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I've been reading about the working of LN. I had this interesting thought, what if we dont need the main blockchain and the miners to have a p2p cash system. Let me explain.

The difference between the current LN and what I thought is, people have channels only with the people they know and trust. There wont be any multisig wallet(may be set a limit for each channel based on their trust of the other person). And when they wanna close the channel, they transact in real life either with bitcoin or fiat (whatever unit they are using). Since it the people they trust there wont be any cheating problem.

This will be a completely p2p system. Would such system work? Am I missing anything?

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You've basically described Ripple (aka XRP). You may want to read up on it - and specifically, criticism of it that can help illuminate why this system does not offer the same benefits that Bitcoin's does.

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  • The difference between ripple and this would be, ripple need a validating node and this is completely only peers – Mani Bharathy Apr 22 at 22:59
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    I think the system described by OP much more closely resembles the old pre-XRP Ripple system by Ryan Fugger. – Pieter Wuille Apr 22 at 23:13
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As Meni and Pieter have pointed out, you seem to be describing the original Ripple system (described and centrally implemented before the Ripple/XRP company, and even before Bitcoin).

One main point that hasn't been mentioned before is that this system isn't based on a bearer asset like Bitcoin but on debt instead. So it would be a F2F (friend-to-friend) debt channel network instead of a P2P cash channel network like Lightning is.

This has many implications that probably prevent such a system from scaling widely. For example, it would be hard for large companies to be part of such a system since they would need to trust all their customers.

I'm not saying that it couldn't work, but it would be a system with very different properties and there is probably a reason why it hasn't taken off long before Bitcoin.

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Under the given assumptions such a system would work. However I highly doubt the assumptions

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