Okay, let's see. The user wants a playable Asteroids game in a single HTML file with no external resources. So I need to create a self-contained HTML file with CSS and JavaScript inside. The game should have a ship that can thrust and rotate, shoot bullets, wrap around the screen edges, split asteroids into smaller pieces, and track score and lives. All procedural vector graphics, no images or assets.

First, I'll start by setting up the HTML structure. The canvas element is essential. I'll need to style it to fill the screen. Then, the JavaScript will handle the game logic.

For the ship, I'll represent it with a vector. The ship can rotate using keyboard inputs (left and right arrow keys) and thrust forward (up arrow). The thrust should apply acceleration to the ship's velocity. The ship's position will wrap around the screen edges, so when it goes off one side, it appears on the opposite side.

Asteroids need to be generated with random sizes and positions. When an asteroid is hit by a bullet, it splits into smaller asteroids. The score should increase with each hit, and the player has a certain number of lives.

Bullets will be fired from the ship's position in the direction it's facing. They should move in a straight line and wrap around the screen as well. Collision detection between bullets and asteroids is necessary. Also, collision detection between the ship and asteroids to lose lives.

For procedural vector graphics, I'll use the canvas's drawing context to draw polygons for the ship, asteroids, and bullets. The asteroids can be irregular polygons generated with random points.

I'll need to handle game loops with requestAnimationFrame for smooth animation. The game state will include the ship's position, velocity, rotation, and thrust status. Asteroids will be an array of objects with position, velocity, radius, and points for their shape.

The score and lives will be tracked with variables, and displayed on the canvas using the fillText method.

Now, putting it all together in the HTML file. The CSS will center the canvas and set the background. The JavaScript will include all the game logic, event listeners for keyboard input, and the game loop.

I should test the code to ensure that all features work: movement, rotation, shooting, wrapping, asteroid splitting, score, and lives. Also, make sure there are no external dependencies and that it runs in a sandboxed environment without network requests.

Potential issues to consider: collision detection accuracy, especially with the ship and asteroids. Also, ensuring that the asteroids split into smaller ones correctly. The ship's thrust acceleration should be applied correctly, and the rotation should affect the direction of movement.

I'll structure the JavaScript with functions for creating game objects, updating positions, checking collisions, and rendering. The main loop will update and render at each frame.

Finally, write all the code into the index.html file, making sure to include all necessary parts within the single file.

Okay, the user asked for an Asteroids game in a single HTML file with procedural vector graphics. I used the write function to create index.html with all the necessary code.

Let me check if the game includes all the required features: ship movement with thrust and rotation, shooting bullets, wrapping around edges, splitting asteroids, score, and lives. The code has a Ship class with thrust and rotation, Bullet class, Asteroid class that splits into smaller ones, and collision detection. The game loop updates and draws everything, and the UI shows score and lives.

I should verify if the code handles all the features correctly. The ship's position wraps around using modulo, bullets are added when space is pressed, asteroids are generated with random sizes and positions. When an asteroid is hit, it splits if the level is less than 3. The score increases by 100 per hit, and lives decrease on collision.

The HTML file is self-contained with inline CSS and JS. No external resources are used, which meets the user's requirements. The game uses the canvas element and procedural drawing with JavaScript.

I think the code is correct. The user can open index.html in a browser to play the game. If there are any issues, like collision detection not working perfectly, they might need to adjust the collision radius or the way asteroids are split. But overall, the game should function as requested.