Very interesting and important essay metaphor "Map = Territory" and in-depth analysis of the fundamental connection of Mathematics and Physics. Very good figurative metaphors, the method of presentation, deep figurative representation of problems in physics and your ideas. I fully agree with the conclusion: "To really bridge the gap between math and physics, one has to build on all pillars in a more general approach until map and territory truly become one."
Today in fundamental science there is a deep crisis of understanding, crisis of representation and interpretation. This profound existential crisis of basic science - universal human problems. Mathematics and Physics require a deep ontological justification (basification). In fundamental Physics is necessary to introduce an ontological standard justification along with the empirical standard.
Ontological revolution Planck-Einstein must be completed. John Wheeler left physicists good covenant: "Philosophy is too important to be left to the philosophers". This problem is well formulated Edmund Husserl in "Origin of Geometry»: "Only to the extent, to which in case of idealization, the general content of spatio-temporal sphere is apodictically taken into account, which is invariant in all imaginable variations, ideal formation may arise, that will be clear in any future for all generations and in such form will be transferable by the tradition and reproducible in identical intersubjective sense ."
Your essay clearly shows that it is necessary the ontological extension of space. My high appreciation.
I invite you to see my analysis of the philosophical foundations of mathematics and physics, the method of ontological constructing of the primordial generating structure, "La Structure mère" as the ontological framework, carcass and foundation of knowledge, the core of which - the ontological (structural, cosmic) memory and information - polyvalent phenomenon of the ontological (structural) memory of Universum as a whole. I believe that the scientific picture of the world should be the same rich senses of the "LifeWorld", as a picture of the world poets and philosophers.