noun, na-adjective, noun which may take the genitive case particle 'no'
already well aware; knowing full well
A formal, somewhat literary yojijukugo meaning one is already fully aware of something, often used to acknowledge prior knowledge or to indicate that something is already understood.
その件については先刻承知しております。
I am already well aware of that matter.
先刻承知の事実だが、改めて確認したい。
It is a fact we are already well aware of, but I would like to reconfirm it.
A yojijukugo combining 先刻 (already, previously) and 承知 (knowing, understanding). The exact historical derivation is uncertain, but it follows a common pattern of four-character compounds used in formal writing.