That definition doesn't make sense, nor it is desirable to have a custodial solution for stablesats, as we can do it in a decentralized way. Also sats are fungible in LN
How would you define the process of putting dollars on the LN?
US dollars will (and should) be centralized. Anything else is a counterfeit of the dollar without regulated backing for debt—on something already stamped with authority of the state. Without regulation on their issuance and backing, they'll never be used or accepted in regulated commerce.
Stabesats are different than what I'm describing. Those require a derivative, usually a perp contract position from a business playing the jurisdiction game, which I don't like for multiple reasons.
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There is no safe way to put dollars on LN, because you cannot run smart contracts on it, so there is no way to do a trustless derivative. All dollars on LN require some level of trust, which is suboptimal at best.
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Yes you can run smart contracts on both the LN and L1. Taproot has brought significantly more functionality, but so has miniscript, we have DLC's, and rumors a PBSTv2 is in the works.
And of course there are safe ways to put dollars on the Lightning Network, TARO and others aim to do just this. Nobody said such things would be decentralized though, because dollars are a nation state currency stamped with authority of the state to begin with. Nobody in a decentralized game should be trying to make centralized nation state fiat function in a decentralized way to begin with. Thusly, I wouldn't touch any digital dollars or digital dollar equivalents that weren't regulated.
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You are just talking about L1 scripting. In LN we don't even have multisig. TARO is not a safe way to put dollars on the LN, they are a way to put IOUs, which carry a counterparty risk. Even your precious regulated instrument carries counterparty risk. Unlike a dollar denominated token that can be redeemed trustlessly in a smart contract at any time for it's equivalent value in BTC. Math > regulation, welcome to bitcoin.
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