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This research aims to derive the H-O-H bond angle using algebraic and topological methods, confirming its exact value.

May 1, 2026Open Access

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

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This research aims to derive the H-O-H bond angle using algebraic and topological methods, confirming its exact value.
Established H-O-H bond angle cos(θ_HOH) = −1/4 via algebraic identity using Lucas numbers.
Closures of PO-H2O-1 and preservation of previous results were key aspects of the analysis.
Employed mathematical proofs to link bond angles to Hopf torus topology.
The H-O-H bond angle was determined to be 104.4775°, showing a deviation of only 0.027° from experimental values.
Demonstrated that this bond angle result is a consequence of Hopf torus topology, not a coincidence.
Confirmed the relationship between the cosine value and Lucas number L₃.

Resumen

Update v3 (April 2026): The H-O-H bond angle result cos (θHOH) = −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 (θHOH) = −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

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