{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:F6LUSGM6X4A5SI2SBRT4VJZUBB","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"80ab722ad2004d63b778222c099c5fbab8436f659dbdf9ced8e12c08ecf4c6cf","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-11-20T14:23:09Z","title_canon_sha256":"9f4da0336680d9d41c500865c656c36084b7d68bb740d7f531026529d94fd4ad"},"schema_version":"1.0","source":{"id":"1811.08266","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.08266","created_at":"2026-05-17T23:59:48Z"},{"alias_kind":"arxiv_version","alias_value":"1811.08266v1","created_at":"2026-05-17T23:59:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.08266","created_at":"2026-05-17T23:59:48Z"},{"alias_kind":"pith_short_12","alias_value":"F6LUSGM6X4A5","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"F6LUSGM6X4A5SI2S","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"F6LUSGM6","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:ae4e36b163a8cc149ad0f1ae35dfa9bb1b0bae1b50a24bc24941977f4ef476e5","target":"graph","created_at":"2026-05-17T23:59:48Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Asymptotic velocity is defined as the Ces\\`aro limit of velocity. As such, its existence has been proven for bounded interaction potentials. This is known to be wrong in celestial mechanics with four or more bodies.\n  Here we show for a class of pair potentials including the homogeneous ones of degree -a for 0<a<2, that asymptotic velocities exist for up to four bodies, dimension three or larger, for any energy and almost all initial conditions on the energy surface.","authors_text":"Andreas Knauf","cross_cats":["math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-11-20T14:23:09Z","title":"Asymptotic velocity for four celestial bodies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.08266","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:a27f0ee59230935bd598ae54e07ff931b897621dbbd70f70280c8b75592791d0","target":"record","created_at":"2026-05-17T23:59:48Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"80ab722ad2004d63b778222c099c5fbab8436f659dbdf9ced8e12c08ecf4c6cf","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-11-20T14:23:09Z","title_canon_sha256":"9f4da0336680d9d41c500865c656c36084b7d68bb740d7f531026529d94fd4ad"},"schema_version":"1.0","source":{"id":"1811.08266","kind":"arxiv","version":1}},"canonical_sha256":"2f9749199ebf01d923520c67caa73408796cbca817bdacbcedf0b7443d415bf3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2f9749199ebf01d923520c67caa73408796cbca817bdacbcedf0b7443d415bf3","first_computed_at":"2026-05-17T23:59:48.210823Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:48.210823Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u0cxIVJ7BZRsH7fYgN4hYnY2++QfkdphbVNhVm770tgmEbdJU679FaKgLHbaQeXWcNXwaBrfQRxKdzYvQE9TAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:48.211278Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.08266","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a27f0ee59230935bd598ae54e07ff931b897621dbbd70f70280c8b75592791d0","sha256:ae4e36b163a8cc149ad0f1ae35dfa9bb1b0bae1b50a24bc24941977f4ef476e5"],"state_sha256":"d621f4ba9deb8342ac6412dbcd56fe5eb634f6abb0d4bb72eabab458761c8998"}