Ten-Thousand-Year math is the hypothetical math beyond the Millenarian level, which would celebrate Apert only once every ten millenia. 

Origins and plausibility

At some unspecified point between the 3680 and 3690 Decenarian Aperts, Orolo tells Erasmas' cohort about a group of avout that showed up during the 3000 Millenarian Apert, claiming to be Ten-Thousanders celebrating their own Apert. Given the flagrant timing incongruence (a Ten-Thousand-Year math, if it existed, would have celebrated Apert in year 10000, not 3000), Erasmas dismisses this story as Orolo checking if the fids had been paying attention. 

It is, however, instructive to look at the story of the Ten-Thousanders in light of a later dialog between Orolo and Erasmas concerning the notion of Causal Domain Shear ---that is, a region of space that becomes entirely causally disconnected from the rest of the cosmos. Orolo then asks whether, if Causal Domain Shear were to happen, time would pass at the same rate inside the Sheared Causal Domain as it does in the rest of the cosmos.

Translating these ideas to the actual cosmos of Arbre, a Ten-Thousand-Year math would be one so removed from the influence of extramuros that Causal Domain Shear happens. This would entail that this math and all information about it would be inaccessible from anywhere else in the Arbre cosmos, including Millenarian maths; as such, there wouldn't be any evidence for the existence of this type of math, leading Arbre inhabitants to agree that there is nothing beyond the Millenarian maths. Furthermore, since nothing forces time to tick at the same rate inside the Sheared Causal Domain as it does in the rest of the Cosmos, it is conceivable that the Ten-Thousanders go through 10000 years while the rest of Arbre only goes through 3000 ---hence their appearance at the 3000 Millenarian Apert.

However, there is nothing in the book suggesting the actual existence of a Ten-Thousand-Year math.

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