= Solution
Both permitted alternatives follow the same condensation–activation–migration sequence. <sodium> <acetate> liberates a useful concentration of <hydroxylamine> from its hydrochloride while providing a buffered medium. <nitrogen> of NH2OH attacks the <ketone> <carbonyl>; <proton transfer> gives a <carbinolamine>. <protonation> of its <carbon>-derived OH and loss of <water>, with <nitrogen> lone-pair donation, then gives the <oxime> after <deprotonation>. The two C=N geometries can be separated.
For the \b[B-to-D route], <oxime O-tosylation> begins when <oxime> <oxygen> attacks <sulfur> of <tosyl chloride> and <chloride> leaves; <triethylamine> accepts the released <proton>. The resulting O-tosyl <oxime> has an excellent leaving group. The $K{-}R_a$ bond, anti to N–OTs, migrates to <nitrogen> while N–O cleaves, giving a ring-expanded <nitrilium ion>. Its local connectivity is $R_s{-}K\equiv N^+{-}R_a$, with the existing scaffold still joining the two paths. <water> attacks the nitrilium <carbon> $K$. <proton transfers> and imidic-<acid (chemistry)>/<amide> <tautomerization> produce D, with <nitrogen> inserted on the aromatic side of the old <carbonyl>.
For the \b[C-to-E route], the same O-tosylation activates the other <oxime> geometry. Now the anti bond is $K{-}R_s$; its migration gives $R_a{-}K\equiv N^+{-}R_s$, and aqueous trapping produces E, with <nitrogen> inserted on the spiro-junction side. \b[Each <Beckmann rearrangement> expands the <ketone>'s six-membered ring to a seven-membered <lactam>.] The original <carbonyl> <carbon> remains the <amide> <carbonyl> <carbon>; <nitrogen> is the inserted atom. In this mechanism the <ketone> <oxygen> is lost during <oxime> condensation, the <oxime> <oxygen> leaves with the <sulfonate> group, and <water> supplies the new <amide> <oxygen>.
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