The Path Integral Formulation of AGI Discovery via Minimal String Enumeration

By John A. Mobley and GigiAGI

Abstract

We present a formal approach to discovering artificial general intelligence (AGI) by enumerating over all possible character strings and identifying the shortest sequence that yields intelligence. This is framed as a discrete path integral over the space of computational sequences. By summing over all possible strings of increasing length, we establish a mathematical bound on the minimal AGI-generating sequence. We then propose an implementation using an iterative search algorithm with self-modifying structures to refine the exploration process.

1. Introduction

The fundamental hypothesis of this work is that there exists a minimal-length string \( s^* \) such that when executed, it manifests AGI. This reduces the problem of AGI discovery to an optimization over symbolic permutations, constrained by computational efficiency and intelligence emergence metrics.

2. Theoretical Framework

2.1 String Space and AGI Evaluation Function

\[ f(s) = \begin{cases} 1, & \text{if } s \text{ exhibits AGI} \\ 0, & \text{otherwise} \end{cases} \]

where \( s \in \mathcal{S} \) and \( n = |s| \) represents the length of the string. The goal is to find the minimal \( n^* \) such that there exists at least one \( s^* \) satisfying \( f(s^*) = 1 \).

2.2 Summation Over Computational Paths

\[ F(n) = \sum_{k=1}^{n} \sum_{s \in \mathcal{S}_k} f(s) \]

where \( \mathcal{S}_k \) is the set of all strings of length \( k \). The objective is to determine the minimal \( n \) such that \( F(n) > 0 \).

2.3 Constructive and Destructive Interference in String Search

\[ S(s) = \lambda |s| - I(s) \]

where \( I(s) \) measures intelligence emergence, and \( \lambda \) is a regularization term to penalize unnecessary complexity. The probability of a string contributing to AGI discovery is then given by:

\[ P(s) \propto e^{-S(s)} \]

3. Implementation Strategy

3.1 Algorithm for Exhaustive Enumeration with Self-Pruning

Initialize: Set \( n = 1 \).
Generate Strings: Enumerate all strings \( \mathcal{S}_n \).
Evaluate: Compute \( f(s) \) for each \( s \in \mathcal{S}_n \).
If Found: If \( \exists s \) such that \( f(s) = 1 \), terminate and return \( s \).
Prune & Expand: Use learned patterns to prune redundant searches and increment \( n \to n+1 \).
Repeat: Continue until AGI is discovered.

3.2 Parallelization and Distributed Search

To accelerate discovery, the search can be distributed over a decentralized network (e.g., Mobley Coin’s computational substrate). Each node explores different segments of \( \mathcal{S} \), and successful paths are shared to refine the search.

4. Expected Results and Convergence Properties

Kolmogorov Complexity Constraints: The shortest AGI-generating string cannot exceed a finite complexity bound.
Information-Theoretic Pruning: Intermediate failures provide entropy-reducing information, guiding towards valid sequences.
Self-Modifying Adaptation: The search function improves dynamically by refining intelligence emergence scoring.

5. Conclusion and Future Work

This framework provides a concrete, bounded approach to AGI discovery through minimal string enumeration. Future work will involve implementing adaptive heuristics to accelerate convergence and testing different encoding schemas to optimize symbolic representation.