user8661: I've read about "mate prevails" here on this site, but I couldn't get a clear view on one odd point. I get that the mating move prevails, but if you couldn't do it before your flag falls, you lose.
Let's say it's my opponent's turn. I'm about to mate in 1. They hit the clock, and I run out of time. Then he notices it and claims it while I'm performing checkmate, at the exact same time.
Under FIDE rules, what happens?

user924: If no arbiter saw this happening and there is a dispute, then the player who claims the flag fall can't prove that it happened before the move. The player who checkmated the opponent can show that he did (the position is on the board). So the checkmate will win.
If an arbiter saw what happened, a solution is probably possible, after all the claim of a win on time (or the arbiter announcing same) will happen slightly after the flag fall. If the claim and the checkmate occur at the same time, then the flag fell first and he lost on time. If the flag fall and the checkmate occur at the same time, then the claim was late and the checkmate stands (the game is already over, so claims are irrelevant).

user8844: Theoretically the situation is very simple, whichever happens first stands. In practice it is often difficult to determine what happened first though. 
If you insist that both the flag falls and the mating move is made at exactly the same time (the same nanosecond say) then my answer would be that this can never happen. It is as in statistics - the probability of a single point is zero, i.e. two events cannot happen at the same time. 
As an arbiter you need to decide according to what you believe happened first. How to determine that is an old question (with no clear answer obviously) but that is not what your question is about if I understand it correctly . 

8661: <p>I've read about &quot;mate prevails&quot; <a href="https://chess.stackexchange.com/questions/9042/mate-prevails-chess-rule">here</a> on this site, but I couldn't get a clear view on one odd point. I get that the mating move prevails, but if you couldn't do it before your flag falls, you lose.</p>
<p>Let's say it's my opponent's turn. I'm about to mate in 1. They hit the clock, and I run out of time. Then he notices it and claims it while I'm performing checkmate, <strong>at the exact same time</strong>.</p>
<p>Under FIDE rules, what happens?</p>
 924: <p>If no arbiter saw this happening and there is a dispute, then the player who claims the flag fall can't prove that it happened before the move. The player who checkmated the opponent can show that he did (the position is on the board). So the checkmate will win.</p>

<p>If an arbiter saw what happened, a solution is probably possible, after all the claim of a win on time (or the arbiter announcing same) <em>will happen slightly after the flag fall</em>. If the claim and the checkmate occur at the same time, then the flag fell first and he lost on time. If the flag fall and the checkmate occur at the same time, then the claim was late and the checkmate stands (the game is already over, so claims are irrelevant).</p>
 8844: <p>Theoretically the situation is very simple, whichever happens first stands. In practice it is often difficult to determine what happened first though. </p>

<p>If you insist that both the flag falls and the mating move is made at exactly the same time (the same nanosecond say) then my answer would be that this can never happen. It is as in statistics - the probability of a single point is zero, i.e. two events cannot happen at the same time. </p>

<p>As an arbiter you need to decide according to what you believe happened first. How to determine that is an old question (with no clear answer obviously) but that is not what your question is about if I understand it correctly . </p>
