{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:7VSRDOMIBMGWJEDNIONLVPUHFM","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":"cb70680549dcb29c11d198efab859987c1e5f906e6f0f642360a087d77fb676d","cross_cats_sorted":["astro-ph.CO","astro-ph.GA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.IM","submitted_at":"2017-12-29T04:49:20Z","title_canon_sha256":"c25e7f250a0fbb451d3747b8115c01e6a368cf403d77f723523697512863cb1c"},"schema_version":"1.0","source":{"id":"1712.10116","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.10116","created_at":"2026-05-18T00:27:03Z"},{"alias_kind":"arxiv_version","alias_value":"1712.10116v1","created_at":"2026-05-18T00:27:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.10116","created_at":"2026-05-18T00:27:03Z"},{"alias_kind":"pith_short_12","alias_value":"7VSRDOMIBMGW","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"7VSRDOMIBMGWJEDN","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"7VSRDOMI","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:386c9b19d9b4f8b6c3e650966ae642819191d0edd7630ead17d4192b37339fed","target":"graph","created_at":"2026-05-18T00:27:03Z","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":"$N$-body simulations study the dynamics of $N$ particles under the influence of mutual long-distant forces such as gravity. In practice, $N$-body codes will violate Newton's third law if they use either an approximate Poisson solver or individual timesteps. In this study, we construct a novel $N$-body scheme by combining a fast multipole method (FMM) based Poisson solver and a time integrator using a hierarchical Hamiltonian splitting (HHS) technique. We test our implementation for collision-less systems using several problems in galactic dynamics. As a result of the momentum conserving nature","authors_text":"Qirong Zhu","cross_cats":["astro-ph.CO","astro-ph.GA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.IM","submitted_at":"2017-12-29T04:49:20Z","title":"A momentum conserving $N$-body scheme with individual timesteps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.10116","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:a8831621265fc0ff3ca09481af21e84da45ceb2d388528d398ce678ee1d11cc6","target":"record","created_at":"2026-05-18T00:27:03Z","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":"cb70680549dcb29c11d198efab859987c1e5f906e6f0f642360a087d77fb676d","cross_cats_sorted":["astro-ph.CO","astro-ph.GA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.IM","submitted_at":"2017-12-29T04:49:20Z","title_canon_sha256":"c25e7f250a0fbb451d3747b8115c01e6a368cf403d77f723523697512863cb1c"},"schema_version":"1.0","source":{"id":"1712.10116","kind":"arxiv","version":1}},"canonical_sha256":"fd6511b9880b0d64906d439ababe872b1dbee838a03c3e9061a844c1c8eccbb4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fd6511b9880b0d64906d439ababe872b1dbee838a03c3e9061a844c1c8eccbb4","first_computed_at":"2026-05-18T00:27:03.899384Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:27:03.899384Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OIfFyJIFP0zaHlu0i5nhIUWiMREJpGLc9fCtSO5yHHFtWptBvmoKl861LKwQcQV0mBUO5YdVBT+VB4ZzF6GPDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:27:03.899899Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.10116","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a8831621265fc0ff3ca09481af21e84da45ceb2d388528d398ce678ee1d11cc6","sha256:386c9b19d9b4f8b6c3e650966ae642819191d0edd7630ead17d4192b37339fed"],"state_sha256":"56e9af1d35dc787646a334deb63639b6c05b6a0186b3ad9ac544eed18eb2b0f3"}