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I assume this default limit of 2^24 is set by some purpose in BOLT #2. But what's the meaning of that? Or is there any test/experiment to support this number?

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The goal was to limit the amount any individual adopter would lose due to bugs in the software. As explained by LN developer Rusty Russell in #bitcoin-lightning FAQ: Why the 0.042 bitcoin limit?:

I guarantee that early releases of lightning clients will have bugs and people will lose money because of them. […] I sleep better at night knowing that, if you lose money because of my bug, I can buy you a beer/coffee in exchange for your story and we’re about even. (emphasis in original)

This answer was sourced entirely from Bitcoin Optech: Large Channels where you can find even more resources on this topic.

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