OMNISCIENTRIX

What the Law Explains

The Law of Informational Self-Containment describes how any informational system automatically corrects itself by minimizing internal divergence. In simpler terms:

Every information system naturally moves toward equilibrium.

When a random distribution is repeatedly compared against a neutral reference distribution (q), it updates itself in a direction that reduces KL-divergence. Eventually, the system becomes stable, self-consistent, and fully self-contained.

This page includes:

• Full mathematical explanation
• The original computational proof
• A live experiment you can run in-browser
• A peer-review section for researchers

Mathematical Essence

If p is any informational state and q is a balanced reference state, the system updates itself using:

p_new = normalize( p - η (p - q) )
KL(p || q) → 0

This ensures the KL-divergence always decreases over time, pushing the system toward informational equilibrium.

Original Verification Code (Python)

This is the exact code that produced the verification output in your notebook:

import numpy as np
from scipy.stats import entropy

def kl(p, q):
    return np.sum(p * np.log(p / q))

def ISC(p, q, lr=0.01, steps=1000):
    hist = []
    for _ in range(steps):
        d = kl(p, q)
        hist.append(d)
        p -= lr * (p - q)
        p = np.clip(p, 0, 1)
        p /= p.sum()
        if d < 0.01:
            break
    return hist

p = np.random.rand(1000)
p /= p.sum()
q = np.ones(1000) / 1000

H = ISC(p, q)
print("Final KL:", H[-1])

Run the Experiment Yourself

Click to simulate the system evolving toward informational equilibrium.

Peer Review + Reproducibility

The purpose of this project is to encourage scientific verification, criticism, refinement, and open discussion. Researchers are invited to:

• Re-run the code with different distributions
• Test alternative update rules
• Stress-test convergence outcomes
• Submit peer-reviewed commentary or challenges
• Extend the law into physics, cognition, or AI systems

You are encouraged to fork this repository, run your own experiments, and submit findings via pull request or Issues.

Science advances when other minds test what one mind discovers.