Universal Radial Eversion and the Symmetry of Spherical Sinkability

We study radial deformations of planar straight-line embeddings that reverse the ordered intersection blocks on every ray from a distinguished point. A strict face system in reciprocal-radius coordinates connects this planar operation to longitudinal deformations of geodesic triangulations of the sphere. Under the radial general-position hypotheses for the planar theorem and the proper generic shortest-path hypotheses for the spherical theorem, we prove universal radial eversion and sinkability–floatability symmetry. We also characterize all eversions by a reciprocal-radius cone, give an exact rational construction, and extend the reversal to proper radial plane straight-line graphs. Version 0.1 preprint. This deposit contains the paper PDF and a complete supplement archive with source and verification materials.