Okay, the user wants a playable Asteroids game in a single HTML file. Let me think about how to approach this.

First, I need to create the HTML structure with a canvas element. The canvas will be the main game area. Then, I'll need to include CSS for styling and JavaScript for the game logic.

For the game mechanics: the ship should thrust, rotate, shoot, and wrap around the screen. Asteroids need to split into smaller pieces when hit. Also, score and lives tracking are required.

Procedural vector graphics mean no images, so everything is drawn with shapes and lines. The ship can be a triangle with a thruster line when moving. Asteroids can be polygons with random points.

I'll start by setting up the canvas and context. Then, define the Ship, Asteroid, and Bullet classes. The ship's rotation and movement need to be handled with trigonometry. Thrust applies acceleration in the direction the ship is facing.

For shooting, the bullets should spawn at the ship's position and move forward. Collision detection between bullets and asteroids is necessary. When an asteroid is hit, it splits into smaller ones if possible.

Wrapping around the screen edges can be done by checking the position and adjusting it to the opposite side when it goes beyond the canvas.

Score and lives will be tracked with variables, updating when asteroids are destroyed or the ship collides.

The game loop will handle updating positions, checking collisions, and redrawing the canvas. I'll use requestAnimationFrame for smooth animation.

Testing each part step by step: first the ship movement, then shooting, collision detection, asteroid splitting, and wrapping. Make sure all elements are contained within the single HTML file without external resources.

Finally, write all the code into the index.html file, including the CSS styles and JavaScript within script tags. Ensure it's self-contained and runs in a browser without any dependencies.

Okay, the user asked for a single-page Asteroids game with specific features. I need to make sure all the requirements are met. Let me check the code I wrote.

First, the HTML structure: canvas element, CSS for full screen and black background. That's covered. The JavaScript handles the game logic. The ship has thrust, rotation, shooting. Bullets are fired in the direction of the ship's angle. Asteroids are procedural with random points. When hit, they split into smaller ones. Score and lives are tracked.

Wait, the collision detection between bullets and asteroids uses a simple distance check. That should work. The wrapping around the screen edges is handled by checking if the position is outside the canvas and resetting it to the opposite side. The game loop uses requestAnimationFrame for smooth animation.

I think all the features are there. The code is self-contained in one file. No external resources. The user can open index.html and play the game. I should confirm that the code is correct and meets all the requirements.