= Solution
The first transformation is an <Achmatowicz rearrangement>, followed by protection and selective reduction; the last is a <Johnson-Claisen rearrangement>.
* Butyllithium removes the furan 2-proton, giving a 2-lithiofuran. Its carbon attacks the <aldehyde> <carbonyl>; <protonation> of the resulting alkoxide gives the furfuryl alcohol. Carbon-carbon bond formation occurs at the lithiated position.
* Electrophilic oxygen transfer from mCPBA to the electron-rich furan gives an oxidized, ring-opened intermediate. Opening the oxygenated furan gives a hydroxy enedicarbonyl: the original furfuryl hydroxyl then attacks the remote <aldehyde> intramolecularly. This expands the five-membered furan into a six-membered <lactol> containing an enone <carbonyl>. The original furfuryl oxygen becomes the pyran ring oxygen; oxidation of the furan supplies the new <carbonyl> and <lactol> functionality.
* Ag$_2$O/MeI converts the <lactol> OH into its methyl <acetal>: oxygen attacks methyl iodide by <SN2 reaction>, with iodide removal and proton transfer. This protects the anomeric position.
* LiAlH$_4$ delivers hydride to the remaining <ketone> <carbonyl>, followed by <protonation>. The methyl <acetal> survives these basic reducing conditions, leaving the depicted allylic alcohol.
* Under weak-acid catalysis, that allylic OH replaces an ethoxy group of triethyl orthoacetate. Loss of another ethanol molecule, with removal of a methyl proton, gives the mixed <ketene acetal> $\mathrm{CH_2=C(OEt)-O-(allyl)}$. A six-electron, chair-like <Claisen rearrangement> breaks the allyl-O bond, forms a bond between the terminal allyl carbon and the ketene-acetal CH$_2$, and moves the ring double bond one position. <Carbonyl> formation gives the $\mathrm{-CH_2CO_2Et}$ substituent.
The <acetal> protects the other oxygenated position during hydride reduction. The orthoester transfers an acetate-derived two-carbon unit through a <ketene acetal>; it does not directly substitute the allylic OH with an intact acetate ion.
<Simple stereoselective version of the Claisen rearrangement by William S. Johnson and colleagues>{ref}
\Image[/past-exam-of-the-chemistry-course-of-the-year-3-of-the-natural-sciences-course-of-the-university-of-cambridge/2022/paper-4-sigmatropic-map.png]
{title=Atom maps for the allylic ketene-acetal and ammonium-ylide rearrangements}
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