Topological Quantization of Light Speed: Cherenkov Radiation as Graviton-Mediated Surgery

We establish a topological foundation for light propagation where the vacuum speed of light c0 emerges as a quantum of curvature flux. In material media, light slowing results from genus increase through virtual handle attachments, with refractive index n topologically quantized. Cherenkov radiation is identified as an emergency topological surgery correcting entropy monotonicity violations whencharged particles exceed the local light speed. Key results: (1) Derivation ofcmed = c0/n from surgery on S2 boundaries (Theorem 1), ( 2) Prediction of dis-crete Cherenkov spectra in crystals (Eq. 17), (3) Quantization of Cherenkov anglecos θc = n(topo)/n(particle) (Eq. 10). The model unifies optics and gravity throughPerelman entropy dynamics.