We introduce semi-double trace and semi-strong trace inspired by newly synthesized coiled-coil protein cages, a graph-theoretic generalization of double trace, to model polypeptide nanostructure self-assembly. Through multi-component double covers built from semi-strong traces, we establish a topological assembly framework. Crucially, we prove that double covers attain strong stability when all components are semi-strong. This model resolves a fundamental design challenge: determining oligomeric states via component counts while establishing stability criteria through cyclic vertex figures. These insights provide rigorous principles for engineering biomimetic nanomaterials with programmable topological stability.