Skip to main Communities My dashboard Log in Sign up There is a newer version of the record available. Published April 17, 2026 | Version 2.0.0 Dataset Restricted Data and Code for "A Sharp Transition in Force Law Recoverability at Three Spatial Dimensions" Authors/Creators tanigawa, masato (Contact person) 1 Show affiliations 1. Oita University Description Source code, simulation data, and experiment results for the paper "A Sharp Transition in Force Law Recoverability at Three Spatial Dimensions." This study investigates whether the recoverability of gravitational force laws from N-body trajectory data depends on the spatial dimension D. Using Interaction Networks (graph neural networks) trained on D-dimensional gravitational N-body simulations (D ∈ {2, 3, 4, 5}), we extract effective force exponents via log-log regression and measure law recovery accuracy across a systematic N × D grid scan (160 independent training runs, ε = 0.1, uniform parameters). The central finding is a sharp transition at D = 3: the R² of force-exponent regression reaches 0.22 at D = 3 but drops below 0.015 for all other dimensions. A two-way ANOVA confirms that spatial dimension accounts for 98.5% of the total variance (η² = 0.98, p < 10⁻¹⁶), while network depth contributes less than 4%. The pattern disappears under Hookean spring forces, establishing that the α = D − 1 coupling between force exponent and spatial dimension is the essential ingredient. Notes (English) Version 2 (2026-04-17): - Added compute_lyapunov.py: max Lyapunov exponent estimation via Rosenstein (1993) method - Added lyapunov_results.csv: per-episode λ_max values showing D=3 peak (bounded chaos signature) - Updated create_figure1.py to 3-panel version matching the published figure - Updated README with Lyapunov analysis instructions - No changes to core simulation data or main results Files Restricted The record is publicly accessible, but files are restricted. Log in to check if you have access. Additional details Dates Submitted 2026-04-07 Date when the dataset was created and first deposited to Zenodo. 66 Views 1 Downloads Show more details All versions This version Views Total views 66 21 Downloads Total downloads 1 0 Data volume Total data volume 2.8 GB 0 Bytes More info on how stats are collected.... Versions External resources Indexed in OpenAIRE Communities Keywords and subjects Keywords computational observability force law recovery spatial dimensions Ehrenfest simulation, gravitational dynamics machine learning Details DOI DOI Badge DOI 10.5281/zenodo.19622008 Markdown [](https://doi.org/10.5281/zenodo.19622008) reStructuredText .. image:: https://zenodo.org/badge/DOI/10.5281/zenodo.19622008.svg :target: https://doi.org/10.5281/zenodo.19622008 HTML <a href="https://doi.org/10.5281/zenodo.19622008"><img src="https://zenodo.org/badge/DOI/10.5281/zenodo.19622008.svg" alt="DOI"></a> Image URL https://zenodo.org/badge/DOI/10.5281/zenodo.19622008.svg Target URL https://doi.org/10.5281/zenodo.19622008 Resource type Dataset Publisher Zenodo Languages English Rights License Creative Commons Attribution 4.0 International The Creative Commons Attribution license allows re-distribution and re-use of a licensed work on the condition that the creator is appropriately credited. Read more Citation Export Technical metadata Created April 17, 2026 Modified April 17, 2026 Jump up About About Policies Infrastructure Principles Projects Roadmap Contact Blog Blog Support Help FAQ Developers REST API OAI-PMH Contribute GitHub Donate Funded by Powered by CERN Data Centre & InvenioRDM Status Privacy policy Cookie policy Terms of Use This site uses cookies. Find out more on how we use cookies Accept all cookies Accept only essential cookies