{"paper":{"title":"Periods of N-body Systems Determined Through Dimensional Analysis","license":"http://creativecommons.org/licenses/by/4.0/","headline":"A generalization of dimensional analysis derives the periods of n-body gravitational systems up to a constant.","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Dan Jonsson","submitted_at":"2026-04-12T10:03:48Z","abstract_excerpt":"A generalization of classical dimensional analysis, presented in a separate article, makes it possible to derive Kepler's third law for the period of a two-body system, up to a multiplicative constant, without solving the equations of motion. Here we show how to derive generalizations of Kepler's third law to n-body systems by the same technique. Our results agree with conjectures by Sun on the period of a classical n-body system and by Semay and Sun on the quantum-theoretical counterpart of the period of a classical n-body system."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Here we show how to derive generalizations of Kepler's third law to n-body systems by the same technique. Our results agree with conjectures by Sun on the period of a classical n-body system and by Semay and Sun on the quantum-theoretical counterpart of the period of a classical n-body system.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The generalization of classical dimensional analysis presented in a separate article is valid and can be applied to derive periods for n-body systems.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Generalized dimensional analysis derives periods for classical and quantum n-body systems that match prior conjectures by Sun and by Semay and Sun.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A generalization of dimensional analysis derives the periods of n-body gravitational systems up to a constant.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"647f999496fb6d3be316bc0acf52b793decf704384fa9b3c488c9f03eb2aa970"},"source":{"id":"2604.10559","kind":"arxiv","version":4},"verdict":{"id":"07014154-1776-4800-9b68-72967158eed1","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-12T02:54:35.504682Z","strongest_claim":"Here we show how to derive generalizations of Kepler's third law to n-body systems by the same technique. Our results agree with conjectures by Sun on the period of a classical n-body system and by Semay and Sun on the quantum-theoretical counterpart of the period of a classical n-body system.","one_line_summary":"Generalized dimensional analysis derives periods for classical and quantum n-body systems that match prior conjectures by Sun and by Semay and Sun.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The generalization of classical dimensional analysis presented in a separate article is valid and can be applied to derive periods for n-body systems.","pith_extraction_headline":"A generalization of dimensional analysis derives the periods of n-body gravitational systems up to a constant."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.10559/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"80db9dc97c5b387bcbf06f0f04f512986bd9a24c361717323e8a0bd516089e06"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}