Build this mobile app now based on the specification below.
The app must be mobile-first and responsive.
Set the HTML <title> element (and any document.title assignments) to exactly: "Made with App Studio".

Name: Test App 123
Specification:

PRD: Test App 123 — Pie Chart Jumper

Overview

A reaction-time game with Flappy Bird-style mechanics. The player controls a pie-chart avatar that jumps through pipes. Score is based on distance (number of pipes passed). Difficulty gradually increases as play progresses. Built as a simple proof-of-concept for a mobile web app.

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Core Features

• Tap to jump — Each tap makes the avatar jump upward. Gravity pulls it back down.
• Pipe obstacles — Pipes of varying height appear from the right side of the screen and scroll left. The avatar must pass through the gap between top and bottom pipes.
• Collision detection — Hitting a pipe or the ground ends the game. A game-over state is shown.
• Distance-based scoring — Score increases by 1 for each pipe successfully passed. High score is tracked during the current session.
• Gradually increasing difficulty — Over time, pipes move faster and/or the gap between top and bottom pipes shrinks. The rate of increase should be gentle but noticeable.
• Restart — After game-over, the player can tap to restart and play again immediately.
• One screen — Gameplay, scoring, game-over, and restart all happen on a single screen.

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Content

• Pie-chart avatar — A circle divided into colorful slices (like a classic pie chart). Slices are random colors. No data labels or values are shown — purely visual.
• Pipes — Simple rectangular obstacles. Color can be neutral (e.g., green or gray) to contrast with the colorful avatar.
• Background — Solid or simple gradient. No complex scenery needed for proof-of-concept.

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Visual Style

• Colorful and playful — The pie-chart avatar provides the main visual interest.
• Clean and minimal — No unnecessary UI elements. Score is displayed clearly at the top of the screen.
• Smooth movement — The avatar jumps with a natural arc. Pipes scroll smoothly from right to left. No choppy animations.

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User Flow

1. Game loads with the avatar stationary in the center-left of the screen.
2. Player taps to start. First pipe appears shortly after.
3. Each tap makes the avatar jump. Miss a tap and the avatar falls.
4. Score increments each time the avatar passes a pipe.
5. Difficulty ramps up gradually.
6. On collision, game-over text and final score appear. Player taps to restart.

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Scope and Constraints

• No backend — All game logic runs client-side in the browser.
• No authentication — No Pi SDK auth or user accounts.
• Single-player only — No multiplayer or leaderboards.
• English UI — All text in English.

Ready to build?
Custom Instructions: Create a fun game

The specification above is final and approved. Implement the app now in code. Do not ask for confirmation, do not summarize what you will build, do not ask follow-up questions.

CRITICAL: Do not modify, remove, or bypass the Pi Network SDK and authentication integration that ships with this template. The app must always initialize the Pi SDK and authenticate the user via Pi on startup. Do not add code that disables, mocks, or skips Pi authentication.