Pythagorean Harmonic Geometry as Oxygen-Curvature Invariance
Abstract (Index)
This research note explores a structural correspondence between classical Pythagorean harmonic ratios and stable geometric configurations observed in oxygen-based molecules.
The work reframes traditional musical intervals not as numerological artifacts, but as curvature invariantsemerging from constrained molecular geometry, particularly in oxygen-centered systems.
Rather than asserting a new physical law, the document proposes that harmonic ratios may encode empirical regularities of vibrational geometry when bond angles are normalized and compared across molecular species.
Within the Oxygen Octave project, this note serves as a conceptual bridge linking molecular curvature, vibrational stability, and historically known harmonic structures, helping to contextualize later quantitative and topological results.
The full argument, numerical mappings, and historical comparisons are provided in the complete Zenodo record.
