Advanced Theoretical Physics and Mathematics
Published October 22, 2025 | Version The_Oxygen_Octave_v1.6_Topological_Validation_and_Comparative_Frameworks.pdf
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The Oxygen Octave – Foundations: Quantitative Correlations Across Vibrational Systems

Creators

Description

The Oxygen Octave – v1.6: Topological Validation and Comparative Frameworks

This updated version (v1.6) expands The Oxygen Octave from a proportional hypothesis into a topologically validated scientific framework linking oxygenic vibrational ratios with harmonic self-organization across molecular and biological systems.

At its core, the model identifies oxygen (O₂) as the harmonic tonic of matter: the reference frequency from which coherent ratios among O₃, H₂O, and O²⁻ emerge as 4/3, 7/6, and √2, defining a “vibrational octave” analogous to musical just intonation. These relationships are verified through octave-folding normalization, eliminating earlier cross-term artifacts (φ ≈ 1.573), and revealing local harmonic coherence rather than spurious numerical resonance.

New in this version

  • Topological validation: Application of Sperner’s Lemma confirms that coherence zones (RGB triangles) are mathematically necessary once O₂ is fixed as the tonic, independent of random distribution.

  • Fractal self-similarity: Multi-scale simulations (n = 6–12) show constant coherence density (~5 %), establishing a vibrational fractal constant.

  • Tuned-medium amplification: When R_local distributions are biased toward oxygenic ratios, coherence density rises to ~22 %, and centroid clustering stabilizes near (0.5, 0.25) — a persistent harmonic attractor across scales.

  • Comparative framework: Introduces Section 5.3, benchmarking The Oxygen Octave against three established falsifiable models — quantum coherence in biology, scale-free networks, and stochastic resonance — confirming equivalent scientific viability and predictive power.

  • Experimental roadmap: Defines clear validation paths via spectroscopy, molecular-dynamics simulation, and bioresonant coupling studies.

Summary

The Oxygen Octave now functions as a unified model of harmonic self-organization, where oxygen’s structural ratios form the bridge between geometry, energy, and biological coherence.

Its combination of quantitative spectroscopy, mathematical topology, and AI-assisted reproducibility positions it as a testable, interdisciplinary foundation for exploring coherence as a universal property of matter.

Data Availability:

All datasets referenced in this work are publicly accessible via NIST, HITRAN, JPL, and IUPAC.

AI-based ratio extrapolations (Grok 2025) are available upon request.

Researchers, collaborators, or institutions interested in testing or expanding this hypothesis are invited to connect and explore possible lines of validation together


Jaime Ojeda
Jaime.ojse@gmail.com

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The Oxygen Octave- Foundations- Quantitative Correlations Across Vibrational Systems .pdf

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Additional details

Dates

Submitted
2025-10-06
Submitted for public preprint release

References

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  • Helmholtz, H. von (1863). On the Sensations of Tone as a Physiological Basis for the Theory of Music. Longmans, Green, and Co.