goes off the top. Options:
a) Clamp y at the top: if player.y < 0 → y = 0, vy = max(vy, 0)? That's a "ceiling" — the player bumps the top. Physically a bit odd but guarantees containment.
b) Reduce the max rise so a full jump from the highest ledge (D top 165, feet 165) stays in the canvas: rise ≤ 165-36 = 129?? But the wall requires a rise of 210+ from the ground. Contradiction — from the ground (feet 440), rise 210 → feet 230, head 194, fine. From D (feet 165), the same jump → feet -77. So a full jump from D always leaves the canvas unless clamped.

So (a): clamp at the top. Actually, is that a problem for gameplay? Jumping from D (the flag ledge) — the player has already won by then (the flag is on D, and reaching D's x-range near the flag wins). Actually, can the player land on D away from the flag and then jump? D spans 680..800; the flag is at 730..750. Landing on D at x=690 (left of the flag): no win yet (no overlap with the flag). Then a full jump: feet 165 → head to 165-242-36 = -113. Clamped at y=0. The player hits the "ceiling," hovers a bit, falls back. A bit odd but harmless and rare. Or, the player can just walk right to the flag (15px gap from D's left edge to the flag… the player lands somewhere on D, walks right, overlaps the flag, wins).

Hmm, actually wait: can the player even reach D without passing through the flag's x-range? C's right edge 665, D's left edge 680. Jumping from C: the player crosses x 680..800 while descending. The player's x-range overlaps the flag [730,750] when the player's x ∈ (706, 750). While descending onto D, the player's feet go from above 165 down to 165. The flag's y-range is 125..165. If the player's feet are above 125 (i.e., the player's bottom < 125) while x-overlapping the flag → no y-overlap (player's bottom above the flag's top… wait, the flag's top is 125; the player's bottom < 125 means the player is entirely above the flag → no overlap). As the player descends, the feet cross 165 (D's top) → snap to D, feet=165, y-range [129,165] overlaps the flag's [125,165] if x-overlaps. So if the player lands on D with x ∈ (706,750) → instant win on landing. If the player lands at x < 706 (e.g., 690), walks right → overlaps the flag → win. Either way, winning on D is guaranteed.

But wait — is it possible to land on D with x > 750 (right of the flag)? From C (x up to 665-24=641… the player's left x on C is up to 665-24=641, right edge 665). Jumping right: the player travels up to 173px → left x up to 641+173 = 814 → clamped to 776 (800-24). So the player can land on D at x=776 (right of the flag). Then walks left to the flag → win. Fine.

So the top clamp: I'll add it — `if (player.y < 0) { player.y = 0; if (player.vy < 0) player.vy = 0; }`. Guarantees containment. Actually hmm, wait: is that "stiff"? Only matters for a full jump from D, which is post-win territory… actually no, it's possible pre-win as noted (landing on D left of the flag, then jumping). Rare. The clamp is a safety net; fine.

Actually, let me reconsider the jump velocity to reduce how often this happens. If max rise is about 230 instead of 242, a full jump from D: feet 165-230 = -65, head -101. Still clamped. Unavoidable given the wall requirement (rise 210+ from the ground; D is 275 above the ground… wait, D top 165, ground 440: 275. So a wall-clearing jump from D's height always exceeds the canvas top by at least 210-275+36… let me compute: feet at 165, rise 210 → feet -45, head -81. Yes, any wall-clearing jump from D leaves the canvas. So the clamp is needed. OK.)

Hmm, wait, actually, let me re-verify: is the wall really 210 above the ground? Wall top 230, ground top 440: 440-230 = 210. Yes.

Now, the jump start window on the ground for clearing the wall — let me simulate exactly. I'll write the code and a test harness.

One more design point: the fixed timestep.

```js
let last = performance.now();
let acc = 0;
function frame(now) {
  acc += (now - last) / 1000;
  last = now;
  if (acc > 0.25) acc = 0.25; // avoid spiral of death after tab switch
  while (acc >= STEP) {
    if (!won) update();
    acc -= STEP;
  }
  draw();
  requestAnimationFrame(frame);
}
```

STEP = 1/60. On a 144Hz monitor, rAF fires 144 times/sec; the accumulator runs about 144/60 = 2.4 steps per second… wait no: 144 frames/sec × (1/144 sec) = 1 sec of game time per second → 60 steps/sec. On 60Hz: 60 rAF × (1/60) = 60 steps/sec. Same speed.

The keydown buffer: set player.buffer = BUFFER_TIME on a fresh press (e.g.repeat is false). Also, if the player is already in the air and presses jump, the buffer counts down — if they land within the buffer window, the jump fires.

Coyote: set coyote = COYOTE_TIME when onGround; decay when airborne.

Let me also double-check the "sink" fix with the new code: standing on a one-way ledge: each step, vy=0→+1 (gravity), y += 1 → feet 1px below the top; one-way check: vy ≥ 0 ✓, prevBottom (= top) ≤ top ✓, bottom ≥ top ✓ → snap back. Stable at exactly the top. No sink. ✓

Tunneling: falling at MAX_FALL=18: prevBottom ≤ top, bottom = prevBottom+18 ≥ top → caught. Even at vy=1000 it's caught (swept). ✓

Now, the horizontal resolution detail: after x += vx, check overlap with solid platforms. But what if the player is standing on the wall top (feet=230) and the ground below… no, the wall is the only solid. Overlap check with the wall: y-range [194,230] vs [230,440]: no strict overlap. ✓

What if the player is on the ground next to the wall (x=276, feet 440, y-range [404,440]) and the wall's y-range [230,440]: 440 > 230 ✓ and 404 < 440 ✓ → overlap when x overlaps. Walking right: x=280 → [280,304] vs [300,320]: overlap ✓ → push to x=276. ✓

Now, the "else" branch for horizontal resolution (vx == 0 but overlapping): can it happen? If the player is overlapping a solid with vx=0, it means they got into that state somehow (e.g., a landing snap put them overlapping? The vertical snap places the feet exactly at the top → no y-overlap. The top clamp… no). It's a safety branch; push out to the nearest side. Fine.

Another subtle point: horizontal resolution uses the current y (before the vertical move). Order: x-move + x-resolve, then y-move + y-resolve. Standard.

But here's a potential issue: the player descends along the wall's face (sliding down after a weak jump). Each frame: x += 4 (holding right) → pushed back to 276. vy increases, y += vy → feet go deeper… the player is on the ground: feet 440, stable. Slides against the wall, stays on the ground. ✓ Not stuck (can move left, or jump — a jump from x=276: ascent; if the jump is strong enough the feet clear 230 and the player can move right over the top).

Now, let me also think about: can the player get onto the wall top and be stuck there? Wall top is 20 wide, player is 24 wide. Standing on the wall top: x ∈ (276, 320). From there, jump right: land

Let's pick g=1.0, v=22: max rise 242px, airtime 0.73s, time above 210px is 16 frames (5 frames of margin over the required 11 frames). Horizontal distance 176px. This should give a comfortable wall-clearance window.

Let's verify: with v=22, g=1.0, the window of t where rise ≥ 210: t1 = (22 - sqrt(484-420))/1 = 22-8 = 14, t2 = 22+8 = 30. So the feet are above the wall's top edge during t ∈ (14, 30) — a 16-frame window. The player's x-overlap with the wall lasts 11 frames (44px / 4). Jump start position: t_a = the moment the right edge reaches 300 = (300 - x0 - 24)/4. Need t_a ≥ 14 → x0 ≤ 276 - 56 = 220. Need t_a + 11 ≤ 30 → t_a ≤ 19 → x0 ≥ 276 - 76 = 200. So the jump start window is x0 ∈ [200, 220] — 20px = 5 frames at speed 4. Hmm, a bit tight. Let's double-check with an exact simulation later.

Actually, wait, I should double-check the direction of the inequality. t_a = (300 - (x0+24))/4 = (276 - x0)/4. For the player not to collide with the wall's side, the feet need to be above 230 (rise ≥ 210) at the moment the right edge first enters the wall's x-range (t_a), and the feet need to stay above 230 until the left edge clears 320 (t_a + 11). Rise ≥ 210 during t ∈ (14, 30). So t_a ∈ [14, 19] → (276-x0)/4 ∈ [14,19] → 276-x0 ∈ [56, 76] → x0 ∈ [200, 220]. A 20px window.

A 20px window = 5 frames of timing. With coyote/buffer it's playable, but let's see if we can widen it. A wider window comes from a larger timeAbove210. v=23, g=1.0: t1 = 23 - sqrt(529-420) = 23-10.44 = 12.56, t2 = 33.44. Window 20.9 frames. t_a ∈ [12.56, 22.44] → x0 ∈ [276-89.8, 276-50.2] = [186, 226] — 40px window. Max rise 264.5 → from the ground, feet reach 175.5, head 139.5 — no problem. From ledge D (feet 165): a full jump puts the head at 165-264.5-36 = -135.5 → clamped at the top (no problem, rare).

v=23, g=1.0: airtime 0.77s, distance 184px. Feels a bit floaty, but it's a "big jump" game. Hmm.

Or g=1.2, v=24: timeAbove210 = 2*sqrt(576-504)/1.2 = 2*8.49/1.2 = 14.1 frames. t1 = (24-8.49)/1.2 = 13, t2 = 27.1. t_a ∈ [13, 16.1] → x0 ∈ [211.6, 224] — 12px. Tight. Worse.

Higher g means less time above the wall → tighter window. So g=1.0 with a higher v is better for the window. v=24, g=1.0: timeAbove210 = 2*sqrt(576-420) = 2*12.49 = 25 frames. t1 = 24-12.49 = 11.5, t2 = 36.5. t_a ∈ [11.5, 25.5] → x0 ∈ [174, 230] — 56px window! Max rise 288 → from the ground, feet reach 152, head 116. Airtime 0.8s, distance 192px. Pretty floaty, but the window is very comfortable.

Trade-off: floatiness vs. window width. For a casual "very small platformer," I'd want a window of about 30–40px (7–10 frames) and an airtime of about 0.7s. v=23, g=1.0 gives a 40px window and 0.77s. Let's go with v=23, g=1.0.

Hmm, wait, but I should also double-check the other jumps with v=23:
- Ground → A (rise 70): time above 70 = 2*sqrt(529-140) = 2*19.7 = 39.4 frames = 158px of travel. A is at x 150..280. From the ground, jump at x0, land on A: feet need to cross 370 while descending over x 150..280. Rise at landing = 70 (descending crossing at t = (23+19.7)/1 = 42.7): x = x0 + 170.8. For landing on A: player's x ∈ (126, 280) (x+24 > 150 → x > 126; x < 280). x0 + 170.8 ∈ (126, 280) → x0 ∈ (-45, 109). So jumping anywhere on the ground from x0 ∈ [0, 109] lands on A (if moving right). Very generous. ✓
- A → back to ground: trivial.
- Wall from ground: window x0 ∈ [186, 226]. Note: this window overlaps with A's x-range (150..280)! If the player is standing on A (feet 370) and jumps with v=23: the wall is only 140 above the feet; time above 140: 2*sqrt(529-252) = 2*16.6 = 33.3 frames; t1 = (23-16.6) = 6.4, t2 = 39.6. From A's right edge x0=256: t_a = (276-256)/4 = 5 < 6.4 → collision at t=5 (feet at 370 - (23*5-12.5) = 370-102.5 = 267.5 > 230 → still below the wall's top edge while the right edge is at 300 → side collision, pushed back). So jumping from A still hits the wall — as expected, A is not a launchpad for the wall. The player has to jump from the ground. But wait — if the player is on A and jumps toward the wall, they get pushed back to x=276... they're on A (feet 370), and the wall's side is at 300: horizontal push sets x = 276, but the player's feet are at 370 — is x=276 still over A? A spans 150..280: player at x=276 → [276, 300] vs A [150,280]: overlaps A ✓ (276 < 280). So the player is pushed to x=276, still over A (1px of overlap... [276,300] ∩ [150,280] = [276,280] ✓). Then they slide down... to the ground? At x=276, is there ground below? Yes, the ground is everywhere. The player falls to the ground at x=276, feet 440. Then they can jump from the ground within the window [186,226]... but they're at 276, outside the window (too close to the wall). They need to move left to 226 or less, then jump. OK, that's fine — playable.

Hmm, wait, actually there's a subtle point: if the player is at x=276 on the ground, touching the wall's face, and jumps straight up (no horizontal movement): the player's x-range [276,300] vs the wall [300,320]: overlap? 276+24=300 > 300? No, 300 > 300 is false → no overlap. So a straight-up jump at x=276 is safe (no x-overlap). The player rises 264.5 → feet 175.5, then falls back to the ground at x=276. Then moves left, jumps within the window. OK.

But, hmm, what if the player jumps at x=275 (right edge 299)? Still no overlap (299 < 300). x=276.5? x is a float... x=276.5 → right edge 300.5 > 300 → overlap → pushed back to 276. No problem.

Now, one more thing to consider: after clearing the wall, where does the player land? From x0 ∈ [186,226], t2 (feet back at 230) = 33.44... wait, that's the moment the feet cross 230 while descending: t = (23 + sqrt(529-420)) = 33.44. x at t2 = x0 + 133.8 ∈ [319.8, 359.8]. Wall top landing requires x ∈ (276, 320): x0 ≈ 186 → x = 319.8 (just barely on the wall top!). For x0 > about 186.2, the player passes over the wall (at the moment the feet cross 230, x > 320) and keeps falling to B (top 300): descending crossing of feet=300: rise = 140: t = (23 + sqrt(529-280))/1 = 23+15.78 = 38.78. x = x0 + 155.1 ∈ [341, 381]. B's x-range: x ∈ (336, 490). ✓ All landings on B.

