'well-substantiated' originates from English, specifically combining the adverb 'well' (Old English 'wel') meaning 'well' and the past-participle adjective 'substantiated' from the verb 'substantiate', which ultimately derives from Latin 'substantia' meaning 'substance'.

'substantia' in Latin gave rise to Medieval/Modern Latin forms related to 'substantiate' (to give substance or real existence). This developed into English 'substantiate' (17th century) and its past participle 'substantiated'; later the adverb 'well' was prefixed to form the compound adjective 'well-substantiated'.

Initially related to giving 'substance' or reality ('to make substantial'), the sense shifted toward 'providing evidence or proof'; today it means 'supported by sufficient evidence'.