Classification of Structure

subatomic, and perhaps atoms themselves (all matters) should be classified not by abstract weights and charge, and moreover by wave-field models for their action. Bosons seem to prefer grouping, and the more there are in a system the more likely it is that all will operate the same. Thus they induce entrainment.

Recent work on this was done by Robert Grant.

§Structure Connectivity Concepts

The tamari lattice is a structure for mapping the combinatoric groups of a set. A visual search for the same demonstrates a powerful range of visual language for describing the structural properties of such networks, extending beyond ordered Hasse diagrams. Analysis of these connectivities includes Catalan numbers. Such connectivities (including flip graphs) occurs not just across flat maps of braids, but polytopes such as a property associahedron, but also N-dimensional structures of connectivity as are the permuhedron and cyclohedrons. But not all structures may be regular polytopes, and rather could be quasiperiodic.

The fibonacci crystal is one such structure, and we see its presence in the study of subatomic dyanmics.

Likewise the abstract polytopes include a class of prismatoids, and the aperiogonal antiprism. Can these prisms existing as a spectra of a commutative ring?

I developed som similar notation schemes between 2006 and 2009 in the research into water braiding structures in a hydrodyanmic equilibrium of hyperbolic envelope.


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