Neither "born" nor "borne" is a word I see used much in the material I edit, but it came up recently:
However, this hypothesis remains untested, and the value of the [thing being discussed] will be born out as [these other things happen in the future].
The author didn't mean born, though. Born is an adjective (e.g., "she is a born sailor," meaning that she has a natural talent for sailing) or part of the verb phrase to be born (e.g., "he was born on December 8). The author was looking for borne, which is the past participle of to bear (e.g., "its value will be borne out," "she has borne two sons," or "the disease was airborne but not foodborne").