Global Nature of Physical Law: Posing of highly sharpened Global Problem of Time between Background Independent and Background Dependent Laws of Physics

See the first two of the below (in reverse order) for my recent exposition of this.

Relational Variables for Graph Theory

Abstract We systematically consider simple relational variables — relative variables, ratio variables and dilatational variables — for Graph Theory. We apply these to simplifying graph inequalities and elucidating a large number Graph-Theoretically significant probability-valued variables. This material has further use in developing network stucture quantifiers. It represents interaction between Similarity Geometry, and basic Shape Theory … Continue reading Relational Variables for Graph Theory

Dirac’s Algorithm for Constrained Systems from the perspective of Order Theory

Abstract Dirac based his theory of constrained systems on Linear Algebra foundations. It is a brackets-algebraic consistency procedure with multiple outcomes, including new constraints dropping out and redeclaring brackets becoming necessary (Dirac brackets). This procedure has not yet been edited, however, to caution about and remove scaffolding structures that turn out to not in general … Continue reading Dirac’s Algorithm for Constrained Systems from the perspective of Order Theory

Spaces of Graphs

Abstract We apply Shape Theory and Order Theory to spaces of graphs. We concentrate onsmall examples which are minimal for exhibiting various nontrivialities.