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Statechains are an original second layer protocol originally developed by Ruben Somsen in 2018, depending on the eltoo (or LN Symmetry) proposal. In 2021 a variation of the original proposal, Mercury, was built by CommerceBlock. In 2024, a further iteration of the original Mercury scheme was built, Mercury Layer.
Like Ark, Statechains depend on a centralized coordinating server in order to function. Unlike Ark, they have a slightly different trust model than a vUTXO in an Ark batch. They depend on the coordinating server to delete previously generated shares of a private key in order to remain trustless, but as long as the server follows the defined protocol and does so, they provide a strong security guarantee.
The general idea of a Statechain is to be able to transfer ownership of an entire UTXO between different users off-chain, facilitated by the coordinator. There is no requirement for receiving liquidity like Lightning, or the coordinator server to provide any liquidity like Ark.