{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:7CWK3TCOHK3XMHQCAZCBCN45RV","short_pith_number":"pith:7CWK3TCO","canonical_record":{"source":{"id":"1504.05957","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2015-04-22T20:00:39Z","cross_cats_sorted":["astro-ph.SR"],"title_canon_sha256":"efab6823097f581b471e34371e0c37e0f3a816a2a8e926fa93c7065ba78bdd34","abstract_canon_sha256":"ed3e62e7184e7d753e8a23214a2574592f2013ee7f74af986d3f758bd22a04ee"},"schema_version":"1.0"},"canonical_sha256":"f8acadcc4e3ab7761e02064411379d8d405d130133a436bca0c4025760514c71","source":{"kind":"arxiv","id":"1504.05957","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.05957","created_at":"2026-05-18T01:37:07Z"},{"alias_kind":"arxiv_version","alias_value":"1504.05957v2","created_at":"2026-05-18T01:37:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.05957","created_at":"2026-05-18T01:37:07Z"},{"alias_kind":"pith_short_12","alias_value":"7CWK3TCOHK3X","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"7CWK3TCOHK3XMHQC","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"7CWK3TCO","created_at":"2026-05-18T12:29:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:7CWK3TCOHK3XMHQCAZCBCN45RV","target":"record","payload":{"canonical_record":{"source":{"id":"1504.05957","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2015-04-22T20:00:39Z","cross_cats_sorted":["astro-ph.SR"],"title_canon_sha256":"efab6823097f581b471e34371e0c37e0f3a816a2a8e926fa93c7065ba78bdd34","abstract_canon_sha256":"ed3e62e7184e7d753e8a23214a2574592f2013ee7f74af986d3f758bd22a04ee"},"schema_version":"1.0"},"canonical_sha256":"f8acadcc4e3ab7761e02064411379d8d405d130133a436bca0c4025760514c71","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:07.356500Z","signature_b64":"hlLG83RBZgEOA0xNm/rmL/tgnIYxautoBsV8J9lVGy2lfFIP72BT8HmJtmNyk4Qm884guIpwuQTtiK7HtKnvBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f8acadcc4e3ab7761e02064411379d8d405d130133a436bca0c4025760514c71","last_reissued_at":"2026-05-18T01:37:07.356048Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:07.356048Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.05957","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:37:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2+snx2PlqRHqEgvBW4egs58X/l7Gqs/rQv+kp0gaeTHrhPqi5U19gf9q3bBt4Gmg1f8yxf3LfFQBC+sij/LvDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T21:01:29.397332Z"},"content_sha256":"244b0a0a6c713124c7119f2eeacabe9e99889ee629a09858993d57f5598aae8a","schema_version":"1.0","event_id":"sha256:244b0a0a6c713124c7119f2eeacabe9e99889ee629a09858993d57f5598aae8a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:7CWK3TCOHK3XMHQCAZCBCN45RV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Timescales of Kozai-Lidov oscillations at quadrupole and octupole order in the test particle limit","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.SR"],"primary_cat":"astro-ph.EP","authors_text":"Joseph M. O. Antognini","submitted_at":"2015-04-22T20:00:39Z","abstract_excerpt":"Kozai-Lidov (KL) oscillations in hierarchical triple systems have found application to many astrophysical contexts, including planet formation, type Ia supernovae, and supermassive black hole dynamics. The period of these oscillations is known at the order-of-magnitude level, but dependences on the initial mutual inclination or inner eccentricity are not typically included. In this work I calculate the period of KL oscillations ($t_{\\textrm{KL}}$) exactly in the test particle limit at quadrupole order (TPQ). I explore the parameter space of all hierarchical triples at TPQ and show that except "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.05957","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:37:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BmTqxTZ4oUwgTw5yv8BsYq5ppraiD24liKc6zdFQqqtsSugXF+B/f7/ZQPA4XYGstFPJJyCzCBlAOhhva9jrAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T21:01:29.397795Z"},"content_sha256":"dbff9cc9d004cb529932854cc4cfc3588425f86d7f0b7eb9aff908d4fed7c92f","schema_version":"1.0","event_id":"sha256:dbff9cc9d004cb529932854cc4cfc3588425f86d7f0b7eb9aff908d4fed7c92f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7CWK3TCOHK3XMHQCAZCBCN45RV/bundle.json","state_url":"https://pith.science/pith/7CWK3TCOHK3XMHQCAZCBCN45RV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7CWK3TCOHK3XMHQCAZCBCN45RV/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":"2026-08-03T21:01:29Z","links":{"resolver":"https://pith.science/pith/7CWK3TCOHK3XMHQCAZCBCN45RV","bundle":"https://pith.science/pith/7CWK3TCOHK3XMHQCAZCBCN45RV/bundle.json","state":"https://pith.science/pith/7CWK3TCOHK3XMHQCAZCBCN45RV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7CWK3TCOHK3XMHQCAZCBCN45RV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:7CWK3TCOHK3XMHQCAZCBCN45RV","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":"ed3e62e7184e7d753e8a23214a2574592f2013ee7f74af986d3f758bd22a04ee","cross_cats_sorted":["astro-ph.SR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2015-04-22T20:00:39Z","title_canon_sha256":"efab6823097f581b471e34371e0c37e0f3a816a2a8e926fa93c7065ba78bdd34"},"schema_version":"1.0","source":{"id":"1504.05957","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.05957","created_at":"2026-05-18T01:37:07Z"},{"alias_kind":"arxiv_version","alias_value":"1504.05957v2","created_at":"2026-05-18T01:37:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.05957","created_at":"2026-05-18T01:37:07Z"},{"alias_kind":"pith_short_12","alias_value":"7CWK3TCOHK3X","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"7CWK3TCOHK3XMHQC","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"7CWK3TCO","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:dbff9cc9d004cb529932854cc4cfc3588425f86d7f0b7eb9aff908d4fed7c92f","target":"graph","created_at":"2026-05-18T01:37:07Z","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":"Kozai-Lidov (KL) oscillations in hierarchical triple systems have found application to many astrophysical contexts, including planet formation, type Ia supernovae, and supermassive black hole dynamics. The period of these oscillations is known at the order-of-magnitude level, but dependences on the initial mutual inclination or inner eccentricity are not typically included. In this work I calculate the period of KL oscillations ($t_{\\textrm{KL}}$) exactly in the test particle limit at quadrupole order (TPQ). I explore the parameter space of all hierarchical triples at TPQ and show that except ","authors_text":"Joseph M. O. Antognini","cross_cats":["astro-ph.SR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2015-04-22T20:00:39Z","title":"Timescales of Kozai-Lidov oscillations at quadrupole and octupole order in the test particle limit"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.05957","kind":"arxiv","version":2},"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":"sha256:244b0a0a6c713124c7119f2eeacabe9e99889ee629a09858993d57f5598aae8a","target":"record","created_at":"2026-05-18T01:37:07Z","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":"ed3e62e7184e7d753e8a23214a2574592f2013ee7f74af986d3f758bd22a04ee","cross_cats_sorted":["astro-ph.SR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2015-04-22T20:00:39Z","title_canon_sha256":"efab6823097f581b471e34371e0c37e0f3a816a2a8e926fa93c7065ba78bdd34"},"schema_version":"1.0","source":{"id":"1504.05957","kind":"arxiv","version":2}},"canonical_sha256":"f8acadcc4e3ab7761e02064411379d8d405d130133a436bca0c4025760514c71","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f8acadcc4e3ab7761e02064411379d8d405d130133a436bca0c4025760514c71","first_computed_at":"2026-05-18T01:37:07.356048Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:07.356048Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hlLG83RBZgEOA0xNm/rmL/tgnIYxautoBsV8J9lVGy2lfFIP72BT8HmJtmNyk4Qm884guIpwuQTtiK7HtKnvBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:07.356500Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.05957","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:244b0a0a6c713124c7119f2eeacabe9e99889ee629a09858993d57f5598aae8a","sha256:dbff9cc9d004cb529932854cc4cfc3588425f86d7f0b7eb9aff908d4fed7c92f"],"state_sha256":"2013fa1532b9341fda5aab193dc9a0b3afdc89ca811d6168bd33bea708eea055"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A2YaxaCz3Vu2usE0o5kO3NAaI4vfV1iITwzWjwKoOJdtNWYGfDf75XI/pqC27AQt1I0k4hnBpCJboJvmuRCCAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T21:01:29.402989Z","bundle_sha256":"a026ab8db6b9cd9497a8f1d3e14aa1107cb67d8304b7cf4848df582c469fe4ce"}}