By "fact" we mean "a piece of information about which there is no serious dispute."

None of these changes is, I venture, subject to serious dispute.

We followed a serious dispute between ducks from, I would say, half a mile away.

The size of the buildup is not in serious dispute.

He said that his office had no serious disputes with other state or Federal prosecutors.

The decision whether to hear the appeal or wait for a better case was evidently the subject of serious dispute within the court.

Beyond that minimum, however, the role of family experience is in serious dispute.

In case of serious disputes, those same friends act as arbitrators.

There is no serious dispute about that in his party.

But, in fact, there is serious dispute, as the briefs themselves make clear.