acceptedly
adv. manner C1 Advanced ac·cept·ed·ly
adv. in a way that is widely believed to be true or correct. You use this when something is generally agreed upon by most people.
adv. in a manner that is generally acknowledged or believed to be true. Often used to describe a widely held opinion or a standard that is not in dispute.
The theory is acceptedly the best explanation for the event.
In many cultures, it is acceptedly the case that the eldest child takes on the most responsibility.
While the initial data was controversial, the subsequent findings are now acceptedly the most reliable evidence available for the study of that specific geological period.
From accepted + -ly.