{"paper":{"title":"Are numerical theories irreplaceable? A computational complexity analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.CD","authors_text":"Dmitry Pavlov, Nickolay Vasiliev","submitted_at":"2017-09-10T23:54:48Z","abstract_excerpt":"It is widely known that numerically integrated orbits are more precise than analytical theories for celestial bodies. However, calculation of the positions of celestial bodies via numerical integration at time $t$ requires the amount of computer time proportional to $t$, while calculation by analytical series is usually asymptotically faster.\n  The following question then arises: can the precision of numerical theories be combined with the computational speed of analytical ones? We give a negative answer to that question for a particular three-body problem known as Sitnikov problem.\n  A formal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.03939","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}