{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:BGEXYXO4FTO7Z35M7ZWCT4GRFG","short_pith_number":"pith:BGEXYXO4","canonical_record":{"source":{"id":"1512.01556","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-12-04T21:00:11Z","cross_cats_sorted":[],"title_canon_sha256":"776687df61ec10074121fc33054b81f482675c36504db5272caf967a4760a7f5","abstract_canon_sha256":"bd94b134d1645a468180788194bdadc5460f8389f176df94816393109b4e0937"},"schema_version":"1.0"},"canonical_sha256":"09897c5ddc2cddfcefacfe6c29f0d1298b70e333a470d93bcbce6708963d454f","source":{"kind":"arxiv","id":"1512.01556","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.01556","created_at":"2026-05-18T01:21:04Z"},{"alias_kind":"arxiv_version","alias_value":"1512.01556v2","created_at":"2026-05-18T01:21:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.01556","created_at":"2026-05-18T01:21:04Z"},{"alias_kind":"pith_short_12","alias_value":"BGEXYXO4FTO7","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"BGEXYXO4FTO7Z35M","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"BGEXYXO4","created_at":"2026-05-18T12:29:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:BGEXYXO4FTO7Z35M7ZWCT4GRFG","target":"record","payload":{"canonical_record":{"source":{"id":"1512.01556","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-12-04T21:00:11Z","cross_cats_sorted":[],"title_canon_sha256":"776687df61ec10074121fc33054b81f482675c36504db5272caf967a4760a7f5","abstract_canon_sha256":"bd94b134d1645a468180788194bdadc5460f8389f176df94816393109b4e0937"},"schema_version":"1.0"},"canonical_sha256":"09897c5ddc2cddfcefacfe6c29f0d1298b70e333a470d93bcbce6708963d454f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:04.010542Z","signature_b64":"JfJLqdSCt5sbg6tQjDaQOwtw+A3XQ3NDRbkYw3eOQvcNTXgTY39WCFR/ceYjDKSsTyRehPTtTPiw8K05yVspDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"09897c5ddc2cddfcefacfe6c29f0d1298b70e333a470d93bcbce6708963d454f","last_reissued_at":"2026-05-18T01:21:04.009863Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:04.009863Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.01556","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":"2026-05-18T01:21:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RgWUn6ZAm7N55mQ3fT7OeBbpy34vJaz+h3eH/STxt63D8zjpNRm8ZPnAsWuZWYS5gfxPV61jyzk5Vkd1a0HMCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T00:46:04.169637Z"},"content_sha256":"a8cb79f4e0bc37430350ab98e74a6949493424518a250cc6a068886acd14b949","schema_version":"1.0","event_id":"sha256:a8cb79f4e0bc37430350ab98e74a6949493424518a250cc6a068886acd14b949"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:BGEXYXO4FTO7Z35M7ZWCT4GRFG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Analytic self-force calculations in the post-Newtonian regime: eccentric orbits on a Schwarzschild background","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Adrian C. Ottewill, Chris Kavanagh, Seth Hopper","submitted_at":"2015-12-04T21:00:11Z","abstract_excerpt":"We present a method for solving the first-order field equations in a post-Newtonian (PN) expansion. Our calculations generalize work of Bini and Damour and subsequently Kavanagh et al., to consider eccentric orbits on a Schwarzschild background. We derive expressions for the retarded metric perturbation at the location of the particle for all $\\ell$-modes. We find that, despite first appearances, the Regge-Wheeler gauge metric perturbation is $C^0$ at the particle for all $\\ell$. As a first use of our solutions, we compute the gauge-invariant quantity $\\langle U \\rangle$ through 4PN while simu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.01556","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":"2026-05-18T01:21:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"opUZ/sEVjzRLhObhmKCUKv75imTSwhUZ2GiM4it3CAmqCHgx+0oAK2ESwDDHwmkMdZklG5JmbyVctcxnjFSKCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T00:46:04.170375Z"},"content_sha256":"efc17c62d0c1ee94c667c52ec439ba8bced7009988b88971a2ece2ded4ac3e43","schema_version":"1.0","event_id":"sha256:efc17c62d0c1ee94c667c52ec439ba8bced7009988b88971a2ece2ded4ac3e43"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BGEXYXO4FTO7Z35M7ZWCT4GRFG/bundle.json","state_url":