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it's hard to argue that a crummy cosmos sidechain bound to Bitcoin with a kludgey solution to finality agreement does not really inherit the security.
If you are referring to Nomic and Babylon chains, they are using bitcoin to improve their own security (clearly so, solving the weak subjectivity problem) but not really "inheriting security" in the same way that an L2 does.
LN thus does not have weaknesses in the same way that Bitcoin has
What do you mean by this? LN does have a different security model than L1, introducing the dependency of the fault proof ("penalty tx") to prevent double-spending, making LN payments vulnerable to short-term miner censorship or L1 congestion.
I think an immediate disqualifier for a protocol to be called layer 3 when it rides on top of LN (and maybe tickles the main chain a bit for such as bonds), is that the network is aiming to achieve a similar goal.
Does LN not aim to achieve a similar goal as bitcoin L1 (p2p payments) only in a more scalable way? In any case, it seems arbitrary to me to say "this layer has the same use-case, so it's not really a new layer". imo the layer terminology should be applied independently of the use-case of the layer, and look moreso at the technical architecture and relationships to other protocols to determine whether it's really a higher layer or something else.
Yes, sidechains benefit from bitcoin but that doesn't mean anything if a small group of the userbase has outsized control over token issuance.
Bitcoin's weakness relates to reorgs and its slow, broadcast propagation pattern. Lightning's weakness is griefers and expiring/stuck channels.
I don't think what bitcoin does is at all similar to LN. There is a much weaker consensus in LN, because it doesn't have to share the state changes, only the p2p information for generating paths and a summary at the end of each channel, the security problems for LN come from mischief with channel partners and channel liquidity.
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