When the next (2nd) millennium prize problem is solved, that year and all future years will resolve yes.
The publication date of the solution (without significant gaps) will be used (UTC). To count, a large majority of the mathematical community has to view it as a valid solution. (This is almost certainly equivalent to the Clay institute offering to award the prize.)
A particular year will resolve no if at least one month into the next year no serious solution has been posted. A solution proposed by anyone not affiliated to a research institute is not considered serious unless a professional mathematician has highlighted it as such. A solution stops counting if it has been debunked a month ago without satisfactory response from the author(s).