{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:5EMUNFFHEA5MFF4T74UBFGWDGO","short_pith_number":"pith:5EMUNFFH","canonical_record":{"source":{"id":"1011.3973","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-11-17T15:10:25Z","cross_cats_sorted":[],"title_canon_sha256":"cbad02cda5f33d41e1e5293075bc50f199328310978c2d51bd2af9bb52342bcc","abstract_canon_sha256":"f3b971c302c2bb0deb1b3f45d8fa13bcf8796362db95cf269ca37ff86a7e7757"},"schema_version":"1.0"},"canonical_sha256":"e9194694a7203ac29793ff28129ac3338ad3cc28145315f7f8baf7d43851da78","source":{"kind":"arxiv","id":"1011.3973","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.3973","created_at":"2026-05-18T04:22:40Z"},{"alias_kind":"arxiv_version","alias_value":"1011.3973v1","created_at":"2026-05-18T04:22:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.3973","created_at":"2026-05-18T04:22:40Z"},{"alias_kind":"pith_short_12","alias_value":"5EMUNFFHEA5M","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"5EMUNFFHEA5MFF4T","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"5EMUNFFH","created_at":"2026-05-18T12:26:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:5EMUNFFHEA5MFF4T74UBFGWDGO","target":"record","payload":{"canonical_record":{"source":{"id":"1011.3973","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-11-17T15:10:25Z","cross_cats_sorted":[],"title_canon_sha256":"cbad02cda5f33d41e1e5293075bc50f199328310978c2d51bd2af9bb52342bcc","abstract_canon_sha256":"f3b971c302c2bb0deb1b3f45d8fa13bcf8796362db95cf269ca37ff86a7e7757"},"schema_version":"1.0"},"canonical_sha256":"e9194694a7203ac29793ff28129ac3338ad3cc28145315f7f8baf7d43851da78","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:22:40.091037Z","signature_b64":"mZjXzNmDn+gUUesbMT8XLq/iWSnYqoBvPeUmU+C9VMnx8gE4s9okFhB2l9pzysvs4DIO1dRYgWJjFuD2qeNtCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e9194694a7203ac29793ff28129ac3338ad3cc28145315f7f8baf7d43851da78","last_reissued_at":"2026-05-18T04:22:40.090624Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:22:40.090624Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1011.3973","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":"2026-05-18T04:22:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BfBsA0+JTmyU1jntpHY83KVqA23ZP/FCSz3C5kBFrBV+AFBoI5SrunGMiG7hMGEeCgSE/Efkm3FPuldA3l+hCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T16:14:32.752473Z"},"content_sha256":"126c150ba910785a356ef7b591e1e210ef9edf9756145eb2f078e480ef0809f5","schema_version":"1.0","event_id":"sha256:126c150ba910785a356ef7b591e1e210ef9edf9756145eb2f078e480ef0809f5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:5EMUNFFHEA5MFF4T74UBFGWDGO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Epicycles and Poincar\\'{e} Resonances in General Relativity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"G. Koekoek, J.W. van Holten","submitted_at":"2010-11-17T15:10:25Z","abstract_excerpt":"The method of geodesic deviations provides analytic approximations to geodesics in arbitrary background space-times. As such the method is a useful tool in many practical situations. In this note we point out some subtleties in the application of the method related to secular motions, in first as well as in higher order. In particular we work out the general second-order contribution to bound orbits in Schwarzschild space-time and show that it provides very good analytical results all the way up to the innermost stable circular orbit."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.3973","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":"2026-05-18T04:22:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OIFxFNBqkq8gC4RaAgiIHCYhv6RwwuM9arFAJy92+OtcVxepJBN7Npc1I6oGc32Il7t3hsCp9bQcLgbZzZwsBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T16:14:32.752818Z"},"content_sha256":"348a8a1238c297d55e6ca4df17b54ba82693129ff0d1c8f3d99847b7aa41afa3","schema_version":"1.0","event_id":"sha256:348a8a1238c297d55e6ca4df17b54ba82693129ff0d1c8f3d99847b7aa41afa3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5EMUNFFHEA5MFF4T74UBFGWDGO/bundle.json","state_url":"https://