Ricci Flow and the Omega-Frame: A Lens-Relative Reading of Perelman's Approach to the Poincaré Conjecture

This note gives a structural reading of Perelman’s Ricci flow approach to the Poincaré conjecture using the language of the Omega-Frame. It explains how the geometry evolves, how singularities are recognized, how surgery allows the flow to continue, and how the flow becomes extinct in finite time in the simply connected case. A round 3-sphere example illustrates the framework in a simple case of extinction. The note also discusses why the evolution appears irreversible at this coarse level of description. It is explanatory only: it offers no new proof, presents no new geometric results, and does not construct a formal model of Ricci flow.