Dear Mr. Cole,

We (Mallick, Hamburger and Mallick (2016, 2017), Mallick (2011)) have developed a proof of the P vs. NP problem of the Millenium Mathematics prize in which we have shown in one of the steps that the mathematical solution of a problem and its statistical experimental verification of a problem using computer science techniques depends on a mathematical topological twist in functor categories of data manifolds where mathematical modelling provides the continuous correspondence necessary for generating networks out of the manifold correspondence by topological twists of the functor algebra (RHMHM Functor Algebra Calculus https://www.econometricsociety.org/users/earl-fitzpatrick-york-mallick-sir-asutosh-mukherjee-university-institute-chair-professor result (8)) to generate network basis diffeotopy of embeddings. This theorem develops a solution to your question which is how are manifolds scientifically related to network topologies in spacextime. I am sure this will be able to explain everything from wind patterns to rainbows and even further metoer showers and astrophyical phenomena some day by cyber programming, but as of now this is an example of a solution.

Soumitra K. Mallick

for RHMHM School of Mathematical Sciences Thinking

Colorado, USA, Tokyo, Japan, New Delhi, India and Kolkata, India

In addition, my question does assume that network flow and manifold flow are about the flows of matter, energy, or information according to the known laws of physics...

"Stock and Flow" you mean - which we have proved can be a solution to the Higgs Mechanism in the Higgs Field of fundamental String Particles which we have also identified experimentally using computer solutions i.e. solution in the AGGNNNetwork space (Mallick, Hamburger, Mallick (2016, 2017, 2018), Mallick (2011) developed on Sullivan, Raychaudhury, Kolokythos, Vrtilek, Kantharia (2012) and further experimentally with cybernetic Econophysics String Matching Field Theory also experimentally verified on spacextime systems classified and systems integrated geodescy in Mallick, Krichel & Novarese (2010) published in Nature.com) with vector diffeotopy of embeddings quantum mechanics of string particles. This research is available on www.researchgate.net/profile/Soumitra_Mallick. This has applications in designing for e.g. Electronic Stock Exchange Network Financial Information Systems and systems integrated Electronic Banking Network Information Systems (Mallick, Ray, Sarkar, Duttachaudhuri & Chakraborty (2007, 2010)). These we have used to develop the Field Theory of Network Econophysics a Fundamental Physics also invention which would become valuable in designing any networked experimental systems in scientific fields we believe.

S.K.Mallick (CA)

for RHMHM School of Mathematical Sciences Thinking

USA, Japan, India