Topological diagnostics for discrete-time quantum walks on non-orientable surfaces (Möbius band, Klein bottle) — Floquet operators, chiral winding numbers, and Z₂ invariants, with a PennyLane circuit backend.

Winding number and point-in-polygon for arbitrary (non-convex, self-intersecting) polygons, pure Python with zero dependencies.

An experimental topological field-memory prototype with vortex encoding and self-repairing field dynamics. It delivers noise-robust AI long-term memory as a complementary alternative to conventional RAG retrieval.