Topologically Stabilized Torsion in Weak-Field Gravity: A Ricci-Flow Framework

We investigate stationary torsional configurations supported by chiral Majorana neutrino currents in linearized gravity. A Ricci-flow-inspired geometric relaxation (with no physical time interpretation) is introduced to drive the metric perturbation toward fixed points sustained by chiral sources while keeping curvature invariants negligible. We show that divergence-free chiral currents can support globally non-trivial torsional holonomy stabilized by topological invariants associated with the fundamental groups pi1(S1) and pi3(S3). Toroidal skyrmionic domains emerge when one chirality dominates, whereas a chiral-flip interference sector enables Moebius-type non-orientable bridges between opposite-chirality regions. In the static limit, a Green-function formulation provides a finite-range Yukawa-type response governed by the neutrino coherence length. These results identify a purely torsional mechanism, independent of local curvature, through which coherent chiral currents may influence effective gravitational behavior in neutrino-rich environments.