Well, it's an LLC once the human initializers withdraw from it, that's the legal trick here. If you mean what is the actual algorithm using the LLC shell, it could be anything. A simple flowchart, a DAC on Ethereum, a NN on AWS, whatever.
That is, whether there's anything that stops a sequence of share sales ending up in a situation where a set of companies between them own all the shares of companies in the set.
(If this ever happened, presumably the last human to sell a share to one of the companies was making a mistake, but humans make mistakes all the time.)
I mean, normally if you wanted to stop this sort of thing you'd do something like introduce a hierarchy of company types and say type N companies may only own shares in companies of type N+1 or higher. But I've never heard of such a rule.
If they ever cared enough to look, I'd imagine.
People get away with illegal or unlawful things all the time because of the unawareness of the authorities, but that doesn't change the nature of those things.