6 COS-SUSY - Collapsing-Structure Supersymmetry: Discrete SUSY Algebras, Superfields, and Symmetry Breaking on a Shell–Filament Graph

COS–SUSY is the supersymmetry extension of the Collapsing-Structure (COS) theory. We formulate local and global SUSY on a discrete cosmological/QFT background built from shells and quantum filaments, and derive shell-wise realizations of the N=1 and N=2 superalgebras. In the COS graph metric, boson–fermion pairing emerges naturally. We prove a Local Closure Theorem showing that part of SUSY survives discretization, while graph-topological deformations trigger explicit or spontaneous breaking. A measurement protocol based on shell operators makes SUSY breaking numerically detectable. We also map interfaces with the COS–SM (Standard Model) and COS–GUT modules, outlining a supersymmetric program within the COS framework and its links to particle-model building.