'Codex in Xcode can probably take an entire ObjC project and convert it to Swift on its own'

Alright, bet.

I handed it the classic SameGame codebase, gave it my coding style markdown file, and said "So this is an old ObjC app for iOS. I would like you to completely convert it 1:1 to modern Swift, with the coding style in mind. Leave no ObjC behind"

No other prompts needed; I needed to update a few legacy things in the xcode project settings (min OS version, Swift version, etc), and got this:

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