Prove or refute the Church–Turing thesis

Establish whether the Church–Turing thesis holds; specifically, determine whether every effectively computable method can be computed by a Turing machine, or provide a counterexample that refutes the thesis.

Background

The paper’s formal argument about AGI’s incomputability is grounded in the Church–Turing thesis, which posits that all effectively computable methods are computable by a Turing machine. The authors explicitly acknowledge that the thesis remains a conjecture and is unproven, making it a central unresolved issue in computability theory.

Because the paper’s main conclusion relies on the Church–Turing framework, the truth or falsity of the Church–Turing thesis directly impacts the scope and interpretation of their results. Clarifying this foundational question would solidify or challenge the theoretical basis for claims about the limits of computation.