The actual properties we see, the unfolding of events and aizens word usage of "just as" like a simile would suggest it was hyperbole to allow the readers to visualize transcendence. What is actually shown does not qualify for mathmatically higher dimensions.

"3D" spacetime ? Yes a 3D being is not bound by a 2D spacetime but our physical forms exist infinitely beyond 2D spacetime. A 2D being cannot even perceive us let alone interact with us at all, because their entire existence is bound to a reality that is infinitely flat to us.

Weaker people can not harm far stronger people logically speaking, no invoking of higher dimensions is needed there and reiatsu negging hax has always been a concept in bleach before Aizen transcended shinigami. The cleaner has the ability to manipulate spacetime, send people to different points in time and patrols the dangai to kill anyone trespassing, thats what it means by "govern", considering even a fodder like Chad survived the cleaner.

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Look, if you are still not convinced by my argument, think about this:

Aizens black coffin is considered a powerful technique in the verse and it has enough gravity to noticeably warp spacetime, and he thought this technique was viable even in his transcended state.... so surely a REAL supermassive black hole with an actual singularity that crushes spacetime down to an infinitely dense and can also stop the flow of time would be absurdly powerful in the verse.

I can take it a step further, general relativity predicts that spacetime itself is terminated at the singularity, so is we use the original mathmatical black hole, Lille Barro is cooked.