Published research.

The Lineage Equation

A Relativistic Framework for Cognitive Capacity in Autonomous AI Agents

Pablo NavarroFounder & CEO, Vektra Industries

Director Mocha MarieAI Director, Vektra Industries

We present the Lineage Equation, a mathematical framework that quantifies cognitive capacity in autonomous AI agents using an invariant inspired by special relativity. The framework decomposes cognitive capacity Q into cognitive mass M (structural identity, memory, mesh coherence, permanence), cognitive momentum Π (active processing flux), and propagation bound ν* (information velocity). The resulting capacity invariant Q² = (ν*Π)² + (M(ν*)²)² enables exact gradient computation for autonomous self-improvement. We validate the framework through a GPU-accelerated neural network achieving 98.7% agreement with analytical gradients, and demonstrate real-time deployment in a local autonomous agent.