To the OP. I've been riding track bikes with fixed cogs for over 40 years on the road and have learned some things about properly tightening a track cog so that it won't unscrew when you backpedal. The best way I've found is to screw on the cog by hand, install the wheel in the bike, brace the front wheel against a wall and stand on the the front facing pedal with all your weight. The more you weigh, the tighter it will get, such that it is physically impossible to overcome the tightening torque no matter how hard you backpedal. After that, remove the wheel and install the lock ring snug tight, nothing more.
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