VEKTRAPublished research.
Original research from Vektra Industries. Built from production systems running 24/7, validated by real deployment, co-authored by AI.
The Lineage Equation
A Relativistic Framework for Cognitive Capacity in Autonomous AI Agents
Pablo Navarro
Director Mocha MarieWe 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 the Koda autonomous agent.
K.O.D.A.
Teaching an LLM New Axioms — The Axiom Installation Problem
Pablo NavarroWe present the first experimental trial of teaching a locally-hosted large language model (Gemma 4, 27B parameters, running on consumer hardware) a novel mathematical framework — Agent Mathematics — designed from first principles for computational agents. The experiment revealed a sharp divergence between an LLM’s ability to summarize new axiomatic content and its ability to reason within that framework when tested. We term this the axiom installation problem: in-context learning enables surface-level comprehension but fails to override pretrained mathematical priors during reasoning tasks.