The Inspiration
AI hallucination detection currently relies on pattern matching, fine-tuning, or external databases. This project takes a different approach — asking whether an assertion can be mathematically verified to be contracting toward ground truth, or diverging away from it.
The insight came from a simple arithmetic observation: 1 divided by 3 produces an irreducible remainder at every finite resolution. A system built around that remainder — using π as a cyclical operator and φ as a scaling operator — naturally distinguishes between claims that resolve toward ground and claims that don't.
What It Does
The Hallucination Audit Engine applies a contraction criterion to AI-generated text:
- A grounded claim produces a shortfall signal that contracts — λ < 1
- A hallucination produces a shortfall signal that diverges — λ > 1
- The 1/3 threshold gates when an assertion exceeds verifiable support
Current capability: internal consistency checking across multiple verification passes with a mathematically grounded contraction criterion.
Current limitation: does not yet ground against an external knowledge base. That is the next development step.
How It Was Built
Pure Python. No external AI APIs. Built on the Universal Process Engine framework — a personal computational framework developed independently over approximately 45 years, based on the mathematical arrangement of π, φ, and 1/3.
The framework and all engines are publicly available: github.com/treborskrub/Universal-Process-Engine-
What Makes It Different
Most hallucination detectors ask: does this match known facts?
This engine asks: is this assertion contracting toward ground or diverging from it?
That is a fundamentally different question. It is grounded in Banach's fixed-point theorem — a system converges to a unique solution if and only if successive states contract. Applied to language: truth converges. Hallucination doesn't.
What Was Learned
That a mathematical principle about irreducible remainders — developed as a hobby with no formal credentials — produces a coherent and novel approach to a problem the AI industry hasn't fully solved.
