acknowledge

(transitive) To admit the knowledge of; to recognize as a fact or truth; to declare one's belief in

(transitive) To own or recognize in a particular quality, character or relationship; to admit the claims or authority of; to give recognition to.

(transitive) To be grateful of (e.g. a benefit or a favour)

(transitive) To report (the receipt of a message to its sender).

(transitive) To own as genuine or valid; to assent to (a legal instrument) to give it validity; to avow or admit in legal form.