So: jump at x0 ≈ 186 → land on the wall top (then jump to B); x0 ∈ (186, 226] → land directly on B. Both are fine. Actually, landing on the wall top: x=319.8, player [319.8, 343.8] vs wall [300,320]: overlap [319.8,320] ✓ (0.2px!). That's a super-tiny overlap — the player is standing on the wall top with only 0.2px of contact. Hmm, that's marginal — one step right and they're off the wall (x=323.8 → [323.8, 347.8] vs wall: no overlap → falls to B anyway, no problem).

Actually, wait, I need to recheck: when the feet cross 230 while descending at x=319.8, does the vertical resolution catch the wall top? The wall is solid: prevBottom ≤ 230 and bottom ≥ 230, x-overlap ✓ → snap to wall top. Yes.

But hmm, there's an ordering issue: horizontal resolution happens before vertical. At t2 (the moment the feet cross 230), the player's x = 319.8: horizontal check: y-range before the vertical move: feet are still above 230 (prevBottom < 230) → no y-overlap with the wall → no push. Then vertical: snap to wall top. ✓

Next, B → C: from B (feet 300, x up to 490-24=466), jump right: need to land on C (top 235, x 545..665). Rise 65. Descending crossing of feet=235: t = (23 + sqrt(529-130)) = 23+19.97 = 42.97. x = x0 + 171.9. For C: x ∈ (521, 665) (x+24 > 545 → x > 521). x0 ∈ (349, 493). From B, x0 ∈ [360-24=336... wait, on B x ∈ (336, 490)]. So x0 ∈ (349, 490) → lands on C. Generous. ✓ Even a full jump from B's left edge (x0=336): x = 507.9 → [507.9, 531.9] vs C [545,665]: no overlap → falls to the ground. So from B's left edge, a full jump misses C (lands on the ground at x=507). The player should jump from B's right half. No problem.

C → D: from C (feet 235, x up to 641), jump right: D top 165, rise 70, gap 15. Descending crossing of feet=165: t = (23 + sqrt(529-140)) = 42.7. x = x0+170.8 ∈ (641+170.8=811.8 → clamped 776). For D: x ∈ (656, 800) (x+24 > 680 → x > 656; x < 800). Jump from C's right edge x0=641: lands at x=776 (clamped) ✓ on D. From C's left edge x0=521: x = 691.8 ✓ on D. So any jump from C moving right lands on D. ✓

D → flag: walk to the flag. ✓

Also, can the player overshoot from B and land on C, or overshoot from C and land on D — yes, as computed. What about jumping from B straight up (no horizontal)? Falls back to B. No problem.

What about jumping from the ground under B (x 360..490, top 300)? A full jump from the ground: feet reach 440-264.5 = 175.5 < 300 → the player passes through B's y-range [300,316] while ascending (one-way: no collision while ascending ✓), then descends and lands on B (if x-overlap). ✓ One-way works.

Now, the top clamp: a full jump from D (feet 165): feet reach 165-264.5 = -99.5 → clamped at y=0 (head at 0... wait, y is the top of the player; feet = y+36. Feet reach -99.5 → y = -135.5 → clamped at y=0, vy=0, then falls. The player hovers at the top for a moment (vy=0, then gravity). Slight hang time. Acceptable.

Also, let's check the tap jump height with v=23, g=1.0, cutoff 0.45:
- Release at frame 1 (vy after 1 frame of ascent ≈ -23+1 = -22... wait, the order: jump sets vy=-23; each step: vy += 1. After k steps, vy = -23+k. If released at step k (keyup between steps), vy *= 0.45 → vy = -0.45(23-k). Then it rises until vy=0: additional frames ≈ 0.45(23-k), additional rise ≈ (0.45(23-k))²/2.
- Total rise ≈ sum. Let me just compute it numerically in a simulation later. Roughly: a 1-frame tap ≈ (23² - 0.8·22²)/2 ≈ (529-387)/2 ≈ 71px. A 2-frame tap ≈ (529 - 0.8·21²)/2 = (529-353)/2 = 88px. A 3-frame tap ≈ (529-0.8·20²)/2 = (529-320)/2 = 104.5. A full hold: 264.5.
- Ledge A requires 70: a 1-frame tap (71) just barely makes it; a 2-frame tap (88) is comfortable. Good.

Coyote 0.1s = 6 frames, buffer 0.12s ≈ 7 frames. Good values.

MAX_FALL: 18. Falling from the top of the canvas (480px): reaches 18 in sqrt(2·480/1) = 31 frames... no wait, v = g·t → t = 18 frames to reach 18. Distance in 18 frames ≈ 18²/2 = 162px, then 18px/frame. Total fall of 480px: 162px in 18 frames + 318px at 18px/f = 17.7 frames → about 36 frames = 0.6s. No problem.

Now — one more important check: the win condition and "the player must never be inside a platform." The flag is not a platform (no collision) — the player can overlap the flag (that's the win). No problem.

Also, "stuck on the wall": the player is pushed to x=276, on the ground, and can move freely. ✓

Now, let's also handle this: when the player is standing on a one-way ledge and walks off the edge — coyote. And the case where the player is standing on a ledge and a jump is buffered... all handled.

Edge case: the player is standing on ledge A, and the wall is 20px to the right (A's right edge 280, wall 300). The player at x=276 on A: [276,300] vs wall [300,320]: no x-overlap (300 > 300 is false). Walk right: x=280 → [280,304] vs wall: x-overlap ✓; y-range [334,370] vs wall [230,440]: overlap ✓ → pushed back to x=276. So on A, the player is also stopped by the wall (they can't walk off A's right edge into the wall's face... wait, A ends at 280; the player at x=276 spans [276,300] — 20px over A, 0px past A's edge... the player's right edge is at 300 = the wall's face. To walk off A's right edge, the player needs x > 280 (left edge past A's right edge) — but at x=280 they're already pushed back by the wall. So the player can't walk off A's right edge — they're blocked by the wall 20px away. They can walk off A's left edge (x < 150... the player at x=149: [149,173] vs A [150,280]: overlap ✓ still on A; x=126: [126,150] vs A: 150 > 150 is false → off A → falls to the ground with coyote). No problem.

So the flow of the level: spawn on the ground → jump to A (optional, rest) → back to the ground → run right, jump from x0 ∈ [186,226] to clear the wall → land on the wall top or B → B → C → D → flag → win.

Hmm, wait, let me actually reconsider: is it OK that A is essentially a "rest/dead-end" ledge? "Jump the ledges" — the player can jump to A. The main route uses B, C, D. I think that's the intended design (A is a warm-up ledge). The bug report says the level must be completable — and it is.

Hmm, but wait — let me reconsider the possibility that the intended route is A → wall top → B, with the wall top as a stepping stone. From A (feet 370), the wall top is 140 above: with v=23, max rise 264.5 — the player can reach it, but the side-collision constraint (the wall is only 20px from A's edge) makes it impossible (t_a = 5 < t1 = 6.4). So no. The ground is the only launchpad. OK.

Now, let's write the code.

Actually, one more consideration for the horizontal resolution: after pushing the player out horizontally, should we also zero out vx? vx is set from input each frame, so there's no issue with residual velocity.

And the "else" branch (vx == 0 but overlapping): push out along the smaller penetration. When could this happen? If the player is standing on the wall top (feet=230, no y-overlap) — no. If the player is on the ground at x=276 (touching, no overlap). It really shouldn't happen; keep it as a safety.

Also: should the ground be included in the solid list for horizontal? No — the ground spans the full width; the canvas clamp handles the edges. But wait: what if the player is inside the ground (feet > 440) and moving horizontally? Can't happen (swept landing). Keep the wall as the only solid.

Now, the win check: also, should the win only trigger when standing on D? The flag's AABB [730,750]×[125,165]: the player can only overlap it while on D (feet 165, y-range [129,165]) or while jumping over D (passing through the flag's y-range at x 730..750 while ascending/descending — e.g., jumping from C to D, the player passes through x 730..750 at feet... hmm: jumping from C (feet 235) to D: the player's feet go up to 235-264.5 = -29.5, then descend to 165. While x-overlapping the flag (x ∈ (706,750)), the feet pass through 165→125→...→165. The flag's y-range is [125,165]. The player's y-range is [feet-36, feet]. Overlap when feet-36 < 165 and feet > 125 → feet ∈ (125, 201). So if the player's feet are between 125 and 201 while x is in (706,750) → win. During a C→D jump, the feet pass through that range while x is in (706,750) → the win triggers mid-air. That's fine — the player is at the flag. Actually, that's good: the win triggers the moment you reach the flag, whether landing or jumping.

But wait — can the player pass through the flag's x-range while above it (feet < 125) and not win, then land to the right of the flag (x > 750)? E.g., a long jump from C: the feet cross (125,201) at x ∈ (706,750) → the win triggers before landing. To avoid the win, the player would have to have feet < 125 (above the flag's top) throughout x ∈ (706,750) — that requires feet ≤ 125 throughout that 44px span = 11 frames. The feet are above 125 (feet < 125, i.e., rise > 110 from D... no wait, from the C→D jump: the feet's max rise is 264.5 from 235 → min feet -29.5. Feet < 125 means rise > 110 from C: time above 110: 2*sqrt(529-220) = 2*17.6 = 35 frames — plenty. So the player can clear the flag entirely and land at x > 750 (e.g., 776). Then walk left to the flag → win. No problem, no softlock.

OK, let's write the code.

```js
const canvas = document.getElementById("game");
const ctx = canvas.getContext("2d");

const platforms = [
  { x: 0, y: 440, w: 800, h: 40 },     // ground
  { x: 150, y: 370, w: 130, h: 16 },
  { x: 300, y: 230, w: 20, h: 210, solid: true },   // the tall wall
  { x: 360, y: 300, w: 130, h: 16 },
  { x: 545, y: 235, w: 120, h: 16 },
  { x: 680, y: 165, w: 120, h: 16 },
];

const goal = { x: 730, y: 125, w: 20, h: 40 };
const spawn = { x: 40, y: 380 };

const player = { x: spawn.x, y: spawn.y, w: 24, h: 36, vx: 0, vy: 0, onGround: false, coyote: 0, buffer: 0 };

// --- physics tuning (all values per fixed 60Hz step) ---
const STEP = 1 / 60;
const GRAVITY = 1.0;
const MOVE_SPEED = 4;
const JUMP_VELOCITY = -23;
const JUMP_CUT = 0.45;     // vy multiplier when jump released early (variable height)
const MAX_FALL = 18;
const COYOTE = 0.1;        // grace after leaving a ledge, seconds
const BUFFER = 0.12;       // jump presses remembered before landing, seconds

let won = false;
const keys = {};
const JUMP_KEYS = ["Space", "ArrowUp", "KeyW"];

addEventListener("keydown", (e) => {
  keys[e.code] = true;
  if (e.code === "KeyR") reset();
  if (JUMP_KEYS.includes(e.code)) {
    e.preventDefault();
    if (!e.repeat) player.buffer = BUFFER;
  }
});
addEventListener("keyup", (e) => {
  keys[e.code] = false;
  if (JUMP_KEYS.includes(e.code) && player.vy < 0) {
    player.vy *= JUMP_CUT;   // variable jump height: releasing early cuts the rise
  }
});
```

Wait, there's an issue with the keyup cutoff: if the player releases the key while ascending after a jump, vy *= 0.45. But if the player is ascending... vy < 0 only happens right after a jump (or after the cutoff). OK. But a subtle bug: if the player releases the key while ascending, the cutoff applies; if they press again (buffer) — they're in the air, so no jump until landing. No problem.

Another subtlety: the keyup cutoff uses `player.vy < 0` — but what if the player is ascending while standing on a ledge... impossible (standing means vy=0).

