Multiple independent formal systems (TMs, lambda calculus, recursion) achieving identical computational boundaries strongly suggests discovering fundamental limits rather than arbitrary choices.

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Computational boundaries(in computability theory): The limits of what problems any computer or mathematical system can solve—some problems are fundamentally unsolvable no matter how powerful the computer is.
Formal system(as used in logic and mathematics): A set of rules and symbols (like mathematical axioms) that you use to prove whether statements are true or false, similar to how a chess game has specific rules that determine what moves are legal.
Fundamental limits(in philosophy of mathematics and computer science): Rules or constraints that exist in nature or logic itself, rather than being caused by human choices or technology—they would be true regardless of how we try to work around them.
Lambda calculus(as used in logic and computer science): A formal mathematical system for studying functions and how they work; it's another way of thinking about computation, alternative to Turing machines.

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