Are some bitcoin nodes known to be run by a particular entity? E.g. do we know which nodes Kraken runs, if any? LN nodes are commonly "claimed" by their owners, but not bitcoin. But ip addresses are leaky, etc. It would be useful for estimating economic weight of various nodes.

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Any way to publicly tie an LN node to the Bitcoin node it relies on?

Not that I'm aware of

If there are ways, they are probably bugs. I imagine that if an LN protocol dev found out there was a way for a third party to identify what backend an LN node was using, they would try to fix that, because it leaks information that is none of the third party's business

That said, you can have some confidence that the LN node must use a backend that supports segwit, and there may be other info you can glean

If they share the same public IP there is probably a high chance they belong together? (If the backend is configured to listen too)

Ah, smart! I may be able to build some useful data using that assumption...

That would give the wrong result, in my case. The Bitcoin node my lightning node uses is Tor-only, while the node using the same IP as the lightning node is completely different. Then there's a third mining node on the same LAN.

don't dig too deep

While Lightning nodes prioritize fast responsiveness and expose their regular IP addresses, most Bitcoin nodes communicate through Tor, making it difficult to infer anything from their IP addresses.

Robosats Lightning nodes run on Tor.