Before seeing your message today, I found a few things that contradict Aizen's claim of having extradimensional perception:
1) If Aizen can gather extradimensional information, why is
AA's role information delivery? If he already sees and knows everything that's happening, AA's role, as explained to us by Ulquiorra, would be irrelevant.
2) If Aizen has extradimensional perception, why does he send Ulquiorra to WoTL to gather information? If he could already see what was happening, he wouldn't need to do that. Especially since he saw the events thanks to Ulquiorra's
eye technique... He even learns why Ulquiorra didn't kill Ichigo, Urahara, and Yoruichi through Ulquiorra's explanation. Okay, I know you weren't the one claiming he could read minds, but this refutes both his mind-reading ability and extradimensional perception.
3) If Aizen could see beyond dimensions, he would also have learned Urahara's plans.
And all of these contradictions I've pointed out occur while Aizen possesses the Hogyoku. In other words, even beyond the contradictions, there's no explicit statement that he obtained this hax through the Hogyoku. To attribute such a significant hax to a character, there would need to be a direct statement. For example, Ichibei could be said to possess such a hax because he was able to interfere in Ichigo's conversation with Zangetsu.
If we assume he might have obtained this hax through the Hogyoku, then since the Hogyoku created Wonderweiss, we could relate his ability to summon Wonderweiss from the HM to this.
As for Caja Negation, this was already something used to punish the Arrancar. So Aizen might be able to see inside a dimension belonging to himself and his army.
