Rearrangement of an oxyallyl cation I am supposed to predict the product of rearrangement of this cation, having been told that it's an oxyallyl cation:



I did have a look at the Wikipedia entry (since it mentions "oxyallyl cation") and not even once does it mention such a compound as I have shown above. This question is from my high school text book chapter on "Aldehydes and Ketones", and I'm not sure I'm even supposed to know what to do here in the first place.

Anyways, I did guess that the negatively charged oxygen atom will donate its lone pair to the positively charged carbon atom1, forming a three member hetero-ring. But, my book gives the correct answer as:



I'm not sure where they dumped the second oxygen atom (and from where they brought an extra carbon atom) to form this all-carbon ring. Also, is that $\ce{-OMe}$ at the ortho position only for ornamental purposes, or does it affect the mechanism in some way?



Source: MS Chouhan; Advanced Problems In Organic Chemistry; 11th ed; page 218 in solution manual, Q91 chapter on Aldehydes and Ketones



1: Yeah I know that all these atoms are in conjugation and the charges are only partially negative/positive.
Count carbon and oxygen atoms in the book's answer versus the original molecule, and infer that the book got it wrong.  One of the carbon atoms in the book's answer should be oxygen.  Question for you:  Which one?