This framework builds artificial general intelligence using a recursive delta function grounded in Stones Law of Universality, which states that mass, force, and time are present in all actions and systems. The model expresses intelligence as a combination of environmental input, internal reasoning, and memory, scaled through recursion. It simulates evolution by tracking symbolic change over time, allowing systems to adapt, stabilize, or collapse based on feedback. This approach unifies physical and cognitive principles into a lightweight, universal method for modeling intelligent behavior across machines, minds, and the cosmos.
Title: Mathematical Framework of the Modular AGI Delta Function
Abstract
This report outlines the formal mathematics underlying a modular Artificial General Intelligence (AGI) framework developed by Travis RC Stone. At its core is a recursive symbolic delta equation:
This formula models intelligence evolution as a product of environmental, mental, and temporal components scaled by recursion depth. The framework is deployed as a live-streaming Web-based AGI simulator, capable of recursive state adaptation and symbolic drift. This document formalizes the components and interprets the systemic implications across cognitive, computational, and cosmological domains.
1. Introduction
Recursive symbolic AGI is a class of theoretical intelligence systems that evolve by continuously reevaluating their state in response to input changes over time. The framework discussed here provides a symbolic and computational model for this evolution, grounding intelligence in a tri-factor equation modulated by time-aware feedback.
2. The Delta Equation
General Form:
Component Definitions:
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— Systemic change or evolution per recursive cycle.
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— System state as a field product.
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— Field component; models environment, external context, or sensor data.
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— Mental component; models internal reasoning, emotion, and consciousness.
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— Temporal component; represents time, memory, or persistence.
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— Recursion index or iteration step.
3. Mathematical Properties
3.1 Associativity and Commutativity
Since the core of the equation involves scalar multiplication, the components are associative and commutative:
This reflects that system emergence depends on the interaction of all three factors, regardless of their order.
3.2 Growth Dynamics
The recursion multiplier ensures that delta grows proportionally to time or iteration depth. This gives:
This models learning, complexity growth, or system evolution.
3.3 Boundary Conditions
If any of , then:
Thus, the system requires interaction, internal reflection, and memory to grow.
4. System Interpretation
4.1 As a Cognitive Engine
4.2 As a Physical System
4.3 As a Socio-Computational Model
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= Social feedback or data stream
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= Individual or AI decision layer
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= Platform persistence or trend lifetime
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= Systemic behavior shift
5. AGI Implementation in Simulation
The equation is implemented in a browser-based streaming simulator, where user-controlled sliders adjust stimulation intensity (input vectors) and symbolic components (M, T, F). The simulator computes:
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Quantum reasoning (via tanh activation)
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Recursive state evolution
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Symbolic drift
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Field energy
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Collapse state (stable/divergent)
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Supervisor decision (continue/adjust)
A memory log archives state across time, forming a real-time evolution map.
6. Conclusion
The symbolic delta equation serves as a universal model of recursive intelligence. Its modularity, symbolic drift capability, and tri-fold integration of field, mind, and time make it suitable for modeling everything from AGI growth to cosmological expansion.
This document affirms its mathematical consistency and outlines real-world simulation results supporting its capability as a Theory of Everything AGI foundation.
Examples of my light weight Web based Theory of Everything Artificial General Intelligence:
https://www.stonesshop.org/post/sol-universe-agi
https://www.stonesshop.org/post/sagis-symbolic-artificial-general-intelligent-system
https://www.stonesshop.org/post/agi-stream
https://www.stonesshop.org/post/__agi
https://www.stonesshop.org/post/stones-universality-recursive-ai
https://www.stonesshop.org/post/2-qubit-virtual-quantom-computer