Hmm, one more: the keyup handler runs between frames (in the event loop). It modifies vy directly. If the key is released during ascent, the next frame continues with the reduced vy. Good.

```js
function reset() {
  player.x = spawn.x;
  player.y = spawn.y;
  player.vx = 0;
  player.vy = 0;
  player.onGround = false;
  player.coyote = 0;
  player.buffer = 0;
  won = false;
}

function update() {
  // horizontal input
  player.vx = 0;
  if (keys.ArrowLeft || keys.KeyA) player.vx = -MOVE_SPEED;
  if (keys.ArrowRight || keys.KeyD) player.vx = MOVE_SPEED;

  // jumping: buffered press + on ground (or coyote grace)
  if (player.buffer > 0 && (player.onGround || player.coyote > 0)) {
    player.vy = JUMP_VELOCITY;
    player.onGround = false;
    player.coyote = 0;
    player.buffer = 0;
  }
  player.buffer = Math.max(0, player.buffer - STEP);
  player.coyote = Math.max(0, player.coyote - STEP);

  // move + resolve horizontally (solid blocks stop you)
  player.x += player.vx;
  for (const p of platforms) {
    if (!p.solid) continue;
    if (player.x + player.w > p.x && player.x < p.x + p.w &&
        player.y + player.h > p.y && player.y < p.y + p.h) {
      if (player.vx > 0) player.x = p.x - player.w;
      else if (player.vx < 0) player.x = p.x + p.w;
      else {
        // overlap with no input (shouldn't happen): nudge out the short way
        const toLeft = player.x + player.w - p.x;
        const toRight = p.x + p.w - player.x;
        player.x += toLeft < toRight ? -toLeft : toRight;
      }
    }
  }
  if (player.x < 0) player.x = 0;
  if (player.x + player.w > canvas.width) player.x = canvas.width - player.w;

  // gravity + move + resolve vertically
  player.vy = Math.min(player.vy + GRAVITY, MAX_FALL);
  const prevBottom = player.y + player.h;
  player.y += player.vy;
  player.onGround = false;
  for (const p of platforms) {
    if (!(player.x + player.w > p.x && player.x < p.x + p.w)) continue;
    const bottom = player.y + player.h;
    if (p.solid) {
      if (bottom > p.y && player.y < p.y + p.h) {
        if (prevBottom <= p.y && player.vy >= 0) {
          player.y = p.y - player.h;   // land on top
          player.vy = 0;
          player.onGround = true;
        } else if (prevBottom >= p.y + p.h && player.vy < 0) {
          player.y = p.y + p.h;        // bonk underside
          player.vy = 0;
        }
      }
    } else if (player.vy >= 0 && prevBottom <= p.y && bottom >= p.y) {
      // one-way ledge: land only when crossing the top surface downward
      player.y = p.y - player.h;
      player.vy = 0;
      player.onGround = true;
    }
  }

  // coyote time: refresh while grounded, decay while airborne
  if (player.onGround) player.coyote = COYOTE;
  // (decay already applied above)

  // safety: never leave the canvas
  if (player.y < 0) { player.y = 0; if (player.vy < 0) player.vy = 0; }
  if (player.y > canvas.height) reset();

  // win: touch the flag
  if (player.x < goal.x + goal.w && player.x + player.w > goal.x &&
      player.y < goal.y + goal.h && player.y + player.h > goal.y) {
    won = true;
  }
}
```

Wait, there's a bug in the coyote logic: I decay coyote at the top of the update (before resolution), then set coyote = COYOTE if onGround after resolution. Let me restructure:

- At the top (after the jump check): if onGround (from the previous frame) → coyote = COYOTE... hmm, actually the standard is: coyote = COYOTE while grounded; when leaving the ground, coyote starts counting down. My approach: at the end of the frame, if onGround → coyote = COYOTE, otherwise coyote -= STEP (floor at 0). Let me do it cleanly:

```js
// at the end:
if (player.onGround) player.coyote = COYOTE;
else player.coyote = Math.max(0, player.coyote - STEP);
```

And the jump check uses the coyote from the previous frame. When the player walks off the edge: the frame they leave, onGround=false → coyote decays from COYOTE over 6 frames. A

Alright, let's write a headless test harness that loads the actual game.js with the DOM stubbed out, and runs physics scenarios against it. I'll put it in /tmp to keep the deliverables directory clean.

Test plan:
1. **Landing / no sinking**: Place the player just above each one-way platform, let them fall, and verify they land exactly on the top surface and stay there for N frames (no sinking).
2. **No tunneling**: Drop the player with a high vy (e.g., vy=50) just above a thin ledge → must land on top.
3. **Wall solidity**: Walk right on the ground → must stop at x=276, must not pass through.
4. **Wall clearance window**: From the ground, holding right, jump at various x0 → find the x0 window that clears the wall and lands on the wall top or B. Verify the window width.
5. **One-way from below**: Jump from the ground under B → pass through B while ascending, land on B while descending.
6. **Coyote time**: Walk off an edge, jump 5 frames later → jump fires.
7. **Jump buffer**: Press jump 6 frames before landing → jump on touchdown.
8. **Variable height**: Compare rise distance of a tap (release after 2 frames) vs a full hold.
9. **Out-of-bounds check**: In every scenario, assert the player stays within the canvas and never overlaps a platform (except when standing exactly on top).
10. **Win**: Stand on D at the flag position → won === true.
11. **Full route**: Scripted playthrough: ground → (A optional) → wall clearance → B → C → D → flag. Verify won=true.

To load game.js in Node, I need to stub the following:
- `document.getElementById` → returns a canvas stub with getContext (returns a no-op ctx) and width/height.
- `addEventListener` → captures handlers.
- `performance.now` — exists in node.
- `requestAnimationFrame` → stub that doesn't loop (or manually drives frames).

game.js calls `frame()` at the end, which calls `requestAnimationFrame(frame)` — my stub can capture the callback so I can drive it manually. However, `update()` is only called inside `frame()` when acc >= STEP. I can drive the rAF stub with a fake clock: each "display frame" advances the fake time by, say, 1/60 sec (60Hz) or 1/144 (144Hz), and calls the callback with the new time. Then the accumulator runs update() deterministically.

Alternatively, I can access `update` directly — it's a top-level function declaration in the script. If I eval the script in a context where `update`, `reset`, `player`, `keys`, etc. are accessible... using `vm` module or indirect eval. Let me use Node's `vm` with a sandbox:

```js
const vm = require('vm');
const fs = require('fs');
const code = fs.readFileSync('game.js', 'utf8');

function makeEnv() {
  const handlers = { keydown: [], keyup: [] };
  let rafCb = null;
  let now = 0;
  const ctx2d = new Proxy({}, { get: (t, k) => (k === 'canvas' ? canvasStub : (...a) => {}) , set: () => true });
  // Simpler: a ctx with the properties used: fillStyle, fillRect, beginPath, moveTo, lineTo, closePath, fill, font, textAlign, fillText
  const ctx2d = { fillStyle:'', font:'', textAlign:'', fillRect(){}, beginPath(){}, moveTo(){}, lineTo(){}, closePath(){}, fill(){}, fillText(){} };
  const canvasStub = { width: 800, height: 480, getContext: () => ctx2d };
  const sandbox = {
    document: { getElementById: () => canvasStub },
    addEventListener: (type, fn) => { handlers[type] = fn; },
    performance: { now: () => now },
    requestAnimationFrame: (cb) => { rafCb = cb; },
    console,
  };
  vm.createContext(sandbox);
  vm.runInContext(code, sandbox);
  return { sandbox, handlers, getRaf: () => rafCb, setNow: (t) => { now = t; } };
}
```

Wait — `requestAnimationFrame` gets called every frame; my stub just saves the latest cb. To drive: `step(ms)`: now += ms; rafCb(now). But the first `frame()` call happens at script load time: `frame()` is called with no argument → `now` is undefined! `acc += (now - last)/1000` → NaN!

In the browser, frame() is first called as `frame()` with no argument → `now` is undefined → `acc += NaN` → NaN → `while (acc >= STEP)` is false → no update, draw, rAF. Then subsequent rAF calls pass a timestamp. So the first frame is a no-op — harmless in the browser (just draws once). In my harness, I'll drive it by calling rafCb(t) with a proper time. But `last = performance.now()` at load time: in my sandbox, performance.now returns my fake `now` (initially 0). Then I call rafCb(16.67): acc += (16.67-0)/1000 = 0.01667 ≥ 1/60 → 1 update. Good.

Actually, to make the harness more robust, I'll drive at 60Hz: every 1000/60 ms → exactly 1 update per display frame. And to test 144Hz independence, I'll drive at 1/144 sec and verify the same number of updates per second (60/sec).

For input simulation, I'll call handlers.keydown({code, repeat:false, preventDefault(){}}) and keyup similarly.

To inspect state, I'll read sandbox.player, sandbox.won.

Note: `won` is a top-level `let` in the vm context — accessible via sandbox? Top-level `let`/`const` in a vm script don't attach to the sandbox object (they live in the context's global lexical environment, not as properties of the global object). Hmm. `var` and function declarations do attach. `let won` → not a property of the sandbox. To read it, I can run additional code in the same context: `vm.runInContext('won', sandbox)` → returns the value. Same for `player` (const → also lexical). So I'll use `vm.runInContext(expr, sandbox)` for reads and for calling functions: `vm.runInContext('reset()', sandbox)`.

Let me write the harness with helpers:
- `get(expr)` → vm.runInContext(expr, sandbox)
- `press(code)`, `release(code)` → call handlers.
- `frames(n)` → drive n display frames at 60Hz.
- `step(ms)` → drive one display frame of ms milliseconds.

Assertions:
- `inCanvas()`: 0 ≤ x, x+w ≤ 800, 0 ≤ y, y+h ≤ 480.
- `notInsidePlatform()`: for each platform, the player's AABB must not strictly overlap the platform's interior... when standing on top: player bottom == platform top → overlap check `player.y + h > p.y && player.y < p.y + p.h` → bottom == p.y → false. Good, strict inequality means "touching" is not "inside".

Scenario details:

**S1: Landing on each platform, no sinking.**
For each one-way platform (A, B, C, D) and the ground: place the player centered above the platform, y = p.y - 100 (feet 64px above), vy=0, then run 120 frames with no input. Check: player lands (onGround), y == p.y - 36 exactly (feet on top), and after 60 more frames, still exactly there (no sinking).

Placements: A: x = 150+130/2-12 = 213. B: 360+65-12 = 413. C: 545+60-12 = 593. D: 680+60-12 = 728. Ground: x=400.

Wait, for D at x=728: the player [728,752] overlaps the flag [730,750] → the win triggers while falling onto D! That's fine for the landing test (won becomes true, and update stops). Hmm, that muddies the "stay in place" check (update stops when won). Let me use x=700 for the D landing test: [700,724] vs flag [730,750]: no overlap. Good.

**S2: Tunneling.** Place the player just above B (x=413, feet at B.top - 5 = 295, i.e., y = 295-36=259), vy = 40 (fast fall). One frame: feet move 40px → 335 > 316 (B's bottom). Must still land on top of B (y = 300-36 = 264, onGround).

**S3: Wall solidity.** Place the player on the ground at x=250, feet 440 (y=404). Hold right for 30 frames. Expected: x stops at 276 (right edge at 300), stays there, onGround, not inside the wall.

**S4: Wall clearance window.** From the ground, for x0 in 150..270 in steps of 2: place at x0 (feet 440), hold right, jump at frame 0 (press and hold), simulate 120 frames, record the outcome: did the player cross x>320 (past the wall) with feet above 230 at crossing? Simpler: record the final resting platform and whether the player ever hit the wall's side (x was pushed back: detect if x == 276 while on the ground at some point after the jump... hmm).

Better metric: track the player's max x and where they ultimately land. If they land on B (feet 300) or the wall top (feet 230) or C/D, clearance succeeded. If they end on the ground with x ≤ 276 (or bounced back), it failed.

Let me define success: after 120 frames, the player is at rest (onGround, vy==0) with feet < 440 (i.e., not on the ground), or feet==440 and x > 320 (landed on the ground past the wall — that's also clearance, but where? There's no ground past the wall... the ground is everywhere; if the player cleared the wall but missed B, they land on the ground at x>320, feet 440. Is that "clearance"? They crossed the wall without hitting it. For the window test, I'll count "cleared the wall" = the player's x ever exceeded 320 (left edge past the wall) without ever being pushed back by the wall while airborne... hmm, simpler: track a `hitWallSide` flag: in the harness, after each frame, check if the player is on the ground (feet 440) and x == 276 and was airborne before → side hit. Or directly: check if the player's right edge was in (300, 320] while feet ≥ 230...

Simplest and most robust: in the harness, after each frame, check: if player.x + 24 > 300 && player.x < 320 && player.y + 36 >= 230 && player.y + 36 <= 440 → the player's body overlaps the wall's x-range at or below the wall top → side collision state. Actually, with correct physics, the player can never strictly overlap the wall's AABB (resolution prevents it). The "side hit" event is: the player was pushed back (x set to 276) while airborne or on the ground. I can detect it by checking whether x was reset: compare x before and after the frame... I can't easily hook inside update.

Alternative: runInContext to instrument: after each frame, if (player.x === 276 && prevX > 276) then hit = true. The push-back sets x to exactly 276. Walking on the ground also ends at 276, but that's the same event (pushed back each frame). So: hitWall = any frame where x === 276 && prevX > 276.

Then the window = the set of x0 where hitWall is false and the player ends with x > 320 (past the wall) — i.e., landed on the wall top/B/C/D or the ground past the wall.

**S5: One-way from below.** Place the player on the ground under B: x=413, feet 440. Hold right? No — jump straight up (no horizontal): press jump, hold. The player ascends through B's y-range [300,316] (x [413,437] overlaps B [360,490] ✓) — must not collide while ascending (feet pass 316→300 while ascending). Then descend → must land on top of B. Check: at the moment of ascending through, the player's feet went below 300 (i.e., the player passed through), and finally landed with feet == 300.

To verify passage: track min feet (max height). If min feet < 300 (feet above B's top... wait, feet < 300 means feet above B's top surface, i.e., the player's bottom went above B's top → the player's body was inside B's x-range at a height above B's top). Hmm, "passing through" means the feet crossed the [300,316] band while ascending. If the max rise is 264, the feet reach 440-264 = 176 < 300 ✓. So min feet ≈ 176 < 300 → passed through. And the final rest: feet == 300 on B.

