{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:LJSZA3YTGK3NKSCEPQAJLNPEV6","short_pith_number":"pith:LJSZA3YT","schema_version":"1.0","canonical_sha256":"5a65906f1332b6d548447c0095b5e4af9eae0084c0c432c25152d10070d95a3b","source":{"kind":"arxiv","id":"1103.1376","version":2},"attestation_state":"computed","paper":{"title":"Symplectic integrators in the shearing sheet","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.GA","astro-ph.IM","math.NA"],"primary_cat":"astro-ph.EP","authors_text":"Hanno Rein, Scott Tremaine","submitted_at":"2011-03-07T20:59:20Z","abstract_excerpt":"The shearing sheet is a model dynamical system that is used to study the small-scale dynamics of astrophysical disks. Numerical simulations of particle trajectories in the shearing sheet usually employ the leapfrog integrator, but this integrator performs poorly because of velocity-dependent (Coriolis) forces. We describe two new integrators for this purpose; both are symplectic, time-reversible and second-order accurate, and can easily be generalized to higher orders. Moreover, both integrators are exact when there are no small-scale forces such as mutual gravitational forces between disk par"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1103.1376","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2011-03-07T20:59:20Z","cross_cats_sorted":["astro-ph.GA","astro-ph.IM","math.NA"],"title_canon_sha256":"d4ce4eb6113f54b6bbf5cee52904576f54662500cecb6ed5c39476f50026835d","abstract_canon_sha256":"c94b4c2c86ba72e3ea2cd8fde4c05fb3d2789207026036cb8cf9b55a98e80c3d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:19:54.528501Z","signature_b64":"wK1dIv2hzY59M2MUNtV/Kddf7eCzyvlGbXeRatoqP+PSX5Kkym5Cm7Vk/46889Prg0BlAQfkzdh02bX8O6XWDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5a65906f1332b6d548447c0095b5e4af9eae0084c0c432c25152d10070d95a3b","last_reissued_at":"2026-05-18T04:19:54.527839Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:19:54.527839Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Symplectic integrators in the shearing sheet","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.GA","astro-ph.IM","math.NA"],"primary_cat":"astro-ph.EP","authors_text":"Hanno Rein, Scott Tremaine","submitted_at":"2011-03-07T20:59:20Z","abstract_excerpt":"The shearing sheet is a model dynamical system that is used to study the small-scale dynamics of astrophysical disks. Numerical simulations of particle trajectories in the shearing sheet usually employ the leapfrog integrator, but this integrator performs poorly because of velocity-dependent (Coriolis) forces. We describe two new integrators for this purpose; both are symplectic, time-reversible and second-order accurate, and can easily be generalized to higher orders. Moreover, both integrators are exact when there are no small-scale forces such as mutual gravitational forces between disk par"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.1376","kind":"arxiv","version":2},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1103.1376","created_at":"2026-05-18T04:19:54.527942+00:00"},{"alias_kind":"arxiv_version","alias_value":"1103.1376v2","created_at":"2026-05-18T04:19:54.527942+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.1376","created_at":"2026-05-18T04:19:54.527942+00:00"},{"alias_kind":"pith_short_12","alias_value":"LJSZA3YTGK3N","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_16","alias_value":"LJSZA3YTGK3NKSCE","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_8","alias_value":"LJSZA3YT","created_at":"2026-05-18T12:26:34.985390+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LJSZA3YTGK3NKSCEPQAJLNPEV6","json":"https://pith.science/pith/LJSZA3YTGK3NKSCEPQAJLNPEV6.json","graph_json":"https://pith.science/api/pith-number/LJSZA3YTGK3NKSCEPQAJLNPEV6/graph.json","events_json":"https://pith.science/api/pith-number/LJSZA3YTGK3NKSCEPQAJLNPEV6/events.json","paper":"https://pith.science/paper/LJSZA3YT"},"agent_actions":{"view_html":"https://pith.science/pith/LJSZA3YTGK3NKSCEPQAJLNPEV6","download_json":"https://pith.science/pith/LJSZA3YTGK3NKSCEPQAJLNPEV6.json","view_paper":"https://pith.science/paper/LJSZA3YT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1103.1376&json=true","fetch_graph":"https://pith.science/api/pith-number/LJSZA3YTGK3NKSCEPQAJLNPEV6/graph.json","fetch_events":"https://pith.science/api/pith-number/LJSZA3YTGK3NKSCEPQAJLNPEV6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LJSZA3YTGK3NKSCEPQAJLNPEV6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LJSZA3YTGK3NKSCEPQAJLNPEV6/action/storage_attestation","attest_author":"https://pith.science/pith/LJSZA3YTGK3NKSCEPQAJLNPEV6/action/author_attestation","sign_citation":"https://pith.science/pith/LJSZA3YTGK3NKSCEPQAJLNPEV6/action/citation_signature","submit_replication":"https://pith.science/pith/LJSZA3YTGK3NKSCEPQAJLNPEV6/action/replication_record"}},"created_at":"2026-05-18T04:19:54.527942+00:00","updated_at":"2026-05-18T04:19:54.527942+00:00"}