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Callisto is a separate blockchain that will have its own clock token. Developers ETC want to avoid changes in the network and large commissions, as it was in the Bitcoin network.
This will happen due to the use of third-party protocols called "sidechain". These changes will lead to the rapid growth of Ethereum Classic and Callisto.
Both networks complement each other and Callisto is the same "daughter" for ETC, such as Omni for Btc, Blitz for Strat and so on...
More detail are reading here