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Game lost?

I've already posted this in the game analysis forum, but probably this is the right place:

I lost this game on time but I'm sure that my opponent can't checkmate me even if I help him.
es.lichess.org/XDMYbm1f
If you move your King to h8 and promote your g-pawn to Bishop on g8, then he can mate you with Kg6 and Be5.
unfortunately he can. You promote to a knight put your king on h8, knight oh h7, Black king on f7 and plays Bh6-g7 mate...or if you promote to a bishop and put that on h7 then same thing - unlucky!
I played from this position against the computer and white wins or draws (if white plays the worst moves)
I played from this position, now without the computer, and black can mate as both of you said. Apparently the computer doesn't want to lose anyway, lol. Thanks
66... Bc6+ 67. Kxc6 Kc8 68. Bg2 Kb8 69. Bh1 Ka8 70. Bg2 Bb8 71. Kb6#
I think it should be a draw if you lose that position on time. However if you made the worst blunders in history they could checkmate you, but only after they give you a free promotion opportunity and an easy win. You'd have to collude with them to lose the game, but it could happen technically.
So the result depends on an assessment or an evaluation of the position? Who evaluates which cases?

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