Topological Data Analysis of Physical Constants (Planck-Boltzmann Descent)

Here we present some monodromic topological dimensionless parameters of thetheore@cal physics. We recently proved that the quantum speed limit (QSL) = 4 = 2! is a cri@calcriterion or a stopped barrier: if the universe radius r < 2 (called great circle radius R=2), there isan inner sheaf universe; if the universe radius r > 2, there is an outer sheaf universe. Our mainobject is, based on a strong Planck-Boltzmann descend with topological data analysis (TDA),construc@ng a robust theore@cal framework of modern quantum physics to illustrate all retractdeforma@ons and exo@c escape deforma@ons of fundamental par@cles and the universe. Wefully faithfully depict all Reeb orbits associated with dynamical mass and velocity.As a co-product, we also give a short geometric proof of Fermat’s Last Theorem (FLT).