{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:LDHHL2HXSMHHCB4YIN2DAKTWG6","short_pith_number":"pith:LDHHL2HX","schema_version":"1.0","canonical_sha256":"58ce75e8f7930e7107984374302a76378fac47965527a73135bc5877b14789c8","source":{"kind":"arxiv","id":"0908.2269","version":2},"attestation_state":"computed","paper":{"title":"A Symplectic Integrator for Hill's Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.EP","authors_text":"D. C. Richardson, R. Barnes, R. P. Perrine, T. Quinn","submitted_at":"2009-08-17T00:39:06Z","abstract_excerpt":"Hill's equations are an approximation that is useful in a number of areas of astrophysics including planetary rings and planetesimal disks. We derive a symplectic method for integrating Hill's equations based on a generalized leapfrog. This method is implemented in the parallel N-body code, PKDGRAV and tested on some simple orbits. The method demonstrates a lack of secular changes in orbital elements, making it a very useful technique for integrating Hill's equations over many dynamical times. Furthermore, the method allows for efficient collision searching using linear extrapolation of partic"},"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":"0908.2269","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2009-08-17T00:39:06Z","cross_cats_sorted":[],"title_canon_sha256":"4b2c5939b675c4b0dc74a908cf1be6e19038b71a871c2d24d24d71bb1c577f05","abstract_canon_sha256":"319e3a52f2716da8d6cd211b801a725d28d0ced6862a6fc5f3189326341f38dc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:12:33.680304Z","signature_b64":"X54U5JA/33WXIVE3k6OLeUxCnBzdA/cNe3WZ5lPgjbtYv4fc7jd+oLt6nxxNW6xZNx8nBFmPGakAU623gnlXAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"58ce75e8f7930e7107984374302a76378fac47965527a73135bc5877b14789c8","last_reissued_at":"2026-05-18T02:12:33.679670Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:12:33.679670Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Symplectic Integrator for Hill's Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.EP","authors_text":"D. C. Richardson, R. Barnes, R. P. Perrine, T. Quinn","submitted_at":"2009-08-17T00:39:06Z","abstract_excerpt":"Hill's equations are an approximation that is useful in a number of areas of astrophysics including planetary rings and planetesimal disks. We derive a symplectic method for integrating Hill's equations based on a generalized leapfrog. This method is implemented in the parallel N-body code, PKDGRAV and tested on some simple orbits. The method demonstrates a lack of secular changes in orbital elements, making it a very useful technique for integrating Hill's equations over many dynamical times. Furthermore, the method allows for efficient collision searching using linear extrapolation of partic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.2269","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":"0908.2269","created_at":"2026-05-18T02:12:33.679775+00:00"},{"alias_kind":"arxiv_version","alias_value":"0908.2269v2","created_at":"2026-05-18T02:12:33.679775+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0908.2269","created_at":"2026-05-18T02:12:33.679775+00:00"},{"alias_kind":"pith_short_12","alias_value":"LDHHL2HXSMHH","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_16","alias_value":"LDHHL2HXSMHHCB4Y","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_8","alias_value":"LDHHL2HX","created_at":"2026-05-18T12:26:00.592388+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/LDHHL2HXSMHHCB4YIN2DAKTWG6","json":"https://pith.science/pith/LDHHL2HXSMHHCB4YIN2DAKTWG6.json","graph_json":"https://pith.science/api/pith-number/LDHHL2HXSMHHCB4YIN2DAKTWG6/graph.json","events_json":"https://pith.science/api/pith-number/LDHHL2HXSMHHCB4YIN2DAKTWG6/events.json","paper":"https://pith.science/paper/LDHHL2HX"},"agent_actions":{"view_html":"https://pith.science/pith/LDHHL2HXSMHHCB4YIN2DAKTWG6","download_json":"https://pith.science/pith/LDHHL2HXSMHHCB4YIN2DAKTWG6.json","view_paper":"https://pith.science/paper/LDHHL2HX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0908.2269&json=true","fetch_graph":"https://pith.science/api/pith-number/LDHHL2HXSMHHCB4YIN2DAKTWG6/graph.json","fetch_events":"https://pith.science/api/pith-number/LDHHL2HXSMHHCB4YIN2DAKTWG6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LDHHL2HXSMHHCB4YIN2DAKTWG6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LDHHL2HXSMHHCB4YIN2DAKTWG6/action/storage_attestation","attest_author":"https://pith.science/pith/LDHHL2HXSMHHCB4YIN2DAKTWG6/action/author_attestation","sign_citation":"https://pith.science/pith/LDHHL2HXSMHHCB4YIN2DAKTWG6/action/citation_signature","submit_replication":"https://pith.science/pith/LDHHL2HXSMHHCB4YIN2DAKTWG6/action/replication_record"}},"created_at":"2026-05-18T02:12:33.679775+00:00","updated_at":"2026-05-18T02:12:33.679775+00:00"}