Prime Harmonic Stability Law: A Universal Framework for Planetary Spacing and Orbital Architecture
Bibliographic record
Abstract
This paper introduces the Prime Harmonic Stability Law, a resonance-based model for planetary system architecture derived from the Resonant Order Theory of Everything (ROTE). By defining a harmonic index n=ln(a/Lref)lnφn = \dfrac{\ln(a / L_{\text{ref}})}{\ln \varphi}n=lnφln(a/Lref), where φ\varphiφ is the golden ratio, we demonstrate that planetary orbits cluster near prime-numbered harmonic shells, analogous to noble gas stability in atomic systems. Analysis of 11 planetary systems (Solar System + 10 exoplanet systems) validates this framework, revealing that over 85% of planets reside within Δn<1\Delta n < 1Δn<1 of a prime shell. The model predicts the existence of additional outer planets (e.g., Planet Nine at ~142 AU) and offers a unified principle linking atomic and cosmic order. This deterministic approach replaces empirical laws like Titius-Bode with a physically grounded, prime-resonance-based architecture.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".