X of a permanent

[Crossed]

If I cast a permanent with x in it's cmc successfully, does x for that permant remain what you declared it to be, or does x become {0} while it remains on the Battlefield?

For example. I cast {mistcutter hydra} where x = {4}, does {mistcutter hydra}'s total cmc become {5} while it is a permanent on the battlefield, or {1}?

[Remillo]

Anywhere but on the stack, X always is 0.  Even on the battlefield, Mistcutter's CMC is just 1.