= Solution
This is an \b[acid-catalysed <alpha-ketol rearrangement>]. Label the original <ketone> <carbon> $C_A$ and the adjacent <tertiary alcohol> <carbon> $C_B$. Protonate the <oxygen> on $C_A$ to activate that <carbonyl>. The appropriately aligned cage C–C <sigma bond> attached to $C_B$ migrates onto $C_A$, while the hydroxyl <oxygen> at $C_B$ supplies its lone pair to form the new $C_B=O$ bond. At the same time the old $C_A=O$ <pi bond> moves onto <oxygen>, which becomes the new $C_A$–OH. <deprotonation> regenerates the acid.
The migration reroutes the bridge rather than removing water: \b[the original <alcohol> <carbon> becomes the <ketone>, and the original <ketone> <carbon> becomes the <tertiary alcohol>]. A productive conformation aligns the migrating sigma orbital with the accepting <carbonyl> pi-star orbital; the <oxygen> lone pair simultaneously overlaps the developing <p orbital> at the donor <carbon>. The cage's geometry controls which adjacent <sigma bond> has the necessary alignment and which less strained skeletal isomer results. A freely rotating isolated <carbocation> or a simple proton shift cannot account for the changed cage connectivity.
\Image[/past-exam-of-the-chemistry-course-of-the-year-4-of-the-natural-sciences-course-of-the-university-of-cambridge/2022/paper-3-ketol.png]
{title=Original atom-tracked alpha-ketol migration and orbital-alignment model}
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