# Dynamic Level Sets

arXiv: https://arxiv.org/abs/2602.22530 · HTML: https://mlsanity.com/paper/2602.22530/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 0 of its 23 references that are in the map.
- First posted on arXiv 26 Feb 2026.

## Abstract (arXiv)

A mathematical concept is identified and analyzed that is implicit in the 2012 paper Turing Incomputable Computation, presented at the Alan Turing Centenary Conference (Turing-100, Manchester). The concept, called dynamic level sets, is distinct from mathematical concepts in the standard literature on dynamical systems, topology, and computability theory. A new mathematical object is explained and why it may have escaped prior characterizations, including the classical result of de Leeuw, Moore, Shannon, and Shapiro that probabilistic Turing machines (with bias p where p is Turing computable) compute no more than deterministic ones. A key mechanism underlying the concept is the Principle of Self-Modifiability, whereby the physical realization of an invariant logical level set is reconfigured at each computational step by an incomputable physical process.