**S6: Coyote.** Place the player on A (feet 370, x=200). Hold right → walk off A's left edge? A's left edge is 150; walking left from x=200: the player's left edge reaches 150 at x=150... the player leaves A when x + 24 ≤ 150 → x ≤ 126. Then falls. At the moment of leaving (the frame onGround becomes false), release right, wait 5 frames, press jump (hold). Expected: the jump fires (vy becomes -23 within 1-2 frames), the player rises.

Check: after pressing jump 5 frames after leaving the edge, within 2 frames vy < 0 (jump executed) and the player's y decreases.

Coyote window is 0.1 sec = 6 frames; pressing at frame 5 should work; also test the boundary: pressing at frame 8 (past coyote) → no jump (player keeps falling). This verifies it's not just "always can jump".

**S7: Buffer.** Place the player above B, falling (x=413, y = 200, vy=0). Let them fall until 6 frames before landing... timing: compute the landing frame: from feet 236 to 300: 64px. With g=1: t frames: sum of vy... vy starts at 0: frame 1 vy=1, ... position after n frames = n(n+1)/2. n(n+1)/2 = 64 → n ≈ 10.9 → lands on frame 11. Press jump (and hold) 6 frames before landing → on touchdown, the jump fires: after landing, within 1 frame vy == -23 (or the player leaves the ground). Check: the player never rests on B (or rests for 0 frames) and vy < 0 right after the crossing.

Simpler: press jump at the moment feet are about 64px above... let me do this: place feet at 300 - 64 = 236 (y=200), vy=0, fall; when feet reach 300-6=294 (6px above, about 6 frames before landing at speed ~6-11px/f...) hmm, at that point the fall speed is about 10px/f, so 6px = less than 1 frame. Let me be more precise: press when feet are at 280 (20px above landing). Fall speed there: v = sqrt(2·1·44)... from 236: v² = 2·1·(280-236) = 88 → v = 9.4. Time to 300: about 2.1 frames. Buffer 0.12 sec = 7.2 frames > 2.1 ✓. So press at feet=280 → jump on touchdown.

Detection: track the minimum y after the press; if the player jumped on landing, the feet never rest at 300 (the jump fires on the landing frame: buffer>0 && onGround → vy=-23, onGround=false — the player is snapped to 300 and immediately launches). So check: at no frame is (onGround && feet==300 && vy==0) true, and eventually vy < 0 and feet < 300.

**S8: Variable height.** From the ground (x=100, feet 440):
- Full hold: press jump, hold until apex, record max rise = 440 - min feet. Expected ≈ 264.
- Tap: press jump, release 2 frames later (after the 2nd update), record max rise. Expected ≈ 88.
- Very short tap: release 1 frame later: ≈ 71.
Check: tap2 < full, tap1 < tap2, and tap2 ≥ 70 (can reach ledge A's height) — actually, verify that a 2-frame tap from the ground reaches ledge A: rise ≥ 70 → yes, about 88.

**S9: Full route (scripted playthrough).**
Route: spawn (40,380) → fall to ground → run right → jump to A (optional; include it: jump around x=60) → land on A → run left off A → fall to ground → run right → jump at x0=210 (within window [186,226]) → clear wall → land on B (or wall top) → run right on B → jump around x=430 → land on C → run right → jump around x=620 → land on D → run right to the flag → win.

Implement a small bot:
- Phase 1: hold right until onGround (ground).
- Phase 2 (optional A): hold right until x ≥ 60, press jump (hold 10 frames, release), until onGround on A (feet 370). Then hold left until off A (x < 126), until onGround on the ground.
- Phase 3: hold right until x ≥ 208, press jump (hold until landing), until feet < 400 (landed on wall top/B).
- Phase 4: hold right until x ≥ 430, press jump (hold), until onGround with feet == 235 (C).
- Phase 5: hold right until x ≥ 620, press jump (hold), until onGround with feet == 165 (D).
- Phase 6: hold right until won.
Timeout: 600 frames; assert won.

Hmm, phase 3: after clearing the wall, if landing on the wall top (feet 230), then phase 4: run right off the wall top → fall to B (feet 300) → then jump to C. Let me make the bot adaptive: after the wall jump, wait until onGround (any platform). Then: if feet == 230 (wall top) or 300 (B): hold right until x ≥ 430... if on the wall top (x about 319), run right: walk off the wall top, fall to B, land at x about 340-350, continue right to 430, jump to C. Works for both.

Phase 4: from B (feet 300) at x=430: jump to C (top 235): the descending crossing lands at x = 430+172 = 602 → on C (x ∈ (521,665)) ✓.
Phase 5: from C (feet 235) at x=620: jump: lands at x = 620+171 = 791 → clamped to 776 → on D ✓. Wait, but during that jump, does the player pass through the flag's x-range with feet in (125,201)? The flag is [730,750]×[125,165]. The player's x is in (706,750) when... the player's x goes 620→776; x ∈ (706,750) is a 44px span = 11 frames. Feet during that span: the player's feet at x=706: t = (706-620)/4 = 21.5 frames after jump; feet = 235 - (23·21.5 - 0.5·21.5²) = 235 - (494.5 - 231.1) = 235 - 263.4 = -28.4?? Wait, that's above the canvas → clamped at y=0 (feet 36). Hmm! A full jump from C (feet 235): max rise 264.5 → feet reach -29.5 → the top clamp kicks in (y=0, feet=36, vy=0). The player hovers at the top for a bit (vy=0, then gravity: next frame vy=1, feet 37...).

So the C→D full jump hits the ceiling. The player hovers at feet=36 for a few frames (vy=0 → falls at 1,2,3... px/f), then descends. During the hover, x keeps increasing (holding right). Let me trace: jump at x=620, t=0. Feet(t) = 235 - 23t + 0.5t² (until clamped). Feet = 36 when 23t - 0.5t² = 199 → 0.5t² - 23t + 199 = 0 → t = [23 ± sqrt(529-398)]/1 = 23 ± 11.45 → t = 11.55 (ascending). At t=11.55, x = 620 + 46.2 = 666.2. Then hover at feet=36, vy=0: while vy<0... after the clamp vy=0; next frame vy=1 → feet 37, x=670.2; vy=2 → feet 39... the player falls from the top: feet = 36 + (t-11.55)(t-11.55+1)/2 (discrete). Feet reach 125 (flag top) when (t-11.55)(t-10.55)/2 = 89 → (t-11.55)² ≈ 178 → t-11.55 ≈ 13.3 → t ≈ 24.9. At t=24.9, x = 620 + 99.6 = 719.6. The flag's x-range (706,750): the player's x ∈ (706,750) is from t = (706-620)/4 = 21.5 to (750-620)/4 = 32.5. At t=21.5, feet: 36 + (10)(11)/2 = 36+55 = 91 < 125 → the player's bottom (91) is above the flag top (125) → no overlap. At t=24.9, feet=125, x=719.6 → the player's x [719.6, 743.6] overlaps the flag [730,750] ✓ (743.6 > 730) and feet=125 = flag top → y-overlap: player [89,125] vs flag [125,165]: 125 > 125? No (strict) → no overlap yet. At t=25: feet ≈ 126.5, x = 720 → player [720,744] ∩ [730,750] ✓, player y [90.5,126.5] ∩ [125,165] ✓ → win at t≈25!

So the C→D full jump wins mid-air (the player passes through the flag). That's fine — the win triggers. Actually, that means the phase 5 "land on D" never happens; the win triggers mid-flight.

But wait — the ceiling hover: is that OK? The player hits the top of the canvas (y=0), hovers for about 13 frames (0.2 sec), then falls. A bit floaty but acceptable. Or I could have the bot jump from C with a shorter hold (release early) to avoid the ceiling: a tap of about 10 frames... a full jump from C rises 264.5; to stay in the canvas, rise ≤ 235-36 = 199 → need a cut. Release when vy reaches... the remaining rise after the cut is (0.45·r)²/2, where r is the velocity at release... total rise = (v² - r²)/2 + (0.45r)²/2 ≤ 199, v=23: (529 - r²)/2 + 0.10125r² ≤ 199 → 264.5 - 0.5r² + 0.10125r² ≤ 199 → 0.39875r² ≥ 65.5 → r² ≥ 164.3 → r ≥ 12.8 → release when vy ≥ -12.8 → vy = -23 + t ≥ -12.8 → t ≥ 10.2 → release after about 11 frames. Then the rise ≈ 199 → feet reach 36 (just at the top). Hmm, tight. Or release at 12 frames: r=11: rise = (529-121)/2 + 0.10125·121 = 204 + 12.3 = 216.3 → feet reach 235-216 = 18.7 > 0 ✓ no clamp.

For the bot, I'll make the C→D jump a 12-frame hold. Actually, simpler: the bot can just do a full jump and let the win trigger mid-air — that's a valid playthrough. But I also want to verify the "land on D and walk to the flag" path (the win via standing on the flag). Let me do two playthroughs:
- P1: full route with full jumps (the win may trigger mid-air on the C→D jump).
- P2: route where the C→D jump is a 12-frame hold → lands on D (x about 776? let me compute: with the cut, the horizontal is the same 4px/f until landing: the landing time is slightly longer... the player lands on D somewhere at x ∈ (656,800)), then walks right/left to the flag → win by standing.

Actually, in P2, after landing on D, walk toward the flag (x 730..750): the player needs x ∈ (706,750). If they land at 776, walk left to 740 → overlap → win.

Let me also double-check the phase 3 wall jump at x0=208: t_a = (276-208)/4 = 17. Rise at t=17: 23·17 - 0.5·289 = 391 - 144.5 = 246.5 ≥ 210 ✓ (feet at 193.5 < 230 ✓). The feet are above 230 during t ∈ (14, 30) → x-overlap with the wall during t ∈ (17, 28) ⊂ (14,30) ✓ no side hit. Landing: descending crossing of feet=230 at t=30: x = 208+120 = 328 → past the wall (320) → not the wall top. Descending crossing of feet=300 at t=38.78: x = 208 + 155.1 = 363.1 → on B (x ∈ (336,490)) ✓.

And the S4 window test will confirm the range.

Now, one thing to double-check in the code: the jump condition `if (player.buffer > 0 && (player.onGround || player.coyote > 0))`. At spawn: the player falls from y=380 (feet 416) to the ground (440): 24px, about 7 frames. onGround is initially false, coyote 0 → no jump until landing. Good.

Another check — the `else` branch: `player.buffer = Math.max(0, player.buffer - STEP)` only runs when the jump doesn't fire. If the jump fires, buffer=0. No problem.

A potential subtle issue: the keyup variable-jump cut `player.vy *= JUMP_CUT` — what if the player releases the key while ascending from a jump, but the key was also used for buffering... no problem.

Another subtle issue: if the player is standing on the ground and holds jump (no new press): buffer is 0 → no re-jump. Walk off a ledge while holding jump: coyote expires (6 frames); if the player is still holding (no new press, buffer=0) → no auto-jump. Correct (no bunny-hop chaining). If the player taps again in the air → buffer → jump on landing. Good.

Edge case: the player is standing on the ground, presses jump (buffer=0.12), the jump fires on the next update. The keyup arrives 3 frames later during ascent → cut. Good.

Now — one more important check: the horizontal resolution loop runs before the vertical move. Consider the player on the ground at x=276 (touching the wall), jumping and ascending: x += 4 → x=280 → [280,304] vs wall [300,320]: x-overlap ✓; y: the player's feet after the jump frame... wait, the order: the jump sets vy=-23 (before the x move). x move: x=280, y is still 404 (feet 440): y-overlap with the wall [230,440]: [404,440] ∩ [230,440] ✓ → push back to x=276. Then vertical: y += -23+1 = -22 → y=382 (feet 418). Next frame: x += 4 → 280 → y [382,418] ∩ [230,440] ✓ → push to 276... the player stays at x=276 while ascending, until the feet clear 230: feet < 230 when y < 194: y = 404 - 22 - 23 - 24... (vy: -22,-23? no: vy starts at -23, each frame vy += 1 before the move: frame 1: vy=-22, y=382; frame 2: vy=-21, y=361; frame 3: vy=-20, y=341; ... feet = 440 - (22+21+20+...). Cumulative: f1:22, f2:43, f3:63, f4:82, f5:100, f6:117, f7:133, f8:148, f9:162, f10:175, f11:187, f12:198 → feet = 440-198 = 242 (y=206); f13: 198+11=209 → feet 231 (y=195); f14: 209+10=219 → feet 221 (y=185). At f13: y=195, feet=231: y-overlap with the wall? [195,231] ∩ [230,440] = [230,231] → overlaps (231 > 230 ✓, 195 < 440 ✓) → x-overlap? At f13, x: was pushed to 276 each frame... x=276 → [276,300] vs [300,320]: 300 > 300 is false → no x-overlap!

Wait — x=276 means the right edge is exactly at 300 = the wall's left face → no x-overlap (strict). So at f13, the x move: x += 4 → 280 → [280,304] ∩ [300,320] ✓ x-overlap; y [195,231] ∩ [230,440]

Wait, there's a problem with S11: `g.get("keys.ArrowRight")` — keys is a top-level const object, so it's accessible via runInContext. But `if (!g.get("keys.ArrowRight")) g.press("ArrowRight")` — pressing every frame will generate a keydown with repeat:false every time → buffer will keep getting reset! That's wrong — in a real game, holding a key only generates one keydown (subsequent ones have e.repeat=true). My harness's press() always uses repeat:false. For S11, I should press only once. Let me fix it: press ArrowRight once at the start, and press/release Space at the appropriate timing.

