Ok let’s start a step earlier then:

How does the peg out work? Nobody on BTC main chain can verify that the transaction submitted to peg out is actually valid ownership, because all that activity happens off chain. So what “keys” are required to write a peg out, and what stops a miner from writing one that has nothing to do with the sidechain?

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There are several ways. On the Sidechain side of things, scripting can assign a token or set amount of tokens that the project and users agree is part of the design, to whoever signed the peg-in. This creates a sidechainnside user and account with forward rights to those tokens.

If some specific set of sidechain scripting favored miners, and thus made users vulnerable, everyone would know and reject the project OR accept it as part of some larger benefit. Let the market decide. Our main contention is that the market and market competition is a greater innovative force than the vitcoin devs and priesthood that have directed it up to now. It's essentially an argument between a communist or capitalist bitcoin future. Are things like RGB, Lightning, ect, market driven innovation or dev (politburo) driven.

The point is, as a user of bitcoin, none of this affects your normal use. You benefit from a means to adopt any potential challenger to bitcoin technology that might arise in the unknowable future, voluntarily. You benefit from a more secure network, through a more decentralized and incentivised miner environment. But if you want to just keep using bitcoin the way you have and never risk it in a sidechain you can.

But i think what interests you is the scaling ability, while maintaining the security and sovereignty features of main bitcoin.

For one potential scaling solution :

Truthcoin.info/blog/thunder

Basicly, Where big blocks are bad on L1 they can be good on a L2.