"Proofs" are a general term for a variety of options for seeing what your file will look like when printed is a proof. Think of it as evidence (proof) that what you put into your digital file will all come out on the printed page exactly as you intend: the right fonts, graphics, colors, margins, and overall positioning.
are used for checking that all text and graphics and colors come out as expected before going to press.
If the contract reads that you are liable for once you OK the proofs for any mistakes - then, regretfully, their negligence and spelling error is at your risk if not caught.
So, regretfully, once you OK'd the proofs - you're stuck with the proof and any errors.
You might have more of an argument if the spelling was incorrect on some common word like the word "the" and they made an error "hte" or something of the like. But when it's a specialized word like the name of an author - then it's your risk if you don't catch the mistake.
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