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Apropos of nothing - a random HP thought.
Where does half the fandom get the impression that Harry is cheating by using a book with notes in it?
They are allowed to use their book while brewing and are supposed to have read up on the potion they are preparing in class.
And in written tests, I doubt they are allowed to use their books anyway, so the notes won't be any help to him there.
The only difference I see between Harry and a Ravenclaw (in this instance) is that the Ravenclaw would have made the notes himself - and probably not in the book, but on a spare bit of paper.

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And this is where I have to sit back and think because, correct me if I'm wrong, but didn't Harry indeed take the steps to verify that the instructions worked? When the notations said to "crush [the roots] with flat side of silver dagger, releases juice better than cutting." (p. 189, Scholastic edition), Harry tried it. And it worked. And, if I recall properly, he did test every notation in the book, though more than most of the experimentation was done in class.
How I wish I had the book with me! If you're right that Harry does work outside of class as well as in class, then you've basically invalidated my argument - I honestly thought he only tested those notes whilst in class. If, however, Harry does only test the HBP's conclusions during class, then he's just coasting along using someone else's work and not doing the extra work needed to justify using his value-added recipe book.
I'm afraid I regard the annotated book as the equivalent of Harry having a personal tutor next to him in a test situation telling him what to do. Had he spent some time in learning the improved instructions by heart, then I would not have a problem with him using the book - and if the book states that Harry did spend his own time testing out the Potions recipes outside of class, then I concede defeat ;)