PAPER–Σ: The Geometric Foundations of Matter and Spacetime: Rigidity, Visibility, and the Topology of Compactification

This paper addresses three foundational questions within the Fracture–Berry–Tension (FBT) framework: (i) how symplectic rigidity serves as a unifying geometric principle underlying both quantum uncertainty and gravitational regularity; (ii) how visible and dark matter sectors are to be distinguished geometrically; and (iii) how black holes should be understood in a six-dimensional symplectic ontology. We show that Gromov’s non–squeezing theorem provides a common geometric explanation for the existence of a minimal action quantum and for the impossibility of true geometric singularities. Building on this, we classify matter sectors in termsof two geometric invariants of compactified surfaces Σ2 ↩→M6 : AΣ =󰁝Σ2…