It’s clearly NOT yours.
It creates a minefield that anyone can mine. If it was meant to be yours, it would be in a can that if anyone else removed stuff from it would set them to suspect or criminal status.
You WANT it to be yours. It’s not.
As the operator of the moon laser, you set the time the rock becomes an asteroid field. You have a distinct advantage. You also can unload your ore much more quickly after mining it at your structure.
But it’s not yours any more than the salvage from a ship you destroy is yours or anymore than the bounties from a mission you accept are yours (someone else can scan you down, warp in and kill the rats before you do) or all the containers at a data or relic site you scan down first are yours.
None of those are yours by right. You have advantages by firing the moon laser or being the one who accepted the mission or being the first to scan down a site. But the advantage is ONLY the fact that you get there first. Not that someone else can’t come along and take it from under your nose.
Doing that is what makes eve… eve.