Geometric description of C-vectors and real Lösungen

We introduce real Lösungen as an analogue of roots. For each mutation sequence arbitrary skew-symmetrizable matrix, we define a family reflections along with associated vectors which are and set curves on Riemann surface. The matrix consisting these is called L-matrix. explain how the L-matrix naturally arises in connection C-matrix. Then conjecture that depends (up to signs row vectors) only seed, can be drawn without self-intersections, providing new combinatorial/geometric description c-vectors.