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Runs out of time and WINS??!!!!!!!!!

All of us know the rule of time: The player who runs out of time loses if the opponent has a chance of checkmating the player who runs out of time (even if theoretically). Otherwise, the match is claimed to be a draw.

However, consider this position (white to move). The only possible scenario is
1.   d4        b5
2.   d5        b4
3.   axb4   a3
4.   b5        a2
5.   b6        a1Q   (or a1R, a1B, a1N)
6.   b7#

It is noticed that none of the two players has any other options. Both players are forced to play the previous line.

One of the chess players in my country asked a question: If this position was in a real tournament and the WHITE player ran out of time before his/her sixth move, what is the decision of the judge?
Some chess coach insist that the white player should win!!!!
They claim that this would be one of the rarest moments that the player who runs out of time wins, as the opponent could do nothing to alter this result even if he/she had the authority to play with both the white and black pieces together.

I wish to know the opinion of everyone who read this especially the grandmasters moderators of this forum, in this critical situation.

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