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Q. I have always thought that the only time one uses capitalization after a semicolon is when it is followed by a proper noun (or a word like I). As a mathematics editor, I’ve encountered capitalization after a semicolon with two different publishers (“No; Possible answer: they can find . . .”). I’ve searched for an answer in CMS but no luck.
A. CMOS probably doesn’t cover this because it’s never come up before! Uppercasing after a semicolon in running text (other than a proper name) is likely to look like an error.