If functions (defining continuity of manifolds?) don’t behave well, such as continuous but non-typical, and hence not smooth, and likewise for our overall Regional volume V_R 3-manifold, which is mainly characterized (hence mathematically more typical) by non-differentiated finer than Planck scale; then is not just our coarser than Planck scale, a very atypical perspective, mathematically speaking?

Might the *nature* of *time* , in regards to our evolving 3-manifold and alleged divergent set, System S≡{U_T’, …} of total universes, wherein U_T≡{{V^3_R}_p}, be considered as both always exponentially changing, and thus analytical; likewise for mapping to integers in such model ?

Thus would the *‘flow* of *time*‘ seem to be smooth and analytical? In contrast, our finite appearing (*coarser* than Planck scale) 3-manifold high perch has just finite order differentiation; whereas the overall coarser to finer 3-manifold is *not* smooth. So our mixture of 2 manifolds would seem to differ in smoothness attribute, as well as continuity, but not in cardinality.

So we would seem to reside in a mixture of 2 topologically inequivalent manifolds, an exponentially changing 1-manifold being well behaved (smooth, and analytical?), but not typical for most manifolds. Whereas the overall coarser to finer 3-manifold is not well behaved (non-smooth), but typical for manifolds; such as 3-manifold version of Weirstrauss function?

That is, what we perceive as a whole, is actually a composite of 2 topologcally inequivalent manifolds, described both as well behaved but not typical for temporal change; while the coarser to finer scale is not well behaved yet typical, in comparison to most other manifolds.

also zankaon website, SRM page.

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