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What does "guarantee" mean here? If you end a function in BEAM with another function call, it's TCO.

Tail Call Optimization is an optimization done by the compile/vm that replace (in assembly terms) a CALL by a JMP. Therefore removing a call stack.

Correct. BEAM does real TCO as far as I'm aware. LYSE has a blurb about it and seems to agree (https://learnyousomeerlang.com/recursion).