Church's Thesis is not a mere empirical conjecture but is supported by the mutual reducibility of all known models of computation, constituting a form of mathematical convergence evidence distinct from physical induction.

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Church's Thesis(Also called the Church-Turing Thesis; surveyed in Section 1.6 of the source text.): The claim that the class REC coincides with the class of effectively computable functions.
Mathematical convergence evidence(what the mutual reducibility of computation models provides as support for Church's Thesis): A type of proof where independent ideas, approaches, or systems all arrive at the same answer or conclusion, suggesting the conclusion is probably correct.
Models of computation(what Church's Thesis claims are all equivalent to each other): Different theoretical systems or machines designed to solve problems using step-by-step instructions; examples include Turing machines, lambda calculus, and other abstract computing frameworks.
Mutual reducibility(the relationship between different models of computation that supports Church's Thesis): The ability of different systems to be converted into or translated into each other without losing power—meaning if one system can solve a problem, so can the other.

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