peroxydisulfate (usually in conjunction with silver catalysis, sometimes copper or other metals) is a fascinating organic reagent that's of use in certain oxidation and free-radical reactions, in organic chemistry
for instance the "Elbs hydroxylation" uses persulfate for para-hydroxylation of phenols (e.g. phenol to hydroquinone)
there's some similarity here in that the species attacking the aromatic ring is an oxygen species, probably the -COO. radical
such free-radical reactions tend to have, at best, "moderate" yields and to produce by-products because of the high reactivity of free-radical intermediates. but intramolecular substitution, as here, seems to improve yields considerably. looks like electron-withdrawing groups on the phenyl ring (e.g. nitro, trifluoromethyl) decrease the yield to roughly 50% or lower. still okay, honestly