'tacit assumption' is correct and usable in written English.
You can use it to describe an assumption that has been made without saying it explicitly. For example: "The tacit assumption in this room was that the decision would go my way."
That quibble aside, however, there also seems to be a tacit assumption that similarity equals descent.
Parents make a tacit assumption of sexual activity, and "that presents a problem for a lot of people," she said.
Even so, that argument — that Iran has already crossed an important line — is the tacit assumption behind the new accord.
Digital camera manufacturers operate on a tacit assumption that everyone has a computer for downloading the images from the camera.
"They seem to employ a tacit assumption that officers need to know this because they are somehow corrupt.
But there's almost a tacit assumption that if something you say has been written down, it is worthy of record.
If the parties shared an incorrect tacit assumption about some low-probability event, performance would be excused (the shared-assumption test).
Deterministic gating models are based on the (often tacit) assumption of a very large number of channels, each having a very small conductance.
The "tacit assumption" among executives "is that life is fundamentally and always a competition". But humility and ambition, he argues, need not be at odds.
What is interesting about Anne Rice is her tacit assumption that there is no such thing as a liberal Christian identity.
What this tacit assumption of an agreed-upon standard requires is that we fall in line with whichever up-to-the-minute theory of desirable sexual dynamics prevails.
