The Hodge theater is just the MCM unit cell. Mochi ripped off my idea and dressed it in absurd jargon. Scholze's point about the impossibility of unequal objects which are isomorphic is resolved as follows, in favor of Mochi. Consider a 4D Minkowski space. The slices of constant proper time are Euclidean 3-spaces. Now, consider a Hilbert space of quantum state vectors. The wavefunctions (the position space representations of the vectors) are functions of the three spatial variables. Namely, if the wavefunction tells you the probability of detecting some property in a volume of space, the wavefunction obviously has to depend on the 3 spatial variables. Now, you can have two Hilbert spaces, containing the exact same state vectors, except the domain of the wavefunctions in one Hilbert space is the Euclidean 3-space at the t_1 slice of Minkowski space while the wavefunctions in the other Hilbert space are functions of the Euclidean 3-space at the t_2 slice of Minkowski space. Although the Hilbert spaces are the same, and although the domain of the wavefunctions in both are just Euclidean 3-space, they are actually different Hilbert spaces since their wavefunctions are depend on (x_1,y_1,z_1) and (x_2,y_2,z_2) respectively. Although all Euclidean 3-spaces can be thought of as the same 3-space, these can't because they are different slices of a Minkowski 4-space.
