sincere (adj.) — 1530s, “pure, unmixed, unadulterated;” also “free from pretense or falsehood,” from French sincere (16c.), from Latin sincerus, of things, “whole, clean, pure, uninjured, unmixed,” figuratively “sound, genuine, pure, true, candid, truthful” (unadulterated by deceit)

genuine (adj.) — “natural, not acquired,” from Latin genuinus “native, natural, innate,” from root of gignere “to beget, produce”

authentic (adj.) — “authoritative, duly authorized” (a sense now obsolete), from Old French autentique “authentic; canonical” (13c., Modern French authentique) and directly from Medieval Latin authenticus, from Greek authentikos “original, genuine, principal,” from authentes “one acting on one’s own authority,” from autos “self” (see auto-) + hentes “doer, being”

earnest (adj.) — “serious or grave in speech or action,” early 14c., ernest, from Old English eornoste (adj.) “zealous, serious,” or from Old English noun eornost “seriousness, serious intent” (surviving only in the phrase in earnest), from Proto-Germanic er-n-os-ti- (source also of Old Saxon ernust, Old Frisian ernst, Old High German arnust “seriousness, firmness, struggle,” German Ernst “seriousness;” Gothic arniba “safely, securely;” Old Norse ern “able, vigorous,” jarna “fight, combat”), perhaps from PIE root er– “to move, set in motion.”