Also, in S11, after 30 seconds it stops holding right (the key remains held — I never release it; the player keeps moving right forever, hits the right wall at x=776, and stays there). maxX will be 776 for both. Hmm, that's trivially the same. Better approach: stop holding right at 30 seconds (release), and compare positions at 60 seconds. Actually, what matters is: the same input timeline (in game time) produces the same physics. The input is: hold right from t=0 to t=30 seconds, jump every 1.5 seconds. After 30 seconds, the player is probably at the right edge or on some ledge... it's complicated. Simpler and more robust comparison: run the identical input script for 60 game-seconds at both refresh rates, and compare the final (x, y, vy). If the fixed timestep is correct, they should be identical (or nearly so — the difference is only in the alignment of input events to steps: keydown events occur at display frame boundaries, which map to slightly different game times at 60Hz vs 144Hz... e.g., a jump at display frame 90: at 60Hz that's exactly t=1.5 seconds; at 144Hz that's t=90/144=0.625 seconds. The input timing differs in game time! So the trajectories will diverge — that's expected and fine (human input timing is arbitrary). The point of bug 5 is that the simulation speed is the same, not that different input timings produce identical results.

So a better test: give the same input at the same game time. Drive the display frames, but schedule inputs based on game time (now), not frame index. E.g., hold right for game time [0, 30 seconds], jump at game times 1.5, 3, 4.5... seconds. At 60Hz, game time advances in exactly 1/60 increments; at 144Hz, in 1/144 increments. Input at game time T: press at the first display frame where now ≥ T. The quantization differs (1/60 vs 1/144), so the jump start could be off by up to 1/144 second ≈ 2.4 game frames... no wait: 1/144 second of display time = 1/144 second of game time (the accumulator converts). The jump press at game time T fires at the first display frame where now ≥ T: at 60Hz that's T + up to 1/60 second; at 144Hz T + up to 1/144. So the jump could start up to 1/60 second (4 game frames) earlier at 144Hz than at 60Hz. That would cause the trajectories to diverge.

Hmm. To make the test deterministic, I should schedule inputs exactly at game step boundaries. Alternative: test frame-rate independence more directly — run the game with no input (or constant input) and compare positions after N game seconds. With constant input (holding right from the start), the only event is the initial keydown at t=0 (same for both). Then the physics is deterministic: after exactly 60 seconds of game time, the state should be identical (the accumulator runs exactly 3600 steps at both Hz — as long as the total time is an exact multiple of the step... at 60Hz: 3600 frames × 1/60 = exactly 60 seconds, 3600 steps. At 144Hz: 8640 frames × 1/144 = exactly 60 seconds → 3600 steps. If the floating-point accumulation is exact, both are exactly 3600 steps... floating point: is 1000/60 ms × 3600 = exactly 60000.0? 1000/60 = 16.666... (repeating in binary). now accumulates: now += 16.666666666666668 each frame. After 3600 frames, now ≈ 60000.000000000something. acc accumulates the same way. The number of steps executed = floor-ish of the accumulated time / STEP. There could be a ±1 step difference due to floating-point rounding. So compare with a tolerance of a few px, or compare the step count.

Actually, the cleanest and most deterministic test: count the number of update() calls. I can instrument it: wrap it... hmm, update is internal. Alternative: measure the player's position after a fixed number of display frames that corresponds to the same game time, and allow a small tolerance (≤ 1 step of motion = 4px).

Let me restructure S11:
- Both: press ArrowRight once at t=0 (before the first frame).
- Run display frames until game time now ≥ 10 seconds (at 60Hz: 600 frames; at 144Hz: 1440 frames).
- Compare x: tolerance 4px (1 step).

The player runs right from x=40: hits the wall at 276 in about 6 frames, and stays there (pushed back every frame). So x = 276 for both — trivially equal. That's boring but valid. Better: compare a dynamic quantity. Alternative: compare the total number of update steps executed. I can expose it by reading something that changes every step... hmm.

Actually — I can count steps by observing the player during a jump: the jump trajectory is deterministic. Let's do this: at t=0 press right, at game time 0.5 seconds (scheduled by display-frame time) release right, at 1.0 seconds press Space (jump), and compare the player's (x,y) at game time 2.0 seconds. The input at 0.5/1.0 seconds: at 60Hz the press lands at t=0.5 (frame 30: now=500.000...ms — 30×16.6667 = 500.00000000000006? close enough), at 144Hz frame 72: 72×6.9444 = 500.0. The keydown sets keys at the display-frame boundary; the accumulator consumes steps after that. The difference in game time of the key event: at 60Hz, frame 30 is at now=500.00000000000006ms; the steps consumed up to that point: floor(500.00000000000006/16.6667) = 30 steps (t=0.5 seconds). At 144Hz, frame 72 is at now=500.0ms → 30 steps (t=0.5 seconds). Same! Because both are exact multiples. 1000/60×30 = exactly 500? 1000/60 = 16.666666666666668 (double); ×30 = 500.00000000000006. And STEP=1/60=0.016666666666666666; 30 steps = 0.5 seconds. acc after 30 frames = 0.50000000000000006 seconds ≥ 30×STEP → 30 steps consumed. At 144Hz: 1000/144 = 6.944444444444445; ×72 = 500.00000000000006? 6.944444444444445×72 = 500.0000000000001? Something like that. 30 steps consumed. Same.

So if I schedule inputs at times that are multiples of 1/12 seconds (the gcd of 1/60 and 1/144), both will consume the same step count. 0.5 seconds and 1.0 seconds are multiples of 1/12 ✓.

So: t=0: press right. t=0.5 seconds: release right, press Space. t=1.0 seconds: release Space. Compare (x, y) at t=2.0 seconds: the player jumps at x=40 (stationary), a full jump... wait, I released right at 0.5 seconds, so the player is stationary at x=40 (fell to the ground in the first 7 frames). The jump is at 1.0 seconds: rises 264.5, lands about 0.73 seconds later at 1.73 seconds. At 2.0 seconds: back on the ground, x=40, y=404. Trivially equal again (stationary). Ugh — a stationary player doesn't exercise the integration much, but it does exercise the jump/landing.

Let's make it more dynamic: hold right the whole time (the player runs into the wall at 276 and stays there — x is constant after 6 frames). Jump at 1.0 seconds while pressed against the wall: the player jumps straight up at x=276 (no horizontal overlap with the wall, as I calculated), rises, and falls back to the ground at x=276. At 2.0 seconds: on the ground at x=276. Compare (x,y,vy): should be identical.

Even better: compare the full trajectory: record (x,y) every 1/12 second (a multiple of the step: 2 game frames) for both simulations, and compare with a tolerance of 0.5px. Let's do that: sample at game times 0, 1/12, 2/12, ... up to 3 seconds. At 60Hz, 1/12 second = exactly 5 display frames; at 144Hz = 12 display frames. Both are exact multiples → the sample lands on an exact step boundary (10 steps).

I'll rewrite S11 following this. I'll also fix the S11 input bug (the repeated press resetting the buffer).

One more check on S7 (buffer): place at feet 236 (y=200), 64px above B. Fall: feet after n frames = 236 + n(n+1)/2. Reaches 280 when n(n+1)/2 = 44 → n ≈ 9.05 → at frame 9, feet = 236+45 = 281 ≥ 280 → press at frame 9. Fall speed at that point ≈ 10px/f. Landing at 300: 19px more → about 2 frames (speed 10, 11). Buffer 0.12 seconds = 7.2 frames ≥ 2 ✓. On the landing frame: the one-way snap sets onGround=true, then... wait — the order within update(): the jump check happens at the top of update (before the vertical move). Let me trace the landing frame: at the top of the frame, the player is in the air (onGround=false, coyote=0 — walked off... no, the player is falling under B, never touched the ground, coyote=0), buffer > 0 (0.12 - 2×0.0167 = 0.087 > 0) → but the jump condition requires onGround || coyote > 0 → false → no jump. buffer decays to 0.07. Vertical: feet cross 300 → snap, onGround=true. Next frame: buffer 0.07 > 0 && onGround → jump! vy=-23. So the jump fires 1 frame after landing. The player never "rests" (rest = onGround && vy==0 && feet==300 observed at the end of a frame: on the landing frame, at the end, onGround=true, vy=0, feet=300 → my `rested` flag gets set! Damn.

The `rested` check in S7: `if (p.onGround && p.vy === 0 && feet(p) === 300) rested = true;` — on the landing frame, before the buffered jump fires (which fires on the next frame), the state at the end of the landing frame is exactly onGround/vy=0/feet=300. So rested=true even though the buffered jump fires 1 frame later. My test would incorrectly fail.

Fix: check for rested with a 2-frame persistence: rested = onGround && vy===0 && feet===300 in two consecutive frames. Or: check that the player eventually leaves B (vy < 0 and feet < 300) within 2 frames of landing. Let me change it: record the frame of landing; then assert that within 2 frames after landing, vy < 0 (the jump fired). Let me restructure S7:

```
let landedFrame = -1, jumpedAfterLanding = false;
for i in 0..120:
  frames(1)
  p = P(g)
  if (landedFrame < 0 && p.onGround && feet(p) === 300) landedFrame = i
  if (landedFrame >= 0 && i > landedFrame && p.vy < 0) { jumpedAfterLanding = true; break }
check(jumpedAfterLanding)
```

Also, the buffer press timing: I'm pressing when feet ≥ 280 — but I need to make sure the press happens while in the air (it does — the player is falling, never on the ground).

Hmm wait, one more subtle point: I placed the player at feet 236 with vy=0, but the player's x=413 is under B; the player falls; also, the player's initial placement: place() sets onGround=false, coyote=0, buffer=0. Then frames(3) — falling. Then the loop until feet ≥ 280. OK.

Another potential issue with S7: the press("Space") in the harness is a keydown with repeat:false → buffer = 0.12. Good.

Now S6 (coyote): place at x=160 on A (feet 370). A spans 150..280. The player [160,184] is on A ✓. Hold left: x decreases by 4/frame: 156, 152, 148, 144, 140, 136, 132, 128, 124... the player leaves A when x+24 ≤ 150 → x ≤ 126. From 160: 156(f1), 152(f2), 148(f3), 144(f4), 140(f5), 136(f6), 132(f7), 128(f8), 124(f9) → at f9, x=124: [124,148] vs A [150,280]: 148 > 150? No → off the ledge. But wait — the ground is at 440; while walking left, the player is on A until the x-overlap is lost. At f8, x=128: [128,152] ∩ [150,280] = [150,152] ✓ still on A (2px). At f9, x=124: no overlap → falls. So leftEdge is detected at f9 (the first frame where !onGround). Then release left, frames(5) → 5 frames airborne (coyote from 0.1 seconds decaying: at the end of the leaving frame, onGround=false → coyote decays from 0.1 to 0.0833; f+1: 0.0667; f+2: 0.05; f+3: 0.0333; f+4: 0.0167; f+5: 0). Hmm! At the 5th frame after leaving, coyote = 0.0167 - ... let me trace precisely:

End of the leaving frame (L): onGround=false → coyote = max(0, 0.1 - 1/60) = 0.0833.
End of L+1: 0.0667. L+2: 0.05. L+3: 0.0333. L+4: 0.0167. L+5: max(0, 0.0167-0.0167) = 0.

My test: after detecting the leaving frame (after frames(1) returns, i.e., at the end of frame L), release left, then frames(5) → now at the end of L+5, coyote = 0. Then press Space → buffer=0.12. Next update: buffer>0 but onGround=false, coyote=0 → no jump. The test would fail!

The issue: my "5 frames after leaving" actually lands on coyote=0. The coyote window is 0.1 seconds = 6 steps: the jump can fire on frames L+1..L+5 (at the top of those frames, coyote > 0: at the top of L+1, coyote=0.0833 ✓ ... at the top of L+5, coyote = 0.0167 ✓; at the top of L+6, coyote = 0 ✗). So the press must be processed before the update of L+6. If I press after the end of L+5 (i.e., after frames(5)), the keydown is handled immediately (event handler), setting buffer=0.12; the next update is L+6, where coyote=0 → no jump.

So to test a successful coyote, I should press after frames(4) (at the top of L+5, coyote=0.0167>0 → the jump fires on L+5). Or press after frames(5) and expect failure (that's the boundary). Let me adjust: success case: press after 4 frames airborne (fires on the 5th frame). Failure case: press after 7 frames airborne (clearly past). Let me also make the success check robust: the jump fires → within 2 frames vy < 0.

Actually, let me reconsider the exact semantics: coyote = 0.1 seconds = 6 steps. The player can jump on the first 6 frames after leaving. My success test presses at frame 5 (0-indexed: after 4 frames) → within the window ✓. Let me use 4 for success and 8 for failure.

Wait, I also need to double-check the timing of the keydown event: in the browser, keydown fires between frames (in the event loop). In the harness, I call press() between frames(1) calls — same thing. The buffer is set immediately; the jump check on the next update sees buffer>0. ✓

Another subtle point in S6: when the player walks off A to the left, they fall from feet 370 to the ground 440 (70px, about 11 frames). The success jump at L+5: vy=-23 at that point; the player had fallen for 5 frames: fall distance = 5×6/2 = 15px → feet 385. The jump rises from 385: max rise 264.5 → feet 120.5. No problem, no collision (x ≈ 124-128, nothing there). ✓

Now, S4 (the wall window): I'm checking `p.x === 276 && prevX > 276` as a side-hit. But consider: the player jumps from x0=274 (just left of the wall): the right edge is 298. Frame 1: x += 4 → 278 → [278,302] x-overlaps the wall; y: feet 440 → [404,440] ∩ [230,440] ✓ → pushed to 276. So hitWall is detected (prevX=278 > 276, x=276) ✓. Good.

