{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:IBYTQ26J6D6IYVPXGGQDSMB3PP","short_pith_number":"pith:IBYTQ26J","canonical_record":{"source":{"id":"astro-ph/0606221","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"astro-ph","submitted_at":"2006-06-09T08:03:40Z","cross_cats_sorted":[],"title_canon_sha256":"79d6a34f4b450aa253fb0ec38957f92ea61665673a6c5b51537e1355e9835ed9","abstract_canon_sha256":"cd523bfb90f5c302173515df4dfde51450d93b7e94d45ecfdc4cab5b6fd515ee"},"schema_version":"1.0"},"canonical_sha256":"4071386bc9f0fc8c55f731a039303b7beac2df049693a0de112f2c1e5efc62fc","source":{"kind":"arxiv","id":"astro-ph/0606221","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"astro-ph/0606221","created_at":"2026-05-18T01:40:30Z"},{"alias_kind":"arxiv_version","alias_value":"astro-ph/0606221v1","created_at":"2026-05-18T01:40:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.astro-ph/0606221","created_at":"2026-05-18T01:40:30Z"},{"alias_kind":"pith_short_12","alias_value":"IBYTQ26J6D6I","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"IBYTQ26J6D6IYVPX","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"IBYTQ26J","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:IBYTQ26J6D6IYVPXGGQDSMB3PP","target":"record","payload":{"canonical_record":{"source":{"id":"astro-ph/0606221","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"astro-ph","submitted_at":"2006-06-09T08:03:40Z","cross_cats_sorted":[],"title_canon_sha256":"79d6a34f4b450aa253fb0ec38957f92ea61665673a6c5b51537e1355e9835ed9","abstract_canon_sha256":"cd523bfb90f5c302173515df4dfde51450d93b7e94d45ecfdc4cab5b6fd515ee"},"schema_version":"1.0"},"canonical_sha256":"4071386bc9f0fc8c55f731a039303b7beac2df049693a0de112f2c1e5efc62fc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:40:30.195162Z","signature_b64":"C6A7vS+RhJvL5LpiquZgupImoIA/VHO8QtYM2Rstn8H9uiiE792GVwE+4dp4YZCwsZmS7wyVnKWNWLcWstLkAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4071386bc9f0fc8c55f731a039303b7beac2df049693a0de112f2c1e5efc62fc","last_reissued_at":"2026-05-18T01:40:30.194496Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:40:30.194496Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"astro-ph/0606221","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:40:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"57FFuVKjLS5MkUSCYswu0kk/DF5cmGsDeeyZKJr1RKgL/pZA+6UwsPrn15awPdKh4abQvbuxON3A6yAQA3UCDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T08:03:44.991900Z"},"content_sha256":"4b3184229accdb9334770af491ebf6a9d85433872c2fe546248497d5169f269c","schema_version":"1.0","event_id":"sha256:4b3184229accdb9334770af491ebf6a9d85433872c2fe546248497d5169f269c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:IBYTQ26J6D6IYVPXGGQDSMB3PP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Computing secular motion under slowly rotating quadratic perturbation","license":"","headline":"","cross_cats":[],"primary_cat":"astro-ph","authors_text":"P. Nurmi, S. Mikkola","submitted_at":"2006-06-09T08:03:40Z","abstract_excerpt":"We consider secular perturbations of nearly Keplerian two-body motion under a perturbing potential that can be approximated to sufficient accuracy by expanding it to second order in the coordinates. After averaging over time to obtain the secular Hamiltonian, we use angular momentum and eccentricity vectors as elements. The method of variation of constants then leads to a set of equations of motion that are simple and regular, thus allowing efficient numerical integration. Some possible applications are briefly described."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"astro-ph/0606221","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:40:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OOm/6KwsouAg2fzupwMPrD5fR1DXLCITWpv51W5NMZnLa82XnONiHuYs30EK3AZq9yviVzyUd1mL5CfRZhZTBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T08:03:44.992562Z"},"content_sha256":"95585eb1263b8fb7beee02eb675d8f95024666202024c4c58bd0644f7d758850","schema_version":"1.0","event_id":"sha256:95585eb1263b8fb7beee02eb675d8f95024666202024c4c58bd0644f7d758850"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IBYTQ26J6D6IYVPXGGQDSMB3PP/bundle.json","state_url":"https://pith.science/pith/IBYTQ26J6D6IYVPXGGQDSMB3PP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IBYTQ26J6D6IYVPXGGQDSMB3PP/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-09T08:03:44Z","links":{"resolver":"https://pith.science/pith/IBYTQ26J6D6IYVPXGGQDSMB3PP","bundle":"https://pith.science/pith/IBYTQ26J6D6IYVPXGGQDSMB3PP/bundle.json","state":"https://pith.science/pith/IBYTQ26J6D6IYVPXGGQDSMB3PP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IBYTQ26J6D6IYVPXGGQDSMB3PP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:IBYTQ26J6D6IYVPXGGQDSMB3PP","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":"cd523bfb90f5c302173515df4dfde51450d93b7e94d45ecfdc4cab5b6fd515ee","cross_cats_sorted":[],"license":"","primary_cat":"astro-ph","submitted_at":"2006-06-09T08:03:40Z","title_canon_sha256":"79d6a34f4b450aa253fb0ec38957f92ea61665673a6c5b51537e1355e9835ed9"},"schema_version":"1.0","source":{"id":"astro-ph/0606221","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"astro-ph/0606221","created_at":"2026-05-18T01:40:30Z"},{"alias_kind":"arxiv_version","alias_value":"astro-ph/0606221v1","created_at":"2026-05-18T01:40:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.astro-ph/0606221","created_at":"2026-05-18T01:40:30Z"},{"alias_kind":"pith_short_12","alias_value":"IBYTQ26J6D6I","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"IBYTQ26J6D6IYVPX","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"IBYTQ26J","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:95585eb1263b8fb7beee02eb675d8f95024666202024c4c58bd0644f7d758850","target":"graph","created_at":"2026-05-18T01:40:30Z","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":"We consider secular perturbations of nearly Keplerian two-body motion under a perturbing potential that can be approximated to sufficient accuracy by expanding it to second order in the coordinates. After averaging over time to obtain the secular Hamiltonian, we use angular momentum and eccentricity vectors as elements. The method of variation of constants then leads to a set of equations of motion that are simple and regular, thus allowing efficient numerical integration. Some possible applications are briefly described.","authors_text":"P. Nurmi, S. Mikkola","cross_cats":[],"headline":"","license":"","primary_cat":"astro-ph","submitted_at":"2006-06-09T08:03:40Z","title":"Computing secular motion under slowly rotating quadratic perturbation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"astro-ph/0606221","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":"sha256:4b3184229accdb9334770af491ebf6a9d85433872c2fe546248497d5169f269c","target":"record","created_at":"2026-05-18T01:40:30Z","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":"cd523bfb90f5c302173515df4dfde51450d93b7e94d45ecfdc4cab5b6fd515ee","cross_cats_sorted":[],"license":"","primary_cat":"astro-ph","submitted_at":"2006-06-09T08:03:40Z","title_canon_sha256":"79d6a34f4b450aa253fb0ec38957f92ea61665673a6c5b51537e1355e9835ed9"},"schema_version":"1.0","source":{"id":"astro-ph/0606221","kind":"arxiv","version":1}},"canonical_sha256":"4071386bc9f0fc8c55f731a039303b7beac2df049693a0de112f2c1e5efc62fc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4071386bc9f0fc8c55f731a039303b7beac2df049693a0de112f2c1e5efc62fc","first_computed_at":"2026-05-18T01:40:30.194496Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:40:30.194496Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"C6A7vS+RhJvL5LpiquZgupImoIA/VHO8QtYM2Rstn8H9uiiE792GVwE+4dp4YZCwsZmS7wyVnKWNWLcWstLkAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:40:30.195162Z","signed_message":"canonical_sha256_bytes"},"source_id":"astro-ph/0606221","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4b3184229accdb9334770af491ebf6a9d85433872c2fe546248497d5169f269c","sha256:95585eb1263b8fb7beee02eb675d8f95024666202024c4c58bd0644f7d758850"],"state_sha256":"33fa56e80f376ac56e17674ea80de5271b318847b88fa27e8388c4846505c0f6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LtRB82b7wYXHMK74CuA/pVZvgmCTZyv/SGV3d9tyQGNfuoZGQQLA35Y4WIkH/fQAUhKWrh0uLog4qEJ9WFJiAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T08:03:44.996615Z","bundle_sha256":"7ae13fb05faa939fc54f06935683debb03c36115758f4f2a7855975a88bf5fdf"}}