📦 Version 3.0 released: Revised and expanded manuscript — submitted to Frontiers in Astronomy and Space Sciences, archived on Zenodo as the definitive preprint.

Author: Salah-Eddin Gherbi
Affiliation: Independent Researcher, United Kingdom
ORCID: 0009-0005-4017-1095
Contact: [email protected]
Concept DOI (always resolves to latest): 10.5281/zenodo.17432971
Latest Version DOI: 10.5281/zenodo.18816002
License: CC BY-NC 4.0

This repository contains the analytical and visualisation scripts accompanying the research:

Salah-Eddin Gherbi (2026)
The Harmonic Architecture of the Solar System:
A Silver-Ratio-Based Hypothesis for Planetary Spacing
Version 3.0 — Revised and expanded manuscript, definitive preprint
Zenodo DOI: 10.5281/zenodo.18816002

This research is the companion paper to the author's book:

Salah-Eddin Gherbi (2026)
Scala Harmonica: The Geometry of Planetary Resonance

The research reinterprets planetary spacing using the Celtic Cross harmonic model — a geometric framework based on algebraic ratios of √2 and its derivatives. The model accurately predicts planetary semi-major axes, identifies the hypothesised lost planet Harmonia at ≈ 2.14 AU, and demonstrates that the Solar System obeys a quantised harmonic order. All included Python scripts reproduce the published figures, tables, and numerical results of the paper.

Substantially revised version submitted to Frontiers in Astronomy and Space Sciences, archived on Zenodo as the definitive preprint. This version supersedes v2.0.

Key Changes:

• Revised and expanded manuscript with improved presentation and cleaner mathematical exposition
• Updated SRHF geometric construction figure (srhf_geometry_circles.png) now shows the full Celtic Cross geometry with labelled harmonic constants $(A, B, C, D)$
• Refined section structure with clearer separation of empirical results, comparative analysis, and speculative connections
• All quantitative results unchanged: MAPE ≈ 0.72%, RMSE ≈ 0.11 AU
• Python scripts updated to reflect consistent SRHF terminology throughout

DOI: 10.5281/zenodo.18816002

📥 PDF: v3.0/Gherbi_2026_Harmonic_Architecture_Solar_System_v3.pdf

Expanded quantitative and methodological foundations, refining both empirical validation and theoretical testability of the Celtic Cross harmonic model.

Key Enhancements:

• Empirical validation: MAPE ≈ 0.72%, RMSE ≈ 0.11 AU across all planetary orbits
• Comparative performance: outperforms classical Keplerian and Titius–Bode models by over an order of magnitude
• Falsifiability framework: explicit testable predictions including harmonic node at 2.14 AU
• Enhanced reproducibility: cryptographic verification and timestamping pipeline

DOI: 10.5281/zenodo.17521488

📥 PDF: Gherbi_2025_Harmonic_Architecture_Solar_System_v_2.pdf

Initial harmonic framework for the Solar System. Celtic Cross geometric model based on √2 ratios. Harmonia orbital prediction at 2.14 AU. Foundational scripts and verification proofs.

DOI: 10.5281/zenodo.17432971

📥 PDF: Gherbi_2025_Harmonic_Architecture_Solar_System_v1_1.pdf

harmonic-architecture-solar-system/
│
├── v3.0/                          ← Version 3.0 (current)
│   ├── scripts/                   ← Python scripts for v3.0
│   ├── figures/                   ← Output figures for v3.0
│   └── proof/                     ← Cryptographic provenance for v3.0
│
├── scripts/                       ← Scripts from v1.0–v2.0 (preserved)
├── figures/                       ← Figures from v1.0–v2.0 (preserved)
├── proof/                         ← Proof archive from v1.0–v2.0 (preserved)
│
├── Gherbi_2025_Harmonic_Architecture_Solar_System_v1_1.pdf
├── Gherbi_2025_Harmonic_Architecture_Solar_System_v_2.pdf
├── README.md
├── README_PROVENANCE.md
└── README_PROTECTION_SUMMARY.md

Note: The scripts/, figures/, and proof/ folders at the repository root belong to v1.0 and v2.0. All v3.0 materials are self-contained within the v3.0/ subfolder.

