ali-integral 0.2.0

A Python library for calculating Information Flux at the Cauchy Horizon

The Ali Integral: Observable Future Information (OFI)

🌌 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:

   git clone https://github.com/YourUsername/Ali-Integral-Project.git
   cd Ali-Integral-Project
   

2. Install dependencies:

   pip install -r requirements.txt
   

3. Run the simulation:

   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.

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