Nematic Order in Curved Skin: From Topological Defects to a Covariant Q-Tensor Theory — An Integrated Framework for the Clinic

This document merges two research manuscripts written by the author into a single, continuous, scientifically grounded whole: 1. Defect Attractors on Curved Biological Surfaces, including the Skin-Hair System (2026) — referred to below as the applied manuscript. This work introduces a minimal active-nematic model (a complex Ginzburg–Landau equation) on a curved sphere, shows through simulation how topological defects, spiral structures and material accumulation arise, and applies this exploratorily to the scalp, hyperkeratosis and hair follicles. 2. Intrinsic Nematic Order on Curved Animal Skin (2026) — referred to below as the theoretical manuscript. This work reformulates the same question on a mathematically stricter footing: an intrinsic, covariant tensor theory (the Q-tensor and the equivalent spin-2 field) valid on any curved surface, including an explicit treatment of boundaries, multiple fibre families, and the limits of the model.