All scripts have been updated to reflect consistent SRHF terminology throughout. The underlying computations, constants, and outputs are unchanged from v2.0.

This folder contains the integrity and authorship verification package for the v3.0 manuscript and associated scripts, consistent with the methodology described in README_PROVENANCE.md.

To verify integrity independently:

sha256sum harmonic_architecture_frontiers_v1.zip
gpg --verify harmonic_architecture_frontiers_v1.zip.asc harmonic_architecture_frontiers_v1.zip
ots verify harmonic_architecture_frontiers_v1.zip.ots

The scripts/, figures/, and proof/ folders at the repository root contain materials from v1.0 and v2.0 and are preserved for continuity and reproducibility.

All code written in Python 3, using standard scientific libraries:

• numpy 1.26
• matplotlib 3.9
• scipy 1.13

All numerical results computed in double precision. Figures exported in PDF/PNG at 600 DPI using Matplotlib.

1. Clone or download this repository:

   git clone https://github.com/salahealer9/harmonic-architecture-solar-system.git
   cd harmonic-architecture-solar-system/v3.0/scripts

2. Install required packages (Python 3.10+):

   pip install numpy matplotlib scipy

3. Run the scripts:

   python srhf_harmonia_optimisation.py
   python srhf_harmonia_orbit.py
   python srhf_hsi_values.py
   python srhf_log_validation.py
   python srhf_percent_deviation.py
   python srhf_ratios_full.py
   python srhf_ratios_zoom.py
   python srhf_residuals_comparison.py
   python srhf_residuals_log.py
   python srhf_residuals_symlog.py
   python srhf_rmse_hsi_basin.py

   Each script produces .pdf and .png outputs in the working directory.

All research scripts and results are cryptographically timestamped and digitally signed to ensure authorship integrity and reproducibility. The v3.0/proof/ folder contains the complete provenance package for this version. Root-level proof/ materials cover v1.0 and v2.0.

See README_PROVENANCE.md for full verification instructions including SHA-256, GPG, and OpenTimestamps procedures.

Please cite the latest version using the v3.0 DOI:

Gherbi, S.-E. (2026). The Harmonic Architecture of the Solar System: A Silver-Ratio-Based Hypothesis for Planetary Spacing. Version 3.0. Zenodo. DOI: 10.5281/zenodo.18816002

@article{gherbi_2026_harmonic_architecture,
  author    = {Gherbi, Salah-Eddin},
  title     = {The Harmonic Architecture of the Solar System:
               A Silver-Ratio-Based Hypothesis for Planetary Spacing},
  year      = {2026},
  publisher = {Zenodo},
  version   = {3.0},
  doi       = {10.5281/zenodo.18816002}
}

@book{gherbi_2026_scala_harmonica,
  author    = {Gherbi, Salah-Eddin},
  title     = {{Scala Harmonica: The Geometry of Planetary Resonance}},
  publisher = {Vektor Publishing},
  year      = {2026},
  isbn      = {9781837095209}
}

For citation of specific earlier versions, see the Version History section above.

This repository is licensed under the Creative Commons Attribution–NonCommercial 4.0 International (CC BY–NC 4.0).

© 2026 Salah-Eddin Gherbi.
You may share and adapt this material for non-commercial purposes, provided appropriate credit is given.

All original research scripts and figures have been cryptographically timestamped and digitally signed to ensure authenticity and provenance.

➡️ README_PROVENANCE.md — full verification instructions
➡️ README_PROTECTION_SUMMARY.md — public summary

Author: Salah-Eddin Gherbi
Email: [email protected]
ORCID: 0009-0005-4017-1095
Repository: harmonic-architecture-solar-system