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Was it legit to draw this game by perpetual ?

With the engine, it says there's a Mate in 8. However, I wouldn't have seen it. I played along a bit... it was a draw.
35...g5+ 36. fxg5 hxg5+ 37. Kxg5 Qh5+ 38. Kf4 Qf5+ 39. Kg3 Bh5 40... Qf3+ 41. Kg2 Qd1+ 42. Kg2 Qe2+ 43. Kg1 Bf3 difficult to calculate until mate but at least you're unlikely to lose by playing this. Over the board I would probably have taken the draw, depending on how much time I had.
i can't say if i would have seen the mate under "normal" conditions (i did feel that the way you phrased the thread implied there was something) but this was my first assessment:
- white has no immediate threat
- Qf3 forces Kh4, and then g6 is at least a perpetual (Qg2-Qh2), and possibly more

so yeah, i do find it at least a bit inaccurate to take the perpetual immediately
Without engine I would say white's king is eventually into trouble and is risking being caught in a mate net somehow. I would try to look for a way to benefit from that. Looking briefly at the position I can't see a forced mate but the character of the position says there eventually is one.

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