{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:3BMYPHUMNSHHROJVX2ELSJUMK7","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":"9dbfd4b797f516538242ee8e61b67dffe3ba261973d4cc21e3de88fe260a4013","cross_cats_sorted":["astro-ph.EP","physics.class-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"astro-ph.SR","submitted_at":"2025-03-25T18:00:03Z","title_canon_sha256":"4144611a3b1bd62445b3941225cfc5a4d58aeb1c5bf0e35a4e8663905c3c0d9e"},"schema_version":"1.0","source":{"id":"2503.19972","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.19972","created_at":"2026-07-05T10:39:29Z"},{"alias_kind":"arxiv_version","alias_value":"2503.19972v1","created_at":"2026-07-05T10:39:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.19972","created_at":"2026-07-05T10:39:29Z"},{"alias_kind":"pith_short_12","alias_value":"3BMYPHUMNSHH","created_at":"2026-07-05T10:39:29Z"},{"alias_kind":"pith_short_16","alias_value":"3BMYPHUMNSHHROJV","created_at":"2026-07-05T10:39:29Z"},{"alias_kind":"pith_short_8","alias_value":"3BMYPHUM","created_at":"2026-07-05T10:39:29Z"}],"graph_snapshots":[{"event_id":"sha256:1e883b24ecea393bf86ea904d40f319b5f70f1c350a41d926cf2b45e2b0cde2a","target":"graph","created_at":"2026-07-05T10:39:29Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2503.19972/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The quadrupole Kozai mechanism, which describes the hierarchical three-body problem in the leading order, is shown to be equivalent to a simple pendulum where the change in the eccentricity squared equals the height of the pendulum from its lowest point: $e_{\\text{max}}^2-e^2=h=l\\left(1-\\cos{\\theta}\\right)$. In particular, this results in useful expressions for the KLC period, and the maximal and minimal eccentricities in terms of orbital constants. We derive the equivalence using the vector coordinates $\\boldsymbol{\\alpha}=\\textbf{j}+\\textbf{e}, \\boldsymbol{\\beta}=\\textbf{j}-\\textbf{e}$ for t","authors_text":"Boaz Katz, Roi D. Basha, Ygal Y. Klein","cross_cats":["astro-ph.EP","physics.class-ph"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"astro-ph.SR","submitted_at":"2025-03-25T18:00:03Z","title":"Kozai Lidov Cycles = Simple Pendulum"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.19972","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":"sha256:49ee080ca444cafd455067054a356ad7d4d8dee140d38f18fe51624d6b269804","target":"record","created_at":"2026-07-05T10:39:29Z","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":"9dbfd4b797f516538242ee8e61b67dffe3ba261973d4cc21e3de88fe260a4013","cross_cats_sorted":["astro-ph.EP","physics.class-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"astro-ph.SR","submitted_at":"2025-03-25T18:00:03Z","title_canon_sha256":"4144611a3b1bd62445b3941225cfc5a4d58aeb1c5bf0e35a4e8663905c3c0d9e"},"schema_version":"1.0","source":{"id":"2503.19972","kind":"arxiv","version":1}},"canonical_sha256":"d859879e8c6c8e78b935be88b9268c57ffedebf101a6a647bd7e42ed7867552c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d859879e8c6c8e78b935be88b9268c57ffedebf101a6a647bd7e42ed7867552c","first_computed_at":"2026-07-05T10:39:29.480428Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:39:29.480428Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0jwzGsh3jiL+UhuwaC00WkL1JJQALWzP+3O9j2t3oUJ+p0wizIYZ0L+dwt33PRQup8FFUg+cWefngaQhzwkSCA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:39:29.480858Z","signed_message":"canonical_sha256_bytes"},"source_id":"2503.19972","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:49ee080ca444cafd455067054a356ad7d4d8dee140d38f18fe51624d6b269804","sha256:1e883b24ecea393bf86ea904d40f319b5f70f1c350a41d926cf2b45e2b0cde2a"],"state_sha256":"ed5e90ef6895e9c9a874ee7ce5fd03b853c3e0b982ce53e89538692bd4075e06"}