# Dual Computational Horizons: Incompleteness and Unpredictability in Intelligent Systems

arXiv: https://arxiv.org/abs/2512.16707 · HTML: https://mlsanity.com/paper/2512.16707/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 12 references that are in the map.
- First posted on arXiv 18 Dec 2025.

## Builds on (most cited first, 4 of 4)

- [Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability](https://mlsanity.com/paper/2103.00065/) (2021)
- [Mechanistic Interpretability for AI Safety -- A Review](https://mlsanity.com/paper/2404.14082/) (2024)
- [Stable Architectures for Deep Neural Networks](https://mlsanity.com/paper/1705.03341/) (2017)
- [Robust AI Security and Alignment: A Sisyphean Endeavor?](https://mlsanity.com/paper/2512.10100/) (2025)

## Abstract (arXiv)

We formalize two independent computational limitations that constrain algorithmic intelligence: formal incompleteness and dynamical unpredictability. The former limits the deductive power of consistent reasoning systems while the latter bounds long-term prediction under finite precision. We show that these two extrema together impose structural bounds on an agent's ability to reason about its own predictive capabilities. In particular, an algorithmic agent cannot verify its own maximal prediction horizon universally. This perspective clarifies inherent trade-offs between reasoning, prediction, and self-analysis in intelligent systems. The construction presented here constitutes one representative instance of a broader logical class of such limitations.