AGI foundational algorithm

Abstract

This paper presents a unified symbolic framework combining Concursive Mapping—a novel model of recursive drift using primed and unprimed symbolic variables—with Extended Recursive Diagnostic Engines that apply collapse logic, weighted feedback, and transfinite operators. At its core is the Concursive Equation:

\Delta_C(x, x{\prime}) = \left( \frac{x{\prime} - x + 2}{x{\prime}} \right) - 2

This equation quantifies symbolic deviation between recursive states, enabling feedback correction, bifurcation awareness, and identity tracking. Integrated with diagnostic logic featuring weighted recursive inputs, derivative-based divergence detection, and symbolic summation, the system models recursive cognition, AI diagnostics, and transfinite feedback mechanisms. The framework generalizes across symbolic systems, providing a foundation for recursive AI, quantum decision loops, and systemic self-correction.

Algorithm:

The algorithm is a symbolic recursive system designed to track how much a system changes over time and make decisions based on that change. It compares two states — one from the past and one from the present — using what’s called the Concursive Equation.

This equation:

written as  \Delta_C(x, x{\prime}) = \left( \frac{x{\prime} - x + 2}{x{\prime}} \right) - 2 

calculates a value that represents the difference or “drift” between those two states. If this value is small, the system is considered stable. If it’s large, the system may be getting worse, and action may be required. The algorithm continuously runs this check in a loop, making it recursive: each new observation feeds back into the system, refining the understanding of what’s happening. If the results are stable and confident, the algorithm may finalize its decision — such as confirming a diagnosis. If the results are diverging, it may escalate the situation — like referring to a specialist. If the situation is unclear, it continues gathering and analyzing more data. This recursive feedback loop allows the system to adapt, monitor, and respond intelligently, making it useful in fields like AI, medicine, physics, or any context where systems evolve over time and need to be tracked and interpreted meaningfully.