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I thought I typed this reply but seems missing, here goes again:
Bridges will never sell above 1.01, of course. Emptying one side while selling for 1.01 is the best they can hope for.
I think there are times when Beeswap makes sense at 1.02. It is way faster than Hive Engine deposit/withdrawal methods.
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Sure, there are. OTOH, there is not much point in discussing those times. Once in a blue moon you can get a huge arbitrage opportunity you need to rush. In (current) practice, they can happen when BeeSwap has been empty for a while. And I do not think this is worth a "fix" as I would rather sell off one side for 1.01010101 (we have nitpick mode on) than miss out maxing in the hope for hitting 1.02 occasionally. Also, if the opportunity is so sweet, the bridge is not going to be fast enough anyway.
Theoretically but maybe not mathematically.