The unglossed headword, Hellenized from the Latin word processus, is a masculine noun in the accusative singular; see generally Sophocles [below] s.vv. pro/kensos and pro/kessos. Of its several meanings, the one likely to be relevant here is the ceremonial public appearance of an emperor or consul.
[In her critical apparatus Adler reports that ms F omitted this entry.]
The headword is first attested at Vitae S. Danielis Stylitae 55.24 (C5 CE): *kai\ pro/kenson poih/sas o( basileu\s a)nh/gagen au)to\n pro\s to\n o(/sion kai\ dihgh/sato au)tw=| th\n e)piboulh\n tou= *)ardabouri/ou kai\ th\n eu)noian tou= *zh/nwnos, (And the Emperor, making a formal procession, led him [the Isaurian Zeno] before the holy man [sc. Saint Daniel the Stylite] and explained to him Ardabourios' subterfuge and Zeno's good will).
The emperor here is Leo I, 400-474 CE, emperor 457-474; OCD(4) s.v. Leo (2), PLRE s.v. Leo (6), and lambda 267. On Ardabourios (Ardaburius, Ardabur, consul 447, d. 471), see also PLRE s.v. Ardabur (1) and alpha 3803. Probably in 466, at the time of the appearance before Saint Daniel, Zeno (Zenon, Tarasicodissa, emperor 474-491, d. 491), a native of Isauria (a mountainous interior region of southern Asia Minor: Barrington Atlas map 66 grids A2-C3; OCD(4) s.v.), presented documents to Leo implicating Ardabourios in a plot with the Persians; see PLRE s.v. Zenon(7), zeta 83, and zeta 84.