{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:OYRP6QNHRLDWGVTQ4C7KJATV22","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":"9f4353d1fb909ed2bf19dcdb90f629b29bf684f81eaa85a4b53076c59fd47320","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-09-06T10:53:13Z","title_canon_sha256":"b4cdcc1592c76533c15cc0fd1d8be0b4f9cec93327e2501edcf440982cf951b3"},"schema_version":"1.0","source":{"id":"1309.1594","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.1594","created_at":"2026-05-18T03:13:59Z"},{"alias_kind":"arxiv_version","alias_value":"1309.1594v1","created_at":"2026-05-18T03:13:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.1594","created_at":"2026-05-18T03:13:59Z"},{"alias_kind":"pith_short_12","alias_value":"OYRP6QNHRLDW","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"OYRP6QNHRLDWGVTQ","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"OYRP6QNH","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:ff7ebfa9b1da545e7523e7e407b43f2b9b579a1918abe5ff407d49a55eb3e711","target":"graph","created_at":"2026-05-18T03:13:59Z","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":"This paper concerns the behaviour of the apsidal angle for orbits of central force system with homogenous potential of degree $-2\\leq \\alpha\\leq 1$ and logarithmic potential. We derive a formula for the apsidal angle as a fixed-end points integral and we study the derivative of the apsidal angle with respect to the angular momentum $\\ell$. The monotonicity of the apsidal angle as function of $\\ell$ is discussed and it is proved in the logarithmic potential case.","authors_text":"Roberto Castelli","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-09-06T10:53:13Z","title":"A study of the apsidal angle and a proof of monotonicity in the logarithmic potential case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1594","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":"sha256:1a52c91afdbfb095bef97cb3f1f8cffbad7d7f3b84a292a3f29a5124af754490","target":"record","created_at":"2026-05-18T03:13:59Z","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":"9f4353d1fb909ed2bf19dcdb90f629b29bf684f81eaa85a4b53076c59fd47320","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-09-06T10:53:13Z","title_canon_sha256":"b4cdcc1592c76533c15cc0fd1d8be0b4f9cec93327e2501edcf440982cf951b3"},"schema_version":"1.0","source":{"id":"1309.1594","kind":"arxiv","version":1}},"canonical_sha256":"7622ff41a78ac7635670e0bea48275d6b35bac89b976ace6a59ebb16ddec4172","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7622ff41a78ac7635670e0bea48275d6b35bac89b976ace6a59ebb16ddec4172","first_computed_at":"2026-05-18T03:13:59.111748Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:13:59.111748Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u6FCHXLCikMN2c/jtiaqQnFfOwPuryn9YPCc7ofWnZV4us+n48X2RcQ97RLM4ZsR3KiA+xTWLEup2wTsrX0EBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:13:59.112521Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.1594","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1a52c91afdbfb095bef97cb3f1f8cffbad7d7f3b84a292a3f29a5124af754490","sha256:ff7ebfa9b1da545e7523e7e407b43f2b9b579a1918abe5ff407d49a55eb3e711"],"state_sha256":"3443a3761df046307b5e87adc80ec6e54a6bee46ce0225aabff33405b209390f"}