Fundamental limits from chaos on instability time predictions in compact planetary systems
Bibliographic record
Abstract
ABSTRACT Instabilities in compact planetary systems are generically driven by chaotic dynamics. This implies that an instability time measured through direct N-body integration is not exact, but rather represents a single draw from a distribution of equally valid chaotic trajectories. In order to characterize the ‘errors’ on reported instability times from direct N-body integrations, we investigate the shape and parameters of the instability time distributions (ITDs) for ensembles of shadow trajectories that are initially perturbed from one another near machine precision. We find that in the limit where instability times are long compared to the Lyapunov (chaotic) time-scale, ITDs approach remarkably similar lognormal distributions with standard deviations ≈0.43 ± 0.16 dex, despite the instability times varying across our sample from 104 to 108 orbits. We find excellent agreement between these predictions, derived from ≈450 closely packed configurations of three planets, and a much wider validation set of $\approx 10\, 000$ integrations, as well as on $\approx 20\, 000$ previously published integrations of tightly packed five-planet systems, and a seven-planet resonant chain based on TRAPPIST-1, despite their instability time-scales extending beyond our analysed time-scale. We also test the boundary of applicability of our results on dynamically excited versions of our Solar system. These distributions define the fundamental limit imposed by chaos on the predictability of instability times in such planetary systems. It provides a quantitative estimate of the instrinsic error on an N-body instability time imprinted by chaos, approximately a factor of 3 in either direction.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.024 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 source (direct Gemma or distilled Codex), 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".