The headword is faultily transmitted as Poithioi both here and already in Photius (pi998 Theodoridis). In fact these are the Spartans' Pythioi (so, correctly, in Timaeus' Platonic Lexicon), 'four persons whose office it was to consult the Delphic oracle on affairs of state' (LSJ s.v.; cf. generally pi 3127, pi 3128, pi 3129, pi 3130). See, for this nominative plural, Herodotus 6.57.2 and (with content akin to the lexicographers' gloss) Xenophon, Constitution of the Lacedaimonians 15.5.