But also: a player who clears the wall and lands on the ground past the wall — can that happen? If the player clears the wall but misses B (lands on the ground at x>320): in my trace, all clearances land on B or the wall top. But if the player jumps with a cut (a short tap) — no, S4 holds Space the whole time (full jump). A full jump from the ground: the trajectory is fixed; landing on B (x0 ∈ (186,226]) or the wall top (x0≈186) — all good. What about x0 = 228, 230 (just outside the window)? t_a = (276-228)/4 = 12 < 14 → at t=12, the right edge is at 300, the rise = 23×12-72 = 204 < 210 → feet 236 > 230 → side hit → pushed to 276 → falls to the ground at 276. hitWall ✓ excluded. Good.

Also in S4, the at-rest break condition: `p.onGround && p.vy === 0 && i > 20` — after landing on B, the player is at rest (holding right: walks right on B... wait, I'm holding ArrowRight the whole time! After landing on B, the player keeps running right: walks off B's right edge (490) at x=466, falls to the ground, runs to the wall... no wait, past the wall (x>320): runs right along the ground to the right edge of the canvas (x=776), and rests there. So the at-rest break happens at the right edge, not on B. That's fine for the window test (cleared = crossed 320 without a side hit). But the player might land on C or D while running right! From the ground at x>320, running right: the player just runs along the ground (no auto-jump) → passes under B (one-way, passes through) → runs to the right edge. Wait — passing under B: the player's head reaches 440-36=404 > 316 (B's bottom) → no vertical overlap with B at all. ✓ Runs to x=776 and rests. OK.

Hmm, but actually, there's a subtle issue with the S4 loop: `if (p.onGround && p.vy === 0 && i > 20) break;` — the player is on the ground at x0 at rest before the jump... no, they're holding right, so they're moving. At i=0..2 they're moving right. No problem.

Also the `maxCross` check: `p.x > 320` — the player's left edge past the wall's right face. ✓

Now, S10 (playthrough): let me re-verify the bot's logic:
- `until(() => P(g).onGround, 60)` — spawn: falls to the ground in about 7 frames ✓.
- Press right, until x ≥ 60 (about 14 frames), press Space (hold). The jump from the ground at x≈60: rise 264.5, lands on A? The landing x = 60+172 = 232 → on A (x ∈ (126,280)) ✓ feet 370.
- until onGround && feet==370 ✓ (lands on A). onA=true. Release Space.
- Press left, until !onGround: walks left on A from x≈232: leaves A at x ≤ 126 (about 27 frames) ✓. until onGround && feet==440: falls 70px, about 11 frames, lands on the ground at x≈124 ✓. Release left.
- Press right, until x ≥ 208: from 124: 21 frames. Press Space (hold). Jump from x≈208: within the window [186,226] ✓. Clears the wall, lands on B (x≈363) or the wall top (x≈319.8, only if x0≈186 — no, x0=208 → lands on B).
- until onGround && feet < 440: lands on B (feet 300) ✓. afterWall=300. Release Space.
- afterWall !== 230, so skip the wall-top branch.
- until x ≥ 430: from 363: 16 frames, walking right on B (B spans 360..490; x=430 → [430,454] is on B ✓). Press Space. Jump from B at x=430: lands on C at x = 430+172 = 602 ✓ (C: x ∈ (521,665)).
- until onGround && feet==235 ✓ onC. Release Space.
- Press right, until x ≥ 620: from 602: 4.5 frames → x=620. Press Space, hold 12 frames, release. From C at x=620 with a 12-frame hold: the cut is at frame 12 (vy at the top of frame 12: -23+12 = -11 → ×0.45 = -4.95). Rise: frames 1-12: sum(23-k) k=1..12 = 12×23 - 78 = 270-78 = 192... wait: the vy values during the rise: f1: -22, f2: -21, ..., f12: -11. Sum = (22+11)×12/2 = 198. Then after the cut: vy = -4.95: f13: vy=-3.95, f14: -2.95, f15: -1.95, f16: -0.95, f17: 0.05 → stops. Additional rise ≈ 3.95+2.95+1.95+0.95 ≈ 9.8. Total ≈ 207.8. Feet: 235-208 = 27 > 0 ✓ no ceiling. Landing: total fall 208 from the apex... lands on D: x at landing: total airtime ≈ 17+about 16 (falling 208px: t(t+1)/2=208 → t≈20) ≈ 37 frames → x = 620+148 = 768 → on D (x ∈ (656,800)) ✓ feet 165.

Hmm wait, but during this jump, does the player pass through the flag's x-range with feet in (125,201)? The player's x ∈ (706,750) is from t=21.5 to t=32.5. Feet at t=21.5: 235 - (rise at 21.5). Rise at 21.5: the player stopped rising at t≈17 (apex, feet 27). Falling: feet = 27 + (t-17)(t-16)/2 (discrete, approximately). At t=21.5: 27 + 4.5×5.5/2 ≈ 27+12.4 = 39.4 < 125 → above the flag top → no overlap. At t=32.5: 27 + 15.5×16.5/2 = 27+128 = 155 → feet 155 ∈ (125,201) ✓ and x=750 → the player [750,774] ∩ [730,750]: 774 > 730 ✓, 750 < 750? No — x=750: player.x < goal.x+goal.w → 750 < 750 is false → no overlap. Close! At t=32: x=748, feet = 27+15×16/2 = 147 → player [748,772] ∩ [730,750] ✓ (772>730, 748<750), y [111,147] ∩ [125,165] ✓ → win at t≈32!

So the C→D jump wins mid-air (the player passes through the flag). So the bot's `until(onGround && feet==165)` never runs — the win triggers first. onD = feet at win time = 147 ≠ 165 → the "landed on D" check fails!

Hmm. I need to make the bot land on D and then walk to the flag. To avoid passing through the flag mid-air, the player must keep their feet below 125 (i.e., feet ≥ 125... no wait: to avoid the flag's y-range [125,165], the player's feet must be ≥ 165 (below the flag bottom = on D) or ≤ 125-36+... the player's y-range [feet-36, feet] must not intersect [125,165]: feet-36 ≥ 165 → feet ≥ 201 (below the flag), or feet ≤ 125 (above the flag top... feet ≤ 125 → the player's bottom is at or above the flag's top → no overlap ✓).

So to pass through the flag's x-range without winning, the player's feet must be ≤ 125 throughout x ∈ (706,750) (11 frames), or ≥ 201. From C (feet 235): the feet go 235 → apex → 165 (landing on D). The feet pass through (125,201) during the descent. To have feet ≤ 125 throughout x ∈ (706,750): the feet must reach ≤ 125 before x=706 and stay ≤ 125 until x=750. Feet = 125 is a rise of 110 from C: the time to reach it on the ascent: 23t - 0.5t² = 110 → 0.5t² - 23t + 110 = 0 → t = [23 ± sqrt(529-220)] = 23 ± 17.58 → t = 5.4 (ascent). x at t=5.4 = 620+21.6 = 641.6. Then the feet stay ≤ 125 until the descent crossing: t = 40.6 → x = 620+162.4 = 782.4 > 750 ✓. So a full jump from C at x=620 keeps the feet above the flag (≤125) throughout the flag's x-range (x 706..750 corresponds to t 21.5..32.5; feet at t=21.5: apex at t=23 (23/1=23 frames to the apex... vy=-23+23=0 at t=23; the apex feet = 235-264.5 = -29.5 → clamped at 36). Hmm, with the ceiling clamp: the feet reach 36 at t≈11.55, hover until t≈24.9 (feet 125). So the feet are ≤ 125 from t=5.4 to t=24.9. The flag's x-range is t 21.5..32.5. At t=24.9..32.5, the feet are in (125, 165+]... at t=25: feet 126.5, x=720 → overlap → win at t≈25 (as I calculated before).

So a full jump from C at x=620 wins mid-air (at t≈25, x≈720). To land on D and walk to the flag, the player must not be at feet ∈ (125,201) while x ∈ (706,750). Options:
- A shorter jump (a cut) so the apex feet > 125... no wait: if the apex feet > 125 (a lower jump), the feet pass through (125,201) on both the ascent and the descent. On the descent, the feet reach 165 (D's top) at x = 620 + 171 = 791 → clamped to 776. The feet cross the (125,201) band on the descent at x ∈ (706,750) → win mid-air again (unless the player's x is outside (706,750) when the feet are in (125,201)).

Hmm, so actually, any C→D jump that crosses x ∈ (706,750) with feet ∈ (125,201) wins. To land on D to the right of the flag (x > 75

Wait, there's still an issue with S11's sampling: `now` is read via `g.get("performance.now()")` — my sandbox's performance.now returns the fake `now`. Good. But the sample condition: I want to sample at exact multiples of 1000/12 ms of game time. At 60Hz, display frames land exactly on multiples of 1000/60 = 16.667ms; 1000/12 = 83.333ms = 5 frames — so every 5th frame lands exactly on a sample time (in floating point, 5×16.666666666666668 = 83.33333333333334; 6×83.33333333333334 = 499.99999999999994... hmm, floating point). The condition `Math.abs(now % (1000/12)) < 1e-6` — now accumulates as now += ms, so after 5 frames now = 5×16.666666666666668 = 83.33333333333334; 83.33333333333334 % 83.33333333333334 = 0 ✓. After 10 frames: 166.66666666666669 % 83.33333333333334 = 83.33333333333335? Let's see: 166.66666666666669 / 83.33333333333334 = 2.0000000000000004 → remainder = 166.66666666666669 - 2×83.33333333333334 = 166.66666666666669 - 166.66666666666668 = 8.47e-14 < 1e-6 ✓. OK, this works. At 144Hz: 1000/12 = 12 frames × 6.944444444444445 = 83.33333333333334 ✓ same.

But my condition also has `|| Math.abs((now + ms) % (1000/12)) < 1e-6` — this is to catch the case where a frame "straddles" a sample time... actually that's wrong: if (now+ms) is a sample time, then after that frame now = sample time, and the first condition catches it. The second condition would cause a double sample when a frame straddles (sample at now+ms, then at now). Hmm, actually, if frames land exactly on the grid (both Hz are exact divisors of 1000/12... 60/12=5 ✓, 144/12=12 ✓), then every sample time is a frame boundary and the first condition suffices. The second condition is redundant but could cause double sampling in edge cases. Let me simplify: just use the first condition. Also, the sample key `Math.round(now*12)/12` — for matching a[i] and b[i], both need to produce the same key sequence. Since both sample at exact multiples of 1/12 second (k/12 seconds), the keys match.

Actually wait, there's a subtle issue: at 60Hz, frame boundaries are at multiples of 1/60 second; sample times are multiples of 1/12 second = every 5 frames ✓. At 144Hz: every 12 frames ✓. Both sample at exactly k/12 seconds. Good.

But the input at now===0: the first `g.frames(1, ms)` runs before now is updated... my loop: check input at current `now` (initial value 0) → press right at t=0 ✓. Then frames(1) → now = 16.67 (60Hz). ... At now=500 (60Hz frame 30): release right ✓. At now=1000 (frame 60): press space ✓. At now=2000 (frame 120): release space ✓. At 144Hz: now=500 is frame 72 (72×6.944444444444445 = 500.0000000000001?) — hmm: 6.944444444444445 × 72: 6.944444444444445 × 72 = 500.00000000000006? Let me compute: 1000/144 = 6.9444444444444444... as a double: 6.944444444444445 (rounded). ×72 = 500.00000000000006? 6.944444444444445 × 72 = 500.00000000000004 (approximately). So `now === 500` might be 500.00000000000004 ≠ 500 → input never fires!

I need to use a tolerance: `if (now >= 500 - 1e-9 && !rightReleased)`. Let me restructure with event flags:

```js
let ev = { right: 0, rightOff: 0, jump: 0, jumpOff: 0 };
// at each loop iteration, before frames:
if (!ev.right && now >= 0) { g.press("ArrowRight"); ev.right = 1; }
if (!ev.rightOff && now >= 500 - 1e-6) { g.release("ArrowRight"); ev.rightOff = 1; }
if (!ev.jump && now >= 1000 - 1e-6) { g.press("Space"); ev.jump = 1; }
if (!ev.jumpOff && now >= 2000 - 1e-6) { g.release("Space"); ev.jumpOff = 1; }
```

This is robust against floating-point drift. Let me rewrite that block.

Alright, let's run the test harness against the new game.js.

Everything is failing, and "ALL TESTS PASSED" is being displayed despite there being failures — this is because the `failures` counter is a module-level variable, and the `check` function is... no wait, `failures` is being incremented. The final line is using the `failures` from the destructured `module.exports` — `const { makeGame, check, failures, ... } = module.exports;` — this is capturing the value of `failures` at the time of destructuring (0), not the live value! Classic bug. Need to either read `module.exports.failures` at the end, or make check update the exports object.

But more importantly: all the physics tests are failing — the player isn't moving at all (feet=340 after falling from 340? place(400, 440-100) → feet=340; even after 60 frames, feet is still 340, onGround=false — the player isn't falling!). The player's x isn't changing either (x=250 stays at 250). So `update()` isn't running at all!

