Molecular Geometry from Hopf Vortex Topology: Bond Angles, Covalent Binding, and the Universal Correlation Constant in the PEW Framework (v3)

Update v3 (April 2026): The H-O-H bond angle result cos(θ_HOH) = −1/4, giving θ = 104.4775° (deviation 0.027° from experiment), is now established as an exact algebraic identity via the Lucas number L₃. Article 14 proves that φ³ − φ⁻³ = L₃ = 4 exactly, so cos(θ_HOH) = −1/L₃ = −1/4 is a consequence of the Hopf torus topology at level n=3, not a numerical coincidence. This closes PO-H2O-1 for the cosine value [A]. All original results of v2 are preserved. MSC: 81V55 · 81Q05 · 92E10 PACS: 31.10.+z · 31.15.-p · 33.15.Dj · 31.25.-v