Modulated Scanning Calorimetry shows the non-reversing heat flow near T_g to display a sharply defined global minimum in the 0.28 < x < 0.40 range, identified with the self-organized phase (SOP) of titled glasses. ³¹P NMR, Raman scattering and constraint counting algorithms suggest this phase to consist of two distinct global morphologies; a Se-rich backbone that has a dimensionality 2 < d < 3, and P-rich ribbons that have d ≃ 1. The ribbons dominate the physical behavior of stressed rigid (0.40 < x < 0.50) glasses with unusual consequences.