/**** 
* Classes
****/ 
// Cactus class: moves left, destroys itself off screen
var Cactus = Container.expand(function () {
	var self = Container.call(this);
	// Attach cactus asset, anchor bottom left
	var cactusSprite = self.attachAsset('cactus', {
		anchorX: 0.5,
		anchorY: 1
	});
	self.speed = 7 + Math.random() * 2; // even slower speed for easier gameplay
	self.update = function () {
		self.x -= self.speed;
		// Destroy if off screen
		if (self.lastX >= -200 && self.x < -200) {
			self.destroy();
		}
		self.lastX = self.x;
	};
	return self;
});
// Cat class: handles jump, gravity, and collision
var Cat = Container.expand(function () {
	var self = Container.call(this);
	// Attach cat asset, anchor bottom left for ground logic
	var catSprite = self.attachAsset('cat', {
		anchorX: 0.5,
		anchorY: 1
	});
	// Cat physics
	self.y = 0;
	self.x = 0;
	self.vy = 0;
	self.isJumping = false;
	self.groundY = 0; // will be set after creation
	// Jump parameters
	self.jumpVelocity = -65;
	self.gravity = 4;
	// Update method for physics
	self.update = function () {
		if (self.isJumping) {
			// If we are hovering, do not apply gravity or move
			if (self.isHovering) {
				// Check if hover time is over
				if (LK.ticks - self.hoverStartTick >= 6) {
					// 100ms at 60 FPS
					self.isHovering = false;
					// Resume falling, keep vy as 0 so gravity starts pulling down
					self.vy = 0;
				}
				// While hovering, do nothing else
				return;
			}
			// Normal jump/fall
			self.vy += self.gravity;
			self.y += self.vy;
			// At apex: vy just turned positive (was going up, now going down)
			if (!self.isHovering && self.vy > 0 && !self.hasHovered) {
				self.isHovering = true;
				self.hasHovered = true;
				self.hoverStartTick = LK.ticks;
				self.vy = 0; // Stop vertical movement during hover
				return;
			}
			// Land on ground
			if (self.y >= self.groundY) {
				self.y = self.groundY;
				self.vy = 0;
				self.isJumping = false;
				self.isHovering = false;
				self.hasHovered = false;
			}
		}
	};
	// Jump method
	self.jump = function () {
		if (!self.isJumping) {
			self.isJumping = true;
			self.vy = self.jumpVelocity;
			self.isHovering = false;
			self.hasHovered = false;
			self.hoverStartTick = 0;
		}
	};
	return self;
});

/**** 
* Initialize Game
****/ 
var game = new LK.Game({
	backgroundColor: 0x000000
});

