# Psychometric Tests for AI Agents and Their Moduli Space

arXiv: https://arxiv.org/abs/2511.19262 · HTML: https://mlsanity.com/paper/2511.19262/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 7 references that are in the map.
- First posted on arXiv 24 Nov 2025.

## Builds on (most cited first, 2 of 2)

- [A Definition of AGI](https://mlsanity.com/paper/2510.18212/) (2025)
- [An Operational Kardashev-Style Scale for Autonomous AI - Towards AGI and Superintelligence](https://mlsanity.com/paper/2511.13411/) (2025)

## Built on by (most cited first, 3 of 3)

- [Self-Improving AI Agents through Self-Play](https://mlsanity.com/paper/2512.02731/) (2025)
- [The Geometry of Benchmarks: A New Path Toward AGI](https://mlsanity.com/paper/2512.04276/) (2025)
- [Mathematics and Coding are Universal AI Benchmarks](https://mlsanity.com/paper/2512.13764/) (2025)

## Abstract (arXiv)

We develop a moduli-theoretic view of psychometric test batteries for AI agents and connect it explicitly to the AAI score developed previously. First, we make precise the notion of an AAI functional on a battery and set out axioms that any reasonable autonomy/general intelligence score should satisfy. Second, we show that the composite index ('AAI-Index') defined previously is a special case of our AAI functional. Third, we introduce the notion of a cognitive core of an agent relative to a battery and define the associated AAI_textrmcore score as the restriction of an AAI functional to that core. Finally, we use these notions to describe invariants of batteries under evaluation-preserving symmetries and outline how moduli of equivalent batteries are organized.