The noun for substantiating: the act of proving a claim with evidence, or the evidence itself. It is a heavy, formal word, and it lives almost entirely in legal papers, official reports, advertising rules and academic writing — 'the claim was made without substantiation', 'the regulator asked for substantiation of the health benefits'. In speech, even careful speakers usually go around it and say 'proof', 'evidence', or just use the verb: 'he could not prove it'. Two useful habits. It is normally uncountable, so you say 'some substantiation', not 'a substantiation'. And it appears most often after 'without' or 'lack of', because the interesting moment is usually the one where evidence is missing. If you are choosing between this and 'proof' in your own writing, 'proof' is nearly always the better choice; use 'substantiation' when you are matching the tone of an official document.

佐證、證實（提出證據支持說法這件事，或那些證據本身）