LoE Reading of Perelman's Ricci Flow: W as the Free Energy of Logic of Existence

We reinterpret Grigori Perelman’s proof of the Poincaré Conjecture within the formal
triad of the Logic of Existence (LoE): (Φorder, R, Φchaos). Without altering mathematics, we
map Perelman’s geometric quantities to LoE postulates: minimization of relational tension
(LoE–I), monotonic resonance (LoE–II), and scale–controlled reconstruction (LoE–III). This
perspective exposes the Ricci flow as a physical manifestation of LoE dynamics where order
emerges from nonlinear negotiation of curvature.