In a manner that relates to or is based on trust, confidence, or fiducial measurements; done in a reliable and trustworthy way.
This adverb form derives from 'fiducial' plus the English adverbial suffix '-ly.' It maintains the sense of trust and reliability from its Latin root while indicating the manner in which something is done.
By adding '-ly' to 'fiducial,' English speakers created a way to describe actions done in a trustworthy, reliable way—you might fiducially rely on something, meaning you can trust it completely.
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