Why? The `frame()` call at load time: `frame()` with no arguments → `now` is undefined → `acc += (undefined - last)/1000` = NaN → `while (acc >= STEP)` is false → draw, rAF(frame) → rafCb gets set. Then my harness calls `rafCb(now)` with a numeric now → acc += (now - last)/1000 — last was performance.now() at load time = my fake now at that point (0). So acc = (16.67-0)/1000 = 0.0167 ≥ STEP → update should run...

Wait, unless the first `frame()` call corrupted `last`: `let last = performance.now()` → 0. First `frame()` (no arg): acc += NaN → acc = NaN. last = undefined! Inside frame: `acc += (now - last)/1000; last = now;` — when now is undefined, last = undefined. Then when the harness calls rafCb(16.67): acc += (16.67 - undefined)/1000 = NaN. acc stays NaN forever → no update ever runs!

In the browser, the first `frame()` call also has `now` as undefined → acc = NaN, last = undefined. Then the rAF callback is called with a real timestamp: acc += (12345.6 - undefined) = NaN!! So the original game has the same latent bug... no wait, the original game's frame() is: `function frame() { if (!won) update(); draw(); requestAnimationFrame(frame); }` — rAF passes a timestamp, but the original code ignores the argument entirely. So in the original code, `now` is never used. My new code uses the rAF timestamp, but the first call `frame()` passes nothing → NaN contaminates acc and last.

Fix: initialize `last = null` and handle it: if last === null → last = now (skip the first delta). Also guard against `now` being undefined. Let me fix game.js:

```js
let last = null;
let acc = 0;
function frame(now) {
  if (last === null) last = now;
  acc += (now - last) / 1000;
  last = now;
  ...
}
```

But if `now` is undefined (initial call): last = undefined, acc += NaN. Hmm. Better:

```js
let last = performance.now();
let acc = 0;
function frame(now) {
  if (typeof now !== "number") now = performance.now();
  ...
}
```

This handles both: the first `frame()` call uses performance.now() (≈ last → delta ~0), and subsequent rAF calls use the timestamp.

Also fix the harness's `failures` destructuring bug: use `module.exports.failures` at the end.

Let me fix both.

Wait, the harness has `const { makeGame, check, failures, ... } = module.exports;` at the top of the main block — `failures` is still being destructured (currently unused except for the shadowing issue... actually, the destructured `failures` is still in scope, but I'm now using `module.exports.failures` as `n`. The destructured `failures` is still shadowing... no wait, I named the new variable `n`, so no conflict. But the destructured `failures` is still there, unused — no problem.

Let me run it again.

Great progress! All physics tests pass. Remaining issues:

1. **S10**: "cleared the wall" fails with feet=370 — the bot's `until(() => P(g).onGround && feet(P(g)) < 440, 120)` — the bot jumped from x≥208, but feet=370 means it landed on ledge A (370)?? How? After jumping from the ground around x≈208, it should clear the wall and land on B (300) or the wall top (230). feet=370 = ledge A. Hmm, wait — let me retrace the bot:

- Fall to ground.
- Press right, until x ≥ 60, press Space (hold). Jump from ground at x≈60 → lands on A (feet 370). ✓ "reached ledge A" ok.
- Release Space. Press left. until !onGround (walks off A's left edge). until onGround && feet==440 (back on ground). Release left.
- Press right. until x ≥ 208. Press Space. until onGround && feet < 440 → should land on B.

But feet=370 was reported. So the player landed on A again?! How? After the wall jump... oh wait. Got it — the bot's wall jump: `until(() => P(g).x >= 208, 90)` — but wait, after returning from A, the player is on the ground at x≈124. Press right → runs to 208 → press Space → full jump → clears wall → lands on B (x≈363, feet 300). Then `until onGround && feet < 440` → immediately true (feet=300). afterWall = 300...

But feet=370 was reported. Hmm, so the player landed on A. How? Let me think... oh wait. I got it. The bot's phase "until(() => P(g).x >= 208, 90)" — but the player is holding... no wait. Hmm, let me actually reconsider: after walking off A to the left and landing on the ground at x≈124, press right. But wait — did the player really walk off A? `until(() => !P(g).onGround, 60)` — walking left on A from x≈232... A's left edge is 150. The player leaves A when x+24 < 150 → x < 126. From 232: 27 frames. OK. Then `until(() => P(g).onGround && feet(P(g)) === 440, 90)` — falls from 370 to 440: about 11 frames. OK, on ground at x≈124.

Then press right, until x ≥ 208: 21 frames. Press Space. Jump.

Hmm wait — but the jump: press("Space") sets buffer=0.12. The jump fires on the next update (onGround ✓). Full hold (Space held until release after landing).

Trajectory from x0≈208: as I calculated, lands on B at x≈363, feet 300. So why feet=370?

Wait... maybe the issue is: `until(() => P(g).onGround && feet(P(g)) < 440, 120)` — this condition could be true even if the player is still ascending... no, onGround is only true when landed. Hmm, feet=370 means it landed on A. To land on A, the player must be over A (x ∈ (126,280)) while descending with feet crossing 370.

Oh wait. I think I got it! The wall jump clears the wall, but... no wait. Hmm, let me think about what happens after landing on B (x≈363, feet 300): the bot releases Space. Then `if (afterWall === 230)` — no (300). Then `until(() => P(g).x >= 430, 90)` — but the player is not holding right! After `g.release("Space")`, no movement keys are held (left was released earlier, right was... wait, was right released? Let me retrace the bot's key state:

1. `g.press("ArrowRight")` — before the A jump. Still held.
2. A jump: press Space, land on A, release Space. (Right still held!)
3. `g.press("ArrowLeft")` — now both right and left held! In update: vx = 0 (both keys → vx=0). The player doesn't move! `until(() => !P(g).onGround, 60)` — the player stands on A forever (vx=0) → times out after 60 frames, still on A!
4. `until(() => P(g).onGround && feet === 440, 90)` — times out (player on A, feet 370).
5. `g.release("ArrowLeft")` — now only right held → player walks right on A... to the wall! Gets pushed against the wall (x=276).
6. `g.press("ArrowRight")` (already held, no-op in real game; in harness press() sends another keydown with repeat:false → buffer=0.12! But onGround → jump fires on next update!). Player jumps from A at x=276... vy=-23, ascends; x is pushed to 276 each frame (y overlap with wall while feet > 230); feet reach 230 at... from A (feet 370): rise 140: t1 = (23-sqrt(529-252))/1 = 23-16.6 = 6.4. At t=6.4, feet=230, x=276 (right edge 300, no x overlap with wall) → then can move right over the wall... wait, x=276, right edge=300: no x overlap. Frame 7: x += 4 → 280 → [280,304] x-overlaps wall; y: feet at t=7: 370-(23·7-24.5) = 370-136.5 = 233.5 > 230 → y overlap → pushed back to 276! Hmm, so the player bounces off the wall's side and can't get over from A (as analyzed: A→wall requires v≥30).
7. Player falls back to A (x=276, feet 370).
8. `until(() => P(g).x >= 208, 90)` — immediately true (x=276 ≥ 208)!
9. `g.press("Space")` — jump from A at x=276 again...
10. `until(() => P(g).onGround && feet(P(g)) < 440, 120)` — player lands on A (feet 370 < 440 ✓) → afterWall = 370.

So the bot's key management is broken: it never released ArrowRight before pressing ArrowLeft. The physics is fine (the player did exactly the right thing: was stopped by the wall, couldn't clear the wall from A — which is correct behavior!).

Bot fix: release ArrowRight before pressing ArrowLeft.

2. **S10 "landed on D" feet=127**: The C→D jump won mid-air (feet=127 at win time — passing through the flag). This is expected behavior (win on flag contact), but my bot intended to land on D first. The win check fired during the C→D jump. Since WON is true, the level is completable — but I want the bot to also verify the "land on D and walk to flag" path. To do that, the C→D jump must not pass through the flag's x range while feet are in (125,201).

From the analysis: jumping from C at x=620 with a 12-frame hold: feet pass through (125,201) during descent at x ∈ (706,750) → mid-air win. To land on D to the right of the flag (x > 750+... to land on D, x must be > 656; to be right of the flag, x > 750), the jump must travel farther: from x=620, landing x = 620 + 4·T, where T = total airtime. For a full jump from C: T ≈ 46 frames → x = 804 → clamped to 776 → lands right of the flag! But a full jump from C goes off the top of the canvas (clamped at y=0, hover, then fall) — and during the hover+descent, the feet pass through (125,201) at x ∈ (706,750) → mid-air win again (as calculated: win at t≈25, x≈720).

Hmm. So any C→D jump that passes through the flag's x range while feet are in (125,201) wins mid-air. To avoid this: the player's feet must be ≤125 (above the flag) or ≥201 (below the flag) throughout x ∈ (706,750).

Option A: Jump from C's right edge (x=641) with a short hop (tap): a small rise (about 70-90px) — feet go from 235 to about 150-165... hmm, feet must reach 165 (D's top) to land on D: rise ≥ 70. A tap2 (73.8px) from C: apex feet = 235-74 = 161. Just above D's top (165) ✓. Landing: x = 641 + 4·T. T for a 74px jump: ascent about 9 frames (vy -23 cut at frame 2: vy=-21·0.45=-9.45... let me stop hand-calculating; total airtime ≈ ascent + descent. Descent from apex 161 to 165: 4px → about 2-3 frames. Total ≈ 13-14 frames → x ≈ 641+54 = 695 → lands on D at x=695 (left of the flag!). Then walk right to the flag → win. And during the jump: does the player pass through the flag's x range (706,750)? Max x = 695 < 706 → never. ✓ No mid-air win.

So the bot's C→D: walk to x=641 (C's right edge), tap jump (2-frame hold), land on D at x≈695, walk right to the flag, win.

Let me verify tap2 from C more carefully with the actual discrete physics... I'll just have the bot do it and check the result. If it lands on D (feet 165) at x < 706, good.

Actually wait — tap2 = 73.8px rise from the ground (S8). From C (feet 235): apex feet = 235 - 73.8 = 161.2 < 165 ✓ (4px above D's top). Descent to D: feet cross 165 → land. x at landing: need total airtime. Let the sim decide; the bot waits for onGround && feet==165 with a 120-frame timeout.

But hmm, one risk: if the tap is slightly short (rise < 70), the player can't reach D's top (165) — feet max 166 > 165 → falls back to C or the ground. tap2 = 73.8 ≥ 70 ✓ with 3.8px margin. A bit tight but the sim is deterministic — if it works in the sim, it works. Let me also double-check that the tap timing in the bot is exactly "release 2 frames after press" — in S8, holdFrames=2 means release after the 2nd update. In the bot: press Space, frames(2), release. Same.

3. **S11**: Sample counts differ (21 vs 13) and trajectories differ (maxDy=252!). The sampling logic is broken. At 60Hz: frames land on multiples of 16.667ms; sample times are multiples of 83.333ms = every 5 frames. Over 3000ms: 36 samples (0, 83.3, ..., 3000). At 144Hz: every 12 frames: also 36 samples. But I got 21 and 13. Why?

`Math.abs(now % (1000/12)) < 1e-6` — now accumulates as now += ms. At 60Hz: now after 5 frames = 83.33333333333334 (5 × 16.666666666666668). 1000/12 = 83.33333333333333. now % (1000/12) = 83.33333333333334 % 83.33333333333333 = 8.47e-14 < 1e-6 ✓. After 10 frames: 166.66666666666669 % 83.33333333333333: 166.66666666666669 / 83.33333333333333 = 2.0000000000000004 → remainder ≈ 166.66666666666669 - 2×83.33333333333333 = 166.66666666666669 - 166.66666666666666 = 2.8e-13 ✓. Hmm, these should pass...

Wait, but the loop: `while (now < totalGameMs)` — now starts at 0; the first sample is at now=0 (before any frame). Then frames... let me count: 60Hz, 3000ms → 180 frames. Sample at every 5th frame: 0, 5, 10, ..., 180 → 37 samples. Got 21. So many samples are being missed → the modulo test is failing for many.

Ah wait — I see the bug: `now % (1000/12)` — but `now` here is the fake clock inside the sandbox, which I read via `g.get("performance.now()")`. That's fine... hmm, let me actually debug: at 60Hz, is `now` really accumulating by 16.666666666666668 each frame? My sandbox: `performance: { now: () => now }`, and `frames(n, ms)` does `now += ms; rafCb(now)`. rafCb = frame → `acc += (now - last)/1000; last = now`. The sandbox's `now` variable is the harness's `now` closure variable — incremented in frames(). So performance.now() returns the harness's now. ✓

Hmm wait, but there's a subtle point: the first `frame()` call at script load: `frame()` with no args → `now` param is undefined → `typeof now !== "number"` → `now = performance.now()` = 0 (harness's now at load) → acc += 0 → no problem, last = 0.

Then the harness: `g.frames(1, ms)` → now = 16.67 → rafCb(16.67) → acc = 0.01667 → 1 update ✓.

So why the missed samples? Let me actually print the values. Actually — ah. I see it. In S11, the input at `now >= 1000 - 1e-6` presses Space → player jumps. The jump trajectory is... that doesn't affect sampling.

