Develops finite-state geometric framework using Bargmann invariants to extract Weyl node chirality and Kitaev chain Z₂ topological distinction from quantum state overlaps, enabling direct probing without continuous band geometry descriptions.

Develops finite-state geometric framework using Bargmann invariants to extract Weyl node chirality and Kitaev chain Z₂ topological distinction from quantum state overlaps, enabling direct probing without continuous band geometry descriptions.