In a way that provides or relates to evidence; according to what can be proven or demonstrated.
From 'evidential' plus the adverb suffix '-ly', which transforms adjectives into adverbs showing manner or quality. This follows a productive pattern in English dating back to Old English.
The suffix '-ly' is so common that we barely notice it, but it transformed hundreds of adjectives into adverbs—it's one of the most productive and useful word-building tools in English.
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