# The Ali Integral: Observable Future Information (OFI)

[![Physics](https://img.shields.io/badge/Physics-General%20Relativity-black)](https://en.wikipedia.org/wiki/General_relativity)
[![Info Theory](https://img.shields.io/badge/Theory-Information-blue)](https://en.wikipedia.org/wiki/Information_theory)
[![Python](https://img.shields.io/badge/Python-3.9%2B-green)](https://www.python.org/)
![Simulation](output/Vision_Theory_Simulation.gif)

## 🌌 Abstract

This project provides a computational implementation of **Vision Theory**, a framework unifying General Relativity and Quantum Information Theory. We introduce a new physical metric, **$I_{Ali}$ (The Ali Integral)**, which quantifies the maximum amount of information ("History of the Future") an observer can decode while falling towards the Cauchy Horizon of a Black Hole.

The simulation resolves the infinite energy paradox by applying:
1.  **Shannon-Hartley Theorem** with dynamic gravitational SNR.
2.  **Lloyd Limit** for computational bounds.

3.  **Thermal Destruction Criteria** (Backreaction/Crash).

## 🚀 Features

*   **Rigorous Physics**: Models gravitational blueshift ($g \propto 1/r$), quadratic energy flux ($F \propto g^2$), and dynamic bandwidth.
*   **Comparison Engine**: Simulates infall for Stellar, Supermassive (Sgr A*), and Ultramassive (TON 618) Black Holes.
*   **Scientific Output**: Automatically generates graphs and a fully formatted PDF research paper (MIT-style).

## 📂 Project Structure

*   `src/physics.py`: Core logic for Shannon Capacity and Integration.
*   `src/plotting.py`: Matplotlib plotting engine for logarithmic scaling and LaTeX rendering.
*   `src/config.py`: Centralized configuration for physical constants ($B_0$, $C_{limit}$, $F_{crit}$).
*   `main.py`: Orchestrator script.

## 🛠️ Installation & Usage

1.  **Clone the repository:**
    ```bash
    git clone https://github.com/YourUsername/Ali-Integral-Project.git
    cd Ali-Integral-Project
    ```

2.  **Install dependencies:**
    ```bash
    pip install -r requirements.txt
    ```

3.  **Run the simulation:**
    ```bash
    python main.py
    ```

4.  **View Results:**
    Check the `output/` folder for the generated PDF paper and high-resolution graphs.

## 📊 The Ali Integral Formula

The total Observable Future Information (OFI) is defined as:

$$ I_{Ali} = \int_{0}^{\tau_{crash}} \min \left( B(\tau) \log_2(1 + SNR(\tau)), \ C_{Lloyd} \right) d\tau $$

Where $C_{Lloyd}$ is the fundamental quantum limit of computation.

---
*Author: Ali* | *Version: 10.0 (Final Scientific Release)*