Establish the Modest Physical Church–Turing thesis

Establish whether the Modest Physical Church–Turing thesis holds; specifically, determine whether every physical process that constitutes a computing system is computable by a Turing machine.

Background

The paper distinguishes between Bold and Modest formulations of the Physical Church–Turing thesis. While there is a common agreement favoring the Modest form, the authors explicitly note that this agreement remains unproven.

Resolving the status of the Modest Physical Church–Turing thesis would clarify the relationship between physical computation and Turing machine computability, with implications for understanding whether certain physical or biological processes (including aspects of human intelligence) fall within Turing-computable bounds.

References

With the advent of digital computers and the rapid advancements of information theory since the original work of Church and Turing, a common agreement (although yet unproven) has settled among researchers in favor of the Modest Physical CT.

— On the Computability of Artificial General Intelligence (2512.05212 - Mappouras et al., 4 Dec 2025) in Section 4.1(c) (Origins of Human’s General Intelligence)