The idea is that the sidechains are merge-mined, Jorge, on account of using the same hashing algorithm.
That is
one of the things that sidechains CAN be. The paper does npt say that they have to be merge-mined, or that they use that same algorithm, or even that their blockchain is anywhere like the bitcoin blockchain. In fact, alternative blockchain designs was one of the things that the sidechains were supposed to experiment with.
@ wider bitcointalk: I and seemingly everyone else don't always have time to reply to all of this gizzard of a troll's willful distortions and contortions, suffice to say that unaddressed Stolfi posts are still staggeringly dishonest despite that.
You should spend some time actually trying to understand the things before staking your reputation on defending them.