David
102 posts

David
@DavidGauntletin
It's only a matter of time before my concepts show up in groundbreaking work from Bordeaux...again.
Columbus, OH Katılım Kasım 2025
75 Takip Edilen24 Takipçiler

@NASASolarSystem,@NASA, @NASAJPL @NASAAmes @NASAAmes @NASAAmesAcademy
Read:
The distribution of period ratios in multi-planet systems shows a systematic displacement from the exact 2:1 mean-motion resonance.
Using 1038 confirmed multi-planet systems from the NASA Exo- planet Archive (1555 adjacent pairs), we identify 56 pairs within the interval [2.000, 43/21] and measure their mean period ratio as ⟨R⟩ = 2.027±0.004 (boot- strap 95% CI), significantly above exact commensu- rability (p < 10−5 , Wilcoxon) and statistically consistent with our predicted value (p = 0.67, Wilcoxon).
We derive a quantitative model for this offset.
The symplectic transfer matrix T(k) governs near- resonant dynamics; at the stability boundary k = 2, it generates the Hamiltonian M¨obius map g(r) = 2 − 1/r, which drives ratios away from 2.
We show that adding the unique linear state-dependent dissipation γ(r) = 3−r—stronger near resonance, vanishing far from it—converts g exactly into the Jacobsthal map f(r) = 1+2/r, whose iterates are the Jacobsthal ratios J(n+1)/J(n) converging to 2.
The deviation identity
J(n + 1)/J(n) − 2 = (−1)n/J(n) places the dominant low-order attractor above 2:1 at 43/21 = 2 + 1/21, defining a resonance window of width ∆ = 1/21. Spectral-edge depletion near the boundary distributes systems withinthis window as
ρ(x) ∝ √ x,
yielding
⟨R⟩ − 2 = 3
5 ∆ = 1
35 ≈ 0.02857,
predicting
⟨R⟩ = 71/35 ≈ 2.0286.
A KS test on the wider interval [1.95, 2.10] gives p = 0.80.
Four independent lines of evidence support the framework:
(i) REBOUND N-body migration simulations cluster at 43/21 = 2.048, not 2.000;
(ii) TRAPPIST-1 non-adjacent period ratios align with Jacobsthal values (permutation p = 0.0004);
(iii) the Beta Pictoris system architecture at 30– 36 AU matches the Jacobsthal framework, independently confirmed at 30–35 AU;
(iv) Monte Carlo experiments confirm the √ ϵ edge exponent under migration-weighted ensembles.
The model has no free parameters.
doi.org/10.5281/zenodo…
English

Finally done
doi.org/10.5281/zenodo…
Titus bode keppler resolution
Also new sequence discovery
doi.org/10.5281/zenodo…
English

doi.org/10.5281/zenodo…
&
doi.org/10.5281/zenodo…
Whittled down to 2 papers.
English