/**** 
* Game Code
****/ 
;
// --- GAME CODE ---
// Game constants
var GROUND_Y = 2200; // y position of ground (bottom of screen minus margin)
var CAT_START_X = 400;
var CAT_START_Y = GROUND_Y;
var CACTUS_SPAWN_MIN = 40; // min frames between cacti (more frequent)
var CACTUS_SPAWN_MAX = 80; // max frames between cacti (more frequent)
// Game state
var cat;
var cacti = [];
var score = 0;
var scoreTxt;
var nextCactusTick = 0;
var gameOver = false;
// Speed multiplier for game progression
var speedMultiplier = 1;
var SPEED_MULTIPLIER_INCREMENT = 0.08; // how much to increase per score
var SPEED_MULTIPLIER_MAX = 3; // cap the speed increase
// Add score text to GUI
scoreTxt = new Text2('0', {
	size: 120,
	fill: 0xFFFFFF
});
scoreTxt.anchor.set(0.5, 0);
LK.gui.top.addChild(scoreTxt);
// Create cat
cat = new Cat();
cat.x = CAT_START_X;
cat.y = CAT_START_Y;
cat.groundY = CAT_START_Y;
game.addChild(cat);
// Touch/click to jump
game.down = function (x, y, obj) {
	if (!gameOver) {
		cat.jump();
	}
};
// Main update loop
game.update = function () {
	if (gameOver) return;
	// Update cat
	cat.update();
	// Spawn cactus
	if (nextCactusTick <= 0) {
		var cactus = new Cactus();
		cactus.x = 2048 + 100; // spawn just off right edge
		cactus.y = GROUND_Y;
		cactus.lastX = cactus.x;
		// Apply speed multiplier to cactus
		cactus.speed = cactus.speed * speedMultiplier;
		game.addChild(cactus);
		cacti.push(cactus);
		// Calculate minimum jump window: time to complete a jump (up, hover, down)
		// Estimate: jump up (abs(cat.jumpVelocity)/cat.gravity), hover (6 ticks), fall (same as up)
		// Total jump time in ticks
		var jumpUpTicks = Math.ceil(Math.abs(cat.jumpVelocity) / cat.gravity);
		var hoverTicks = 6;
		var jumpTotalTicks = jumpUpTicks + hoverTicks + jumpUpTicks;
		// Calculate cactus travel time from spawn to cat.x
		var cactusTravelDistance = 2048 + 100 - CAT_START_X;
		var avgCactusSpeed = (7 + 8.5) / 2 * speedMultiplier; // average speed, adjusted by multiplier
		if (avgCactusSpeed < 1) avgCactusSpeed = 1; // avoid divide by zero
		var cactusTravelTicks = cactusTravelDistance / avgCactusSpeed;
		// Minimum interval: enough time for cat to land and jump again before next cactus arrives
		// Add a small buffer (e.g. 10 ticks)
		var minInterval = Math.max(jumpTotalTicks + 10, 20);
		// Randomize interval, but always >= minInterval
		var spawnInterval = minInterval + Math.floor(Math.random() * 30);
		// Clamp to a minimum of 10 ticks for extreme speeds
		if (spawnInterval < 10) spawnInterval = 10;
		nextCactusTick = Math.floor(spawnInterval);
	} else {
		nextCactusTick--;
	}
	// Update cacti, check for collision and scoring
	for (var i = cacti.length - 1; i >= 0; i--) {
		var cactus = cacti[i];
		cactus.update();
		// Remove if off screen
		if (cactus.x < -200) {
			cactus.destroy();
			cacti.splice(i, 1);
			continue;
		}
		// Collision detection (only trigger on first intersect)
		if (!cactus.lastWasIntersecting && cat.intersects(cactus)) {
			// Game over
			LK.effects.flashScreen(0xff0000, 800);
			LK.showGameOver();
			gameOver = true;
			return;
		}
		// Scoring: passed cactus (cat.x > cactus.x + cactus.width/2) and not already scored
		if (!cactus.scored && cat.x > cactus.x + cactus.width / 2) {
			score++;
			scoreTxt.setText(score);
			cactus.scored = true;
			// Increase speed multiplier, capped at max
			speedMultiplier += SPEED_MULTIPLIER_INCREMENT;
			if (speedMultiplier > SPEED_MULTIPLIER_MAX) speedMultiplier = SPEED_MULTIPLIER_MAX;
		}
		cactus.lastWasIntersecting = cat.intersects(cactus);
	}
};

===================================================================
--- original.js
+++ change.js
@@ -148,11 +148,25 @@
 		// Apply speed multiplier to cactus
 		cactus.speed = cactus.speed * speedMultiplier;
 		game.addChild(cactus);
 		cacti.push(cactus);
-		// Next spawn in random interval, but faster as speed increases
-		var spawnInterval = (CACTUS_SPAWN_MIN + Math.floor(Math.random() * (CACTUS_SPAWN_MAX - CACTUS_SPAWN_MIN))) / speedMultiplier;
-		// Minimum interval clamp
+		// Calculate minimum jump window: time to complete a jump (up, hover, down)
+		// Estimate: jump up (abs(cat.jumpVelocity)/cat.gravity), hover (6 ticks), fall (same as up)
+		// Total jump time in ticks
+		var jumpUpTicks = Math.ceil(Math.abs(cat.jumpVelocity) / cat.gravity);
+		var hoverTicks = 6;
+		var jumpTotalTicks = jumpUpTicks + hoverTicks + jumpUpTicks;
+		// Calculate cactus travel time from spawn to cat.x
+		var cactusTravelDistance = 2048 + 100 - CAT_START_X;
+		var avgCactusSpeed = (7 + 8.5) / 2 * speedMultiplier; // average speed, adjusted by multiplier
+		if (avgCactusSpeed < 1) avgCactusSpeed = 1; // avoid divide by zero
+		var cactusTravelTicks = cactusTravelDistance / avgCactusSpeed;
+		// Minimum interval: enough time for cat to land and jump again before next cactus arrives
+		// Add a small buffer (e.g. 10 ticks)
+		var minInterval = Math.max(jumpTotalTicks + 10, 20);
+		// Randomize interval, but always >= minInterval
+		var spawnInterval = minInterval + Math.floor(Math.random() * 30);
+		// Clamp to a minimum of 10 ticks for extreme speeds
 		if (spawnInterval < 10) spawnInterval = 10;
 		nextCactusTick = Math.floor(spawnInterval);
 	} else {
 		nextCactusTick--;