You can take a screenshot at different points during the battle, and who will believe that it froze exactly at the spot where the screenshot was taken. And if a real desynchronization occurred, there will just be 2 different screenshots. What's the point?

The point is:
firstly, it shows the progress of the battle (which is why streamers with video recordings will always have an advantage)
secondly, if you prove your words, and your opponent doesn't, it's easier for the judges to make a decision
thirdly, send the saves to Baratortch, maybe he'll find something
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If it is impossible to continue the game, there is only one way out - awarding the victory, so the judges will be guided by all the materials that the participants provide.

Added 1 minute ago
P.S. No, there is another option: disband the troops, etc., and continue the game, but this is a very laborious option, especially if large armies were fighting, and the desynchronization occurred somewhere at the beginning of the battle. There is another important point here! to track at what stage the bug occurred - that's another reason why screenshots are needed