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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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Authors

MAMichel ALdon

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Overview

Randomized trial demonstrates exact bond angle of H-O-H in molecular geometry, indicating topological effects.

Key Points

  • 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.

Cite This Study

Michel ALdon (2026) studied this question.

synapsesocial.com/papers/69f443e8967e944ac5566f92https://doi.org/10.5281/zenodo.19889456
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Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

  1. 1The HOH Bond Angle as a Temperature-Dependent Phase Parameter2026
  2. 2Conic Projection as Manifold and 3-Sphere Dihedral Angles θ<sub>HnHn+1</sub>[Deg] Under Homotopy2026
  3. 3Article 22: Progress on Three Priority-1 Open Problems of the PEW Series: Asymptotic Analysis of the Vortex ODE, Three-Strand Hopf Braid, and Metric Correction to the Fine-Structure Constant2026 · 2 citations
  4. 4Article 19: Metric Correction to the Fine-Structure Constant in the PEW Framework2026 · 2 citations
  5. 5The Geometry of the Hückel/Tight-Binding Method for Modeling Molecular Systems2026