Connectivity Geometry Framework

This paper systematically proposes the "Connectivity Geometry Framework". Traditional physics usually regards spacetime as a continuous and smooth background; however, it still faces profound bottlenecks when dealing with fundamental problems such as the quantization of gravity, the nature of dark matter and dark energy, and the lack of first-principles origins for the parameters of three-generation fermions. This framework proposes a new underlying picture: the bottom layer of the universe is a discrete spin network with a step size of k=3. Relying on this topological network, fundamental physical concepts are geometrically reconstructed: gravity originates from the topological breaking of entanglement minimal cuts, gauge fields are the topological bifurcation of the u(3) algebraic closure, and fermions correspond to topological defects on the network. This framework achieves the geometric unification of fundamental interactions and provides falsifiable quantitative predictions such as the Lattice QCD Clover coefficient 1.391 ± 0.029 and the dark energy equation of state w ≈ -0.980, offering a falsifiable underlying paradigm for discrete geometric physics.