Create a complete, fully functional Flappy Bird clone in Flutter that can be compiled and run immediately without any manual modifications. Follow these requirements strictly:
CRITICAL REQUIREMENTS:

Provide ALL code in a single, complete main.dart file
Use ONLY native Flutter widgets and packages - no external dependencies beyond the Flutter SDK
All graphics must be drawn programmatically using CustomPainter - NO image assets
The code must be production-ready and require zero modifications to run

GAMEPLAY MECHANICS:

Tap anywhere to make the bird flap upward
Gravity constantly pulls the bird downward
Bird must navigate through gaps between pipes
Collision with pipes, ground, or ceiling ends the game
Score increases by 1 for each pipe successfully passed
Game over screen with score display and restart button
Pipes should scroll from right to left continuously
Gap between pipes should be consistent and challenging but fair
Physics should feel similar to original Flappy Bird (responsive but difficult)

VISUAL REQUIREMENTS (all code-based using CustomPainter):

Yellow bird with simple rounded body and wing
Green pipes similar to Super Mario Bros style
Light blue sky background
Ground/floor at bottom with a different color
Score displayed at top center
Simple game over overlay with final score and Tap to Restart text

TECHNICAL IMPLEMENTATION:

Use a game loop with setState() or AnimationController for updates
Implement proper collision detection (rectangle/circle collision)
Bird should have rotation that changes based on velocity (tilts up when flapping, tilts down when falling)
Smooth 60 FPS animation
Responsive tap detection across entire screen
Proper game state management (playing, game over)
Random but consistent pipe gap positioning

CODE STRUCTURE:
Organize the code with:

Main game widget
CustomPainter classes for bird, pipes, and background
Game logic class or methods for physics, collision, scoring
Clear constants for tuning (gravity, jump velocity, pipe speed, gap size)

Provide the complete, ready-to-run code now. Include helpful comments explaining key sections.