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If hysterisis is “to lag” then what is “to lead” in greek?
The verb ‘to lead” is hegeōmai, but that’s not quite what you’re asking.
hysterisis is a noun, derived from the verb hysterizō “to come after, to come late” (e.g. to lag), which in turn comes from the adjective hysteros “latter, last”. Your question sounds like it’s asking “what’s the opposite of hysteresis?” The opposite noun would have to come from a verb derived from proteros “earlier” or prōtos “earliest, first”.
The verb exists: prōteuō “to be first, hold first place”. The corresponding noun, prōteusis, has been used at least once, in a monastery legal deed from 1012, although its meaning in context is “precedence, foremost position” (that is, holding first place).