You searched for: “presumably
presumably, supposedly
presumably (pri ZOOM uh bli) (adverb)
Regarding how something is assumed to be true without specific facts: Walt was presumably not aware that it would be sunny in the afternoon.
supposedly (suh POHZ uhd li) (adverb)
Pretendingly, allegedly, believingly: Ronda was supposedly Wilber's best friend and he could not imagine that she would tell such lies about him.

Supposedly the family should be able to drive to the city and home again in three hours.

David supposedly was to have started the new job last week. He had hoped to receive the contract to sign two weeks ago; but it was presumably delayed in the mail.