From a Gravity-Calibrated Helix to Neutrino Oscillation Correspondences: A Third Cross-Sector Comparison of the Frozen TEF Shape Parameter

Xiaodan Wu

doi:10.5281/zenodo.22150998

Abstract

This paper is the third cross-sector comparison in a TEF sequence built around the same dimensionless helical shape parameter $q = a / R = 0.556324180045 \dots$ . The value of $q$ was fixed in Paper I by a gravity-calibrated one-cycle condition, before any neutrino observable entered the analysis, and was inherited without reoptimization by Paper II in a conditional fine-structure correspondence. Motivated by the electrically neutral and colorless character of active neutrinos, the present work carries the same frozen $q$ into neutrino oscillation data. Two post-hoc but coefficient-free correspondences are recorded: $q^{2} = 0.3094965933 \dots$ , compared with JUNO’s $sin^{2} θ_{12} = 0.3092 \pm 0.0087$ , and $q^{6} = 0.0296461034 \dots$ , compared with $r_{ν} = Δ m_{21}^{2} /∣Δ m_{3 ℓ}^{2} ∣$ . Current JUNO and NuFIT 6.1 values give $r_{ν} ≃ 0.02975$ for normal ordering and $r_{ν} ≃ 0.02988$ for inverted ordering, both compatible with $q^{6}$ at present precision. Eliminating $q$ gives the prospective phenomenological test $r_{ν} ≃ sin^{6} θ_{12}$ ; this is not an independent third piece of evidence. No neutrino mechanism is claimed. For the Euclidean circular-helix ansatz, $q$ also satisfies the exact Frenet-Serret identity $q = τ / κ$ , giving it an intrinsic dimensionless geometric meaning. A future theory would need a common relativistic spectral operator whose eigenvectors and mass-squared eigenvalue gaps generate the two frozen correspondences without inserting them by hand.

Research Context

This preprint carries the dimensionless helical shape parameter fixed in the first TEF paper into a sector for which it was not fitted. Active neutrinos provide a comparatively clean comparison because they are electrically neutral and colorless while participating in the weak interaction.

Using the frozen value $q = 0.556324180045 \dots$ , the paper records two numerical correspondences: $q^{2}$ is close to JUNO’s measured solar mixing quantity $sin^{2} θ_{12}$ , and $q^{6}$ is close to the ratio of the solar and atmospheric-scale mass-squared splittings. With the ordering-independent convention $r_{ν} = Δ m_{21}^{2} /∣Δ m_{3 ℓ}^{2} ∣$ , eliminating $q$ yields a prospective relation between independently measurable neutrino observables:

r_{ν} ≃ sin^{6} θ_{12} .

The preprint does not claim to derive neutrino mixing, the PMNS matrix, or a neutrino mass spectrum. It identifies a mathematical question for future work: whether a common relativistic spectral operator derived from the same geometry can produce both the relevant mixing overlap and mass-squared eigenvalue gaps without inserting either mapping by hand.

Methodological Boundaries

No continuous neutrino parameter is fitted in the comparison, but the downstream mappings $q^{2}$ and $q^{6}$ were identified after examining the neutrino sector and therefore carry a mapping-choice and look-elsewhere burden. From this release onward, the numerical targets are frozen for prospective comparison rather than adjusted to preserve agreement.

The relation between the geometric parameter and neutrino observables remains phenomenological until a dynamical or spectral mechanism is constructed. The reported agreements may ultimately be accidental.

Publication Status

Version 4.2 is publicly archived on Zenodo as a preprint under the Creative Commons Attribution 4.0 International license. Its version-specific DOI is 10.5281/zenodo.22150998; the concept DOI for the complete version history is 10.5281/zenodo.22150997. The preprint has not undergone peer review.

The retained LaTeX source, numerical checks, checksums, and release metadata are maintained in the public TEF research repository. The repository supplements the authoritative Zenodo PDF rather than replacing the archival record.

Relationship to the Companion Manuscripts

The paper inherits its helical parameter from A Helical Spacetime Ansatz Linking the Planck Scale and Electroweak Mixing and follows its use in From a Gravity-Calibrated Helix to a Conditional Fine-Structure Correspondence. It should be read as an out-of-sector numerical test of that pre-existing parameter, not as an independent fit to neutrino data.

Citation

Zenodo citation

Wu, X. (2026). From a Gravity-Calibrated Helix to Neutrino Oscillation Correspondences: A Third Cross-Sector Comparison of the Frozen TEF Shape Parameter (Version 4.2). Zenodo. https://doi.org/10.5281/zenodo.22150998

@misc{wu2026neutrino,
  author = {Wu, Xiaodan},
  title = {From a Gravity-Calibrated Helix to Neutrino Oscillation Correspondences: A Third Cross-Sector Comparison of the Frozen TEF Shape Parameter},
  year = {2026},
  publisher = {Zenodo},
  version = {4.2},
  doi = {10.5281/zenodo.22150998},
  url = {https://doi.org/10.5281/zenodo.22150998}
}

Version History

v4.2 - August 29, 2026

Public preprint release on Zenodo. Version DOI: 10.5281/zenodo.22150998.

v0.2 - August 20, 2026

Previous public working manuscript. Added the torsion-to-curvature interpretation of $q$ , a direct observable relation, and an explicit spectral-operator problem while preserving the numerical results as empirical correspondences.