The Harmonic Architecture of the Solar System

A Silver-Ratio-Based Hypothesis for Planetary Spacing
Salah-Eddin Gherbi · Independent Researcher, United Kingdom
ORCID: 0009-0005-4017-1095

Revised preprint, published on Zenodo: 10.5281/zenodo.23301593

Read the v3.1 PDF in this repository · Zenodo record

Version 3.1 corrects the numerical reporting, comparator definitions, data-provenance statements and interpretative limitations of the historical versions, without changing the Silver-Ratio Harmonic Framework (SRHF) mathematical prescription.

The fixed prescription describes nine observed Solar System bodies (eight planets and Pluto, a dwarf planet) with MAPE 0.792970% and RMSE 0.105821 AU, using the explicitly declared rounded semi-major axes and Earth = 1 AU normalization. The hypothetical Harmonia node at approximately 2.142136 AU is not observed and is excluded from the observational error scores.

For the same six classical planets under the stated C6 evaluation protocol, the respective MAPE values are 0.8954% for fixed SRHF, 2.6806% for the specified Titius–Bode model and 17.5152% for the idealised Kepler-solids construction. These are descriptive comparisons under particular prescriptions, not evidence that SRHF is uniquely or physically preferred.

The empirically fitted outer-five optimum, 2.143687394 AU, is distinct from the fixed Silver node. The Harmonic Spread Index (HSI) measures the dispersion of percentage residuals; it is not a measure of gravitational stability. The model is a phenomenological spacing hypothesis, not an established planetary formation mechanism, a detection of a lost planet, proof of physical quantisation, or a demonstrated statistical-significance result.

The orbital inputs are author-adopted rounded values compiled from earlier published reference materials; the precise source editions, orbital-element conventions and reference epochs have not been fully reconstructed. See the manuscript for the full methods, tests, and limitations.

This public branch preserves historical v1.0–v3.0 scripts, figures and provenance materials. The v3.1 manuscript PDF is published here and on Zenodo.

The separately audited SRHF v3.1.0 Python source-only software release is now public. Its 18-file curated package is available in software/srhf-v3.1/, under the signed software-v3.1.0 Git tag, and in the independent Zenodo Software record. Historical scripts, figures and proofs may report superseded results or interpretations and should not be confused with the corrected release.

• Historical v3.0 materials
• Historical root-level scripts
• Historical root-level figures
• Historical provenance notes
• Historical protection summary

The v3.1 scientific manuscript uses 14 figure inclusions. Eleven scientific graphic assets have identified generator scripts; three retained graphic assets do not have independently matched generator scripts. Reproducibility claims are limited to the documented scope.

The previously reported historical numerical scores and claims should not be treated as corrected v3.1 results. Past Git history and preprints are preserved as historical records, not silently rewritten.

The v1.0 and v2.0 manuscript PDFs are preserved in their historical Zenodo records and Git history rather than duplicated at the repository root.

Gherbi, Salah-Eddin (2026). The Harmonic Architecture of the Solar System: A Silver-Ratio-Based Hypothesis for Planetary Spacing. Version 3.1. Zenodo. https://doi.org/10.5281/zenodo.23301593

@misc{gherbi_2026_srhf_v31,
  author    = {Gherbi, Salah-Eddin},
  title     = {The Harmonic Architecture of the Solar System: A Silver-Ratio-Based Hypothesis for Planetary Spacing},
  year      = {2026},
  version   = {3.1},
  publisher = {Zenodo},
  doi       = {10.5281/zenodo.23301593}
}

Companion book: Gherbi, Salah-Eddin (2026). Scala Harmonica: The Geometry of Planetary Resonance. Vektor Publishing. ISBN 9781837095209.

The v3.1 manuscript and author-controlled figures use the CC BY-NC 4.0 licence, subject to the stated source/rights scope. The historical repository files retain their applicable historical licences and notices. The 13 identified author-controlled Python source files in the v3.1.0 software package are released under MIT, as documented in SOURCE_LICENSE_SCOPE.md. Third-party dependencies and other repository materials retain their applicable separate licensing terms.

Signed Git commits, file hashes and release-review evidence were retained in the author's separate working history. The public manuscript and curated software releases do not publish the private scientific-audit branch, private review records or draft packages. See README_PROVENANCE.md for historical public provenance instructions.

Salah-Eddin Gherbi · ORCID
Email: salahealer@gmail.com