[6] COS-SUSY - Collapsing-Structure Supersymmetry: Discrete SUSY Algebras, Superfield Interfaces, and Symmetry Breaking on a Shell-Filament Background

COS–SUSY is the supersymmetry interface module of the Collapsing-Structure (COS) program. It investigates how supersymmetric structures can be formulated on a discrete shell–filament background, focusing on shellwise, quasi-local rigid SUSY rather than a complete nonperturbative or supergravity realization.

The manuscript formulates discrete $\mathcal{N}=1$ and $\mathcal{N}=2$ superalgebraic structures under explicit locality, grading, domain, and closure assumptions. It introduces shellwise supergenerators, effective momentum/transport operators, discrete-background correction terms, vertex/edge superfield interfaces, and compatibility conditions with gauge and chiral structures.

Boson–fermion spectral pairing is analyzed in controlled unbroken sectors, while graph-topological changes are treated as sources of structural or regulator-induced SUSY splitting. The paper develops Ward-identity diagnostics, closure-defect tests, Gauss-constraint compatibility checks, Ginsparg–Wilson/overlap chirality conditions, BPS/central-charge examples, and numerical protocols for detecting SUSY breaking.

Interfaces with COS–SM and COS–GUT are mapped at the level of field content, superpotentials, R-charges, threshold effects, and MSSM/GUT-oriented extensions. These connections remain interface-level and partly open, providing checkpoints for a future supersymmetric COS model-building program.