Hmm, let me debug by printing the sampled `now` values. Actually, let me reconsider: `Math.round(now * 12) / 12` — for the sample key. 60Hz: now=83.33333333333334 → ×12 = 1000.0000000000002 → round = 1000 → /12 = 83.33333333333333. 144Hz: now = 83.33333333333334? At 144Hz: 12 frames × 6.944444444444445 = 83.33333333333334? 6.944444444444445 × 12 = 83.33333333333334 ✓ same.

Rather than guessing, let me actually debug with a quick script. Actually — wait. I think the issue is the while loop condition and sampling: `while (now < totalGameMs)` — after the last frame, now = 3000.0000000000005 (drift) → loop ends. Samples: at 60Hz, frames at k×16.666666666666668. k×16.666666666666668 % 83.33333333333333: k=5: 83.33333333333334 % 83.33333333333333 = 8.47e-14 ✓. k=10: 166.66666666666669 % 83.33333333333333 = ?

Let me compute exactly in JS rather than by hand. Let me run a quick node snippet.

Actually, let me reconsider — maybe the issue is elsewhere: `g.frames(1, ms)` — my frames() function: `for (let i = 0; i < n; i++) { now += ms; rafCb(now); }`. And inside the S11 loop, I call `g.frames(1, ms)` once per iteration, then read now. That's fine.

Hmm wait, actually — I bet the issue is the modulo with a slightly different divisor: 1000/12 in JS = 83.33333333333333 (let me verify: 1000/12 = 83.333...; in double: 83.33333333333333). And 60Hz's ms = 1000/60 = 16.666666666666668. 5 × 16.666666666666668 = 83.33333333333334. 83.33333333333334 % 83.33333333333333 = 8.326672684688674e-14 < 1e-6 ✓.

10 × 16.666666666666668 = 166.66666666666669. 166.66666666666669 % 83.33333333333333: JS: 166.66666666666669 / 83.33333333333333 = 2.0000000000000004 → floor 2 → 166.66666666666669 - 166.66666666666666 = 2.84e-13 ✓.

15 × 16.666666666666668 = 250.00000000000006? 16.666666666666668 × 15 = 250.00000000000003. % 83.33333333333333: 250.00000000000003/83.33333333333333 = 3.0000000000000004 → floor 3 → 250.00000000000003 - 250.00000000000000 = 2.8e-14 ✓.

Hmm, all small. So why 21 samples instead of 37? Let me actually debug. Let me write a quick debug script.

Actually — ah wait. I think I've got it: `while (now < totalGameMs)` and the sampling inside the loop after `g.frames(1, ms)`. At 60Hz: 180 iterations. now values: 16.67, 33.33, ..., 3000.0. Sampling when now % 83.33 < 1e-6: now = 83.33 (k=5), 166.67 (k=10), ..., 3000 (k=180) → 36 samples + initial now=0? No — the initial now=0 is before the loop; the first sample check happens after the first frame (now=16.67). So samples at k=5,10,...,180 → 36. But I got 21.

Unless the jump input at now=1000 changes things... no, sampling is time-based.

Hmm, let me debug empirically. Let me also reconsider the trajectory diff (maxDy=252) — that's huge; suggests the two sims diverged significantly (e.g., one jumped and the other didn't, or the sample alignment is off — comparing sample i of A with sample i of B, but if the sample sets differ, the comparison is garbage).

Let me debug S11 in isolation.

Interesting — floating-point accumulation error grows with each addition (since `now += ms` accumulates rounding error, at k=15 the accumulated time is 249.99999999999994, which is 6e-14 less than 250, and the modulo gives 83.33333333333329 — that is, `t % (1000/12)` wraps around: 249.99999999999994 is slightly less than 3×83.33333333333333 = 249.99999999999999, so the remainder is ≈ 83.33333333333329 (i.e., it's in the last 83.33ms block, not the next block).

So the strict modulo test fails when the accumulated time falls slightly below a multiple. Fix: use a tolerance that accounts for drift: sample when `Math.min(now % T, T - (now % T)) < tol`, with tol around 1e-6... no wait, the problem is that now = 249.99999999999994 is 6e-14 below 250. now % T = 249.99999999999994 % 83.33333333333333 = 83.33333333333329 (remainder within the previous block). T - remainder = 83.33333333333333 - 83.33333333333329 = 4e-13 < 1e-6 ✓. So the "distance to the nearest multiple" test works: `const m = now % T; if (m < tol || T - m < tol) sample`.

Drift: each addition of ms (16.666666666666668) accumulates about 1e-13 of error per step; over 180 frames, the total drift is about 1e-11 — well within the 1e-6 tolerance. Good.

Also, regarding sample key matching between 60Hz and 144Hz: both sample at the nearest multiple of T=83.333ms — the sample index k = round(now/T) gives the same key. Use `Math.round(now / (1000/12))` as the key (an integer second × 12).

So let's fix S11's sampling:
```js
const T = 1000/12;
let m = now % T;
if (m < 1e-6 || T - m < 1e-6) {
  const k = Math.round(now / T);
  if (k !== lastKey) { lastKey = k; samples.push([k, p.x, p.y, p.vy]); }
}
```
The `lastKey` guard prevents double-sampling.

Next, fix the S10 bot: release ArrowRight before pressing ArrowLeft. And the C→D phase: walk to x=641 (the right edge of C), tap-jump (2 frames), land on D at x≈695, then walk right to the flag.

Wait, but there's a problem with the C→D tap: the bot's `until(() => P(g).x >= 620, 90)` — with the new plan, use x >= 641. C spans 545..665; the player's max x on C = 665-24 = 641. So `until x >= 641` → the player is at the right edge of C. Press Space, frames(2), release Space. Then `until onGround && feet === 165`.

Hmm wait, but actually — let me reconsider. Is a 2-frame tap from C (73.8px rise) enough to reach D's top (70px rise)? 73.8 ≥ 70 ✓, with a 3.8px margin. And the landing x: from x=641, airtime: let me estimate the discrete trajectory: press at t0 (buffer), jump fires on the next step. vy sequence: f1: -22, f2: -21 (then keyup: vy = -21×0.45 = -9.45), f3: -8.45, f4: -7.45, f5: -6.45, f6: -5.45, f7: -4.45, f8: -3.45, f9: -2.45, f10: -1.45, f11: -0.45, f12: +0.55 (vy crosses zero during this frame; the frame's displacement is +0.55). Ascent displacement: 22+21+8.45+7.45+6.45+5.45+4.45+3.45+2.45+1.45+0.45 = 90.45?? Wait, that's more than 73.8. Hmm, let me recompute: 22+21 = 43; +8.45 = 51.45; +7.45 = 58.9; +6.45 = 65.35; +5.45 = 70.8; +4.45 = 75.25; +3.45 = 78.7; +2.45 = 81.15; +1.45 = 82.6; +0.45 = 83.05. Hmm, 83px? But S8 measured tap2 = 73.8 from the ground.

Wait — S8's tap2: holdFrames=2 means release when `i+1 >= 2`, i.e., after the 2nd update... let me re-check S8's loop: `for i in 0..120: frames(1); maxFeet = min(...); if (holdFrames !== null && i + 1 >= holdFrames) release`. So at i=0: 1st frame, then i+1=1 < 2, no release. i=1: 2nd frame, i+1=2 ≥ 2 → release. So the release happens after 2 updates: the vy at that point: jump at t0 (vy=-23). Frame 1: vy = -23+1 = -22, y -= 22. Frame 2: vy = -21, y -= 21. Then keyup: vy = -21×0.45 = -9.45. Frame 3: vy = -8.45, y -= 8.45. ... Ascent: 22+21+8.45+7.45+6.45+5.45+4.45+3.45+2.45+1.45+0.45 = 83.05? But S8 said 73.8.

Hmm, discrepancy. Oh wait — the keyup event: in the harness, `g.release("Space")` is called between frames (right after the 2nd frames(1)). The keyup handler runs immediately: vy *= 0.45 → at that point vy = -21 (after frame 2's gravity... no wait. Let me retrace: at the moment of the jump (update at t0): vy = -23 (set by the jump). Then update 1: vy += 1 → -22; y += -22. Update 2: vy += 1 → -21; y += -21. After update 2, the harness releases: vy = -21 × 0.45 = -9.45. Update 3: vy += 1 → -8.45; y += -8.45. Update 4: vy = -7.45; y += -7.45. Update 5: vy=-6.45; y+=-6.45. U6: -5.45. U7: -4.45. U8: -3.45. U9: -2.45. U10: -1.45. U11: -0.45. U12: vy = +0.55; y += 0.55 (feet start descending). Total rise = 22+21+8.45+7.45+6.45+5.45+4.45+3.45+2.45+1.45+0.45 = let me add carefully: 22+21=43. 43+8.45=51.45. +7.45=58.9. +6.45=65.35. +5.45=70.8. +4.45=75.25. +3.45=78.7. +2.45=81.15. +1.45=82.6. +0.45=83.05. So rise ≈ 83px, not 73.8?!

But S8 measured 73.8. So my trace is wrong somewhere. Hmm. Let me think... Oh! MAX_FALL / gravity order: in update, vy += GRAVITY happens after the jump check. Jump at t0: vy=-23. Then y += vy? No wait — let me re-check the order in update():

```
// jump check (sets vy = -23)
// x move
// vy = min(vy + GRAVITY, MAX_FALL)   ← vy becomes -22
// y += vy
```

So the first frame of the jump: vy = -22, y -= 22. As I traced. Hmm.

Then why did S8 measure 73.8? Let me recompute the sum: 22, 21, then after the cut: 8.45, 7.45, 6.45, 5.45, 4.45, 3.45, 2.45, 1.45, 0.45, and the next would be -0.55 → wait, after 0.45, vy += 1 → 0.55 (positive → descent). So ascent frames: -22, -21, -8.45, -7.45, -6.45, -5.45, -4.45, -3.45, -2.45, -1.45, -0.45 → sum of magnitudes: 22+21+8.45+7.45+6.45+5.45+4.45+3.45+2.45+1.45+0.45.

8.45+7.45 = 15.9; +6.45 = 22.35; +5.45 = 27.8; +4.45 = 32.25; +3.45 = 35.7; +2.45 = 38.15; +1.45 = 39.6; +0.45 = 40.05. Total = 43 + 40.05 = 83.05.

Hmm, so the expected tap2 ≈ 83, but the measurement was 73.8. A 9.25px discrepancy. What am I missing?

Oh wait. I got it — in S8, `maxRise(holdFrames)`: `g.place(100, 440); g.frames(3); g.press("Space");` — press after 3 frames. Then the loop: `for i in 0..120: frames(1); maxFeet=min; if (i+1 >= holdFrames) release`. For holdFrames=2: release after the 2nd frame of the loop. But the jump fires one frame after the press (buffer)! So: press at time T. Loop i=0: frames(1) → update: buffer>0 && onGround → jump fires (vy=-23), then vy→-22, y-=22. maxFeet = 440-22. i=1: frames(1) → vy=-21, y-=21. Release. Same as my trace. Rise 83.

Hmm, so why 73.8? Let me actually measure the trajectory in the harness to see what's happening. Maybe... the keyup handler: `if (JUMP_KEYS.includes(e.code) && player.vy < 0) player.vy *= JUMP_CUT;` — at the moment of release, vy = -21 < 0 → vy = -9.45 ✓.

Wait, maybe the issue is: `g.frames(3)` before the press — the player settles on the ground (from spawn... no, place() sets the position directly). place(100, 440): feet=440, on the ground, but onGround=false, coyote=0. frames(3): update 1: vy=1, y+=1 → feet 441 → one-way: prevBottom=440 ≤ 440 ✓ bottom=441 ≥ 440 ✓ → snap to 440, onGround=true. So after 3 frames, on the ground ✓.

Press Space → buffer=0.12. Loop i=0: update: buffer>0 && onGround → vy=-23, onGround=false, buffer=0. vy = -23+1 = -22. y -= 22 → feet 418. maxFeet=418. i=1: vy=-21 → feet 397. Release: vy = -9.45. i=2: vy=-8.45 → feet 388.55. i=3: -7.45 → 381.1. i=4: -6.45 → 374.65. i=5: -5.45 → 369.2. i=6: -4.45 → 364.75. i=7: -3.45 → 361.3. i=8: -2.45 → 358.85. i=9: -1.45 → 357.4. i=10: -0.45 → 356.95. i=11: vy=0.55 → feet 357.5 (descent begins). minFeet = 356.95 → rise = 440-356.95 = 83.05.

So the expected value is 83.05, but S8 said 73.8. So something in the actual code differs from my model. Let me debug: print the per-frame vy and feet during the tap2 run.

Actually — hmm, wait. Maybe the keyup event: in the harness, `release(code)` calls `handlers.keyup({ code })`. In game.js, the keyup handler: `keys[e.code] = false; if (JUMP_KEYS.includes(e.code) && player.vy < 0) player.vy *= JUMP_CUT;`. No problem there.

But wait — in S8's loop, the release happens after `frames(1)` — but `frames(1)` calls `rafCb(now)`, which may run multiple updates if acc allows... at 60Hz, exactly 1 update per frames(1). OK.

Hmm, let me just debug it empirically anyway.

The default path for GAME in harness.js is `path.join(__dirname, "..", "..", "game.js")` — when required from an eval with cwd /tmp/ledge-test, process.argv[2] is undefined → the default gets used → /game.js. Need to set process.argv[2] before the require. Let's set it inside the -e script.