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Hilbert space in multiverse type 3

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Can the dimensions of a Hilbert space in a type 3 multiverse be considered spatial in nature ? Or are they considered as waves that are not valid for H1-B ?
 
A Hilbert Space is inherently infinite dimensional in the sense that it accounts for all possible quantum "degrees of freedom" a particle within the system can take. Can be spatial or not, depends entirely on the context? Do you have proof it pertains to spatiality? If so, then you'll get a H1-B structure, otherwise no.
 
Why people keeping thinking that Hilbert Space by default is always infinite dimensional???, it is literally isn't the case
 
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