Might Planck finer scale also be descriptive for rm minimum modified global radius stage for 3-manifold i.e. for 3-volume in SRM Spiral Rotation Model; that is, at earliest transition stage of Big Bang i.e. Big Expansion? For such extremely early transient stage, might there be a sea of gravity waves; thus revealing a description of the Planck scale for all stages? In SRM, one entertains the simplifying assumption that one always has mass and curvature description for all equiangular spiral stages of 3-manifold’s cyclical trajectory; hence always a greater than Planck scale. Conservatively then perhaps ~4 orders of magnitude (~10-29 cm.?) greater than Planck scale? Is this then the smaller scale 3-volume ‘world’ that we came from?
For extremely transient very early stage, one allegedly would have extreme deformations of 3-manifold. Yet tangent vector, and hence differentiation, geodesics, in addition to mass and curvature, are still allegedly descriptive. However no alleged change of topology for such stage, nor for any stage. That is, no handles, nor multi-connectedness, nor patches of manifold missing. Also geodesics allegedly never end; rather no longer defined on still finer Planck scale.
Such extreme curvature of manifold allegedly is associated with resistance to such deformations i.e. so-called inertia of manifold. The latter allegedly being a special case of the greater generality: as if manifolds want to be left unperturbed; that is, if disjoint or intersecting, then always so. So resistance to deformation, and no topological change i.e. no handles, no change in connectedness, no loss of, nor sudden mixing, of elements of sets – that is, no change in continuity.
However such extreme deformations, and resistance to deformations, is herein considered associated with copious quanta creation from physical vacuum; thus contributing to stress tensor and thus to further extremes of deformations i.e. extreme curvature. Would this seem consistent with fermion mass spectrum , exponentially increasing in mass and number of generations, increasingly shorter transitions; that is, a maximizing of entropy in comparison to alternative scenarios? Thus consistent with the adage ‘anything not forbidden, will occur’? TMM
Weirstrauss function: continuous, but nowhere differential. Like for finer than Planck scale?