"https://pith.science/pith/BGEXYXO4FTO7Z35M7ZWCT4GRFG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BGEXYXO4FTO7Z35M7ZWCT4GRFG/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":"2026-06-01T00:46:04Z","links":{"resolver":"https://pith.science/pith/BGEXYXO4FTO7Z35M7ZWCT4GRFG","bundle":"https://pith.science/pith/BGEXYXO4FTO7Z35M7ZWCT4GRFG/bundle.json","state":"https://pith.science/pith/BGEXYXO4FTO7Z35M7ZWCT4GRFG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BGEXYXO4FTO7Z35M7ZWCT4GRFG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:BGEXYXO4FTO7Z35M7ZWCT4GRFG","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":"bd94b134d1645a468180788194bdadc5460f8389f176df94816393109b4e0937","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-12-04T21:00:11Z","title_canon_sha256":"776687df61ec10074121fc33054b81f482675c36504db5272caf967a4760a7f5"},"schema_version":"1.0","source":{"id":"1512.01556","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.01556","created_at":"2026-05-18T01:21:04Z"},{"alias_kind":"arxiv_version","alias_value":"1512.01556v2","created_at":"2026-05-18T01:21:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.01556","created_at":"2026-05-18T01:21:04Z"},{"alias_kind":"pith_short_12","alias_value":"BGEXYXO4FTO7","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"BGEXYXO4FTO7Z35M","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"BGEXYXO4","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:efc17c62d0c1ee94c667c52ec439ba8bced7009988b88971a2ece2ded4ac3e43","target":"graph","created_at":"2026-05-18T01:21:04Z","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 present a method for solving the first-order field equations in a post-Newtonian (PN) expansion. Our calculations generalize work of Bini and Damour and subsequently Kavanagh et al., to consider eccentric orbits on a Schwarzschild background. We derive expressions for the retarded metric perturbation at the location of the particle for all $\\ell$-modes. We find that, despite first appearances, the Regge-Wheeler gauge metric perturbation is $C^0$ at the particle for all $\\ell$. As a first use of our solutions, we compute the gauge-invariant quantity $\\langle U \\rangle$ through 4PN while simu","authors_text":"Adrian C. Ottewill, Chris Kavanagh, Seth Hopper","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-12-04T21:00:11Z","title":"Analytic self-force calculations in the post-Newtonian regime: eccentric orbits on a Schwarzschild background"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.01556","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:a8cb79f4e0bc37430350ab98e74a6949493424518a250cc6a068886acd14b949","target":"record","created_at":"2026-05-18T01:21:04Z","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":"bd94b134d1645a468180788194bdadc5460f8389f176df94816393109b4e0937","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-12-04T21:00:11Z","title_canon_sha256":"776687df61ec10074121fc33054b81f482675c36504db5272caf967a4760a7f5"},"schema_version":"1.0","source":{"id":"1512.01556","kind":"arxiv","version":2}},"canonical_sha256":"09897c5ddc2cddfcefacfe6c29f0d1298b70e333a470d93bcbce6708963d454f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"09897c5ddc2cddfcefacfe6c29f0d1298b70e333a470d93bcbce6708963d454f","first_computed_at":"2026-05-18T01:21:04.009863Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:04.009863Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JfJLqdSCt5sbg6tQjDaQOwtw+A3XQ3NDRbkYw3eOQvcNTXgTY39WCFR/ceYjDKSsTyRehPTtTPiw8K05yVspDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:04.010542Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.01556","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a8cb79f4e0bc37430350ab98e74a6949493424518a250cc6a068886acd14b949","sha256:efc17c62d0c1ee94c667c52ec439ba8bced7009988b88971a2ece2ded4ac3e43"],"state_sha256":"e43a2fb799d9af1ca3a4679cb63b6fafdc6d6b595ff3a2013c8a1d2658055239"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EZD/UbnziyYDkrGgca0S3EwvHUymrpLMyaGDdX+kF9Ow3sgFLIl0FzND8YvruXFsBqYETD5iOuD4cCO2kh67Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T00:46:04.173854Z","bundle_sha256":"6532dbbda123b9efcb2a002f2b3944694d71bd07a75f3136859968632377a3fe"}}