pith.science/pith/5EMUNFFHEA5MFF4T74UBFGWDGO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5EMUNFFHEA5MFF4T74UBFGWDGO/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":"2026-06-02T16:14:32Z","links":{"resolver":"https://pith.science/pith/5EMUNFFHEA5MFF4T74UBFGWDGO","bundle":"https://pith.science/pith/5EMUNFFHEA5MFF4T74UBFGWDGO/bundle.json","state":"https://pith.science/pith/5EMUNFFHEA5MFF4T74UBFGWDGO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5EMUNFFHEA5MFF4T74UBFGWDGO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:5EMUNFFHEA5MFF4T74UBFGWDGO","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":"f3b971c302c2bb0deb1b3f45d8fa13bcf8796362db95cf269ca37ff86a7e7757","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-11-17T15:10:25Z","title_canon_sha256":"cbad02cda5f33d41e1e5293075bc50f199328310978c2d51bd2af9bb52342bcc"},"schema_version":"1.0","source":{"id":"1011.3973","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.3973","created_at":"2026-05-18T04:22:40Z"},{"alias_kind":"arxiv_version","alias_value":"1011.3973v1","created_at":"2026-05-18T04:22:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.3973","created_at":"2026-05-18T04:22:40Z"},{"alias_kind":"pith_short_12","alias_value":"5EMUNFFHEA5M","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"5EMUNFFHEA5MFF4T","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"5EMUNFFH","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:348a8a1238c297d55e6ca4df17b54ba82693129ff0d1c8f3d99847b7aa41afa3","target":"graph","created_at":"2026-05-18T04:22:40Z","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":"The method of geodesic deviations provides analytic approximations to geodesics in arbitrary background space-times. As such the method is a useful tool in many practical situations. In this note we point out some subtleties in the application of the method related to secular motions, in first as well as in higher order. In particular we work out the general second-order contribution to bound orbits in Schwarzschild space-time and show that it provides very good analytical results all the way up to the innermost stable circular orbit.","authors_text":"G. Koekoek, J.W. van Holten","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-11-17T15:10:25Z","title":"Epicycles and Poincar\\'{e} Resonances in General Relativity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.3973","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":"sha256:126c150ba910785a356ef7b591e1e210ef9edf9756145eb2f078e480ef0809f5","target":"record","created_at":"2026-05-18T04:22:40Z","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":"f3b971c302c2bb0deb1b3f45d8fa13bcf8796362db95cf269ca37ff86a7e7757","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-11-17T15:10:25Z","title_canon_sha256":"cbad02cda5f33d41e1e5293075bc50f199328310978c2d51bd2af9bb52342bcc"},"schema_version":"1.0","source":{"id":"1011.3973","kind":"arxiv","version":1}},"canonical_sha256":"e9194694a7203ac29793ff28129ac3338ad3cc28145315f7f8baf7d43851da78","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e9194694a7203ac29793ff28129ac3338ad3cc28145315f7f8baf7d43851da78","first_computed_at":"2026-05-18T04:22:40.090624Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:22:40.090624Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mZjXzNmDn+gUUesbMT8XLq/iWSnYqoBvPeUmU+C9VMnx8gE4s9okFhB2l9pzysvs4DIO1dRYgWJjFuD2qeNtCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:22:40.091037Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.3973","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:126c150ba910785a356ef7b591e1e210ef9edf9756145eb2f078e480ef0809f5","sha256:348a8a1238c297d55e6ca4df17b54ba82693129ff0d1c8f3d99847b7aa41afa3"],"state_sha256":"59893d8b36752bf8fd8df5835373a13927aa2b35c3dd7ef901edf863fa04c7ec"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LrNzTZhOk00dDBJtXkSgiBFr3smgEDDgRF8wF12N1ttPL7c0MiWKXDJQL8SW2YXCziEfFp1SziN0ZnZxRySmAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T16:14:32.755234Z","bundle_sha256":"988771736773cdf754805a81a3cafc26a9507898761159278570efd68b9e6092"}}