What does it mean to prove the halting problem is undecidable "using arithmetization"?

In version gamma of the ACM/IEEE/AAAI Computer Science Curricula 2023, on page 50, one of the illustrative learning outcomes for the "Computational Models and Formal Languages" section of the curriculum states that students should be able to

Use arithmetization and diagonalization to prove Turing Machine Halting/Undecidability.

I am quite familiar with using a diagonalization argument to prove that the halting problem is undecidable, but what does it mean to use arithmetization to prove this result? I don't believe I've come across a proof using this technique in any texts I've read before. Everybody seems to go with the diagonalization argument.

I would guess/assume that by "arithmetization", they mean the concept that every Turing machine can be associated with a bit-string or natural number (the fact that we can encode a description of a Turing machine as a bit-string and hence as a natural number). See, e.g., https://en.wikipedia.org/wiki/Halting_problem#Formalization.

In other words, the requirement is not that students should know how to use diagonalization to prove Turing Machine Halting/Undecidability, and also know how to use arithmetization to prove Turing Machine Halting/Undecidability. It is not that there are two separate ways to prove the undecidability of the halting problem and students should know both. Rather, it is that there is a standard proof of the halting problem, and this proof relies on both diagonalization and on "arithmetization" as defined above, and students should know the standard proof and grok those two aspects of it.

StackExchange Computer Science Q#162901, answer score: 14