From my understanding, in order to retrieve tokens on a side-chain, you would have to send your XMR to some address that would then be unlocked when you burn the side-chain tokens.

How could Monero verify that anything has actually occurred on the side-chain and unlock the XMR?

dEBRUYNE answered the following in relation to a side-chain question:

To prevent issues with the mainchain we would have to implement a cryptographic proof, i.e., the amount of XMR that went into the sidechain would have to be equal to the amount of XMR that goes back into the "mainchain".

I guess I'd like a little more explanation of what the cryptographic proof would be / how it would be implemented?

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    Why are you interested in sidechains for Monero? – pl55 Oct 22 '16 at 6:46
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    This text is to provide information to people whom are wondering what sidechains are and how they benefit monero....The idea behind a sidechain is to allow a different protocol to be used on the sidechain other than what is offered on the mainchain without the necessity of changing coins and incurring fees... an example would be for faster transactions... So you would transfer your Monero A coins which is as we know now > over to a Monero X sidechain which allows "faster" transactions and then moving the remainder of the coins back over to the Mainchain after you have finished. See below – Lurker Mar 29 '17 at 21:48
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    In theory the coins dont actually get passed from one chain to another but are infact stored on the mainchain in an un-accessible wallet until cryptographic proof is provided from the sidechain of the new balance... The mainchain will then give back your applicable balance proven by the sidechain, and the remainder of the coins will be subsequently burned. – Lurker Mar 29 '17 at 21:50
  • @Lurker, I think you have got yourself an answer there? – Prof. Falken Nov 1 '17 at 7:50
  • Unfortunately my comment doesn't answer as to how verification/ cryptographic proof can be performed or implemented. – Lurker Nov 20 '17 at 12:41

The proofs would be 1) a multisig 2-2 transaction initially created on the main-chain and 2) the multiple parties signing (to spend agreed balances) at settlement. What happens on the side-chain is irrelevant to the main-chain as all it need care about is the XMR are locked up in the 2-2 multisig and at some point they may be spent (so long as the signatories agree, e.g. sign).

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