The Universally Compact Multi-Networks Bundle of the Nature: the clustering machinery approachable self-controlling and self-building mechanisms in natural processes, physical universes, and their ingredients

The structures both Natural Processes, NPs and their Ingredients, Is, NPaIs are considered as Distributed Complex Multi-Network, DCMN involving Is through Equivalency and Compatibility Principles, ECPs related with Electromagnetically Suitable Schemes, ESSs. The variations of DCMN’s electromagnetically derivable compatibility characteristics built the characteristics of NPs’ Is. The Natural Mappings, NMs govern NPs as involving Topological Transformations, TTs among NPaIs through suitable functor-like and/or hyper-functor representations of NPaIs’ Data, NPaIs’D with mechanism’s topology in inflective spaces and single point spaces with NMs by Manifold Environs, MEs.

The motivating point for an effective universality network is to fix occurrences of interactions and couplings and then to extract their ECPs’ traces according to Inversely Relation Mechanism, IRM, say push↑↓pull effect; therefore, the continuous self-calibration needs self-collections of NPaIs’D that provides self-conservation principles so prevents both incompatibilities and instabilities in topological structures for NPaIs through their MEs.

The method, say Equivalency Machinery Approaches for Universe Categories, designs self-optimization and self-control processes of universally equivalent DCMN of MEs and develops a compact and accurate model for Realizable Universes’ Bundles, RUsBs. The fact sketches self-optimization characteristic on NPaIs like a DCMNs Machinery, M say RUsBs’M Cluster through TTs.