{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:YMBOSSTIOYPFSTFPRTKPGTDOO3","short_pith_number":"pith:YMBOSSTI","canonical_record":{"source":{"id":"0906.0313","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2009-06-01T16:56:25Z","cross_cats_sorted":["astro-ph.CO","astro-ph.GA","astro-ph.HE"],"title_canon_sha256":"3cac688089bfe78cb2df012788f26bfbfb7c7507d9aa7f9a97db99a75ed9c737","abstract_canon_sha256":"4ddfeca6486c765ef3e0e1d1f6ebc43b8587208c21e1b65e1518a97ffef6282a"},"schema_version":"1.0"},"canonical_sha256":"c302e94a68761e594caf8cd4f34c6e76c235c8ad0196717f693fcad5aef91f63","source":{"kind":"arxiv","id":"0906.0313","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0906.0313","created_at":"2026-05-18T02:51:57Z"},{"alias_kind":"arxiv_version","alias_value":"0906.0313v3","created_at":"2026-05-18T02:51:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.0313","created_at":"2026-05-18T02:51:57Z"},{"alias_kind":"pith_short_12","alias_value":"YMBOSSTIOYPF","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"YMBOSSTIOYPFSTFP","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"YMBOSSTI","created_at":"2026-05-18T12:26:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:YMBOSSTIOYPFSTFPRTKPGTDOO3","target":"record","payload":{"canonical_record":{"source":{"id":"0906.0313","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2009-06-01T16:56:25Z","cross_cats_sorted":["astro-ph.CO","astro-ph.GA","astro-ph.HE"],"title_canon_sha256":"3cac688089bfe78cb2df012788f26bfbfb7c7507d9aa7f9a97db99a75ed9c737","abstract_canon_sha256":"4ddfeca6486c765ef3e0e1d1f6ebc43b8587208c21e1b65e1518a97ffef6282a"},"schema_version":"1.0"},"canonical_sha256":"c302e94a68761e594caf8cd4f34c6e76c235c8ad0196717f693fcad5aef91f63","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:51:57.371723Z","signature_b64":"q22KGc2PBbkhDzU6u91i3g5hX412BZPxr+qpy/6EOdcdeVwNzkznpRfBvxlwGf84txZSmxtfyBPMQ95TjhHIAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c302e94a68761e594caf8cd4f34c6e76c235c8ad0196717f693fcad5aef91f63","last_reissued_at":"2026-05-18T02:51:57.371184Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:51:57.371184Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0906.0313","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:51:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AOxi0vHz3UEy3RpjvRA3+GodwpPB7uCQr0+hKhrMcOM/Ww8MC8pRD/TLn1HxPW9TUaMIA8sfD7FsUwTCFiUUDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T19:40:16.539659Z"},"content_sha256":"cb649496955fb189700d69cb472a2c15331da5e74a3d6c8ae0118b0b5aa715c9","schema_version":"1.0","event_id":"sha256:cb649496955fb189700d69cb472a2c15331da5e74a3d6c8ae0118b0b5aa715c9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:YMBOSSTIOYPFSTFPRTKPGTDOO3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Post-Circular Expansion of Eccentric Binary Inspirals: Fourier-Domain Waveforms in the Stationary Phase Approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.CO","astro-ph.GA","astro-ph.HE"],"primary_cat":"gr-qc","authors_text":"Clifford M. Will, Emanuele Berti, K. G. Arun, Nicolas Yunes","submitted_at":"2009-06-01T16:56:25Z","abstract_excerpt":"We lay the foundations for the construction of analytic expressions for Fourier-domain gravitational waveforms produced by eccentric, inspiraling compact binaries in a post-circular or small-eccentricity approximation. The time-dependent, \"plus\" and \"cross\" polarizations are expanded in Bessel functions, which are then self-consistently re-expanded in a power series about zero initial eccentricity to eighth order. The stationary phase approximation is then employed to obtain explicit analytic expressions for the Fourier transform of the post-circular expanded, time-domain signal. We exemplify "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.0313","kind":"arxiv","version":3},"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":"2026-05-18T02:51:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J8Q79RgzcFXKswDW7TtvyX+POKw0lH6qCXTtb9vFqEMiI9UfncukwxwDoongpDc1yo+2E+IpWCfTe/efxnqRAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T19:40:16.540146Z"},"content_sha256":"9dc14c34b55e1f5d4cdd1114b206144162ca13ae289b918148c14e23b51ee89c","schema_version":"1.0","event_id":"sha256:9dc14c34b55e1f5d4cdd1114b206144162ca13ae289b918148c14e23b51ee89c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YMBOSSTIOYPFSTFPRTKPGTDOO3/bundle.json","state_url":"https://pith.science/pith/YMBOSSTIOYPFSTFPRTKPGTDOO3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YMBOSSTIOYPFSTFPRTKPGTDOO3/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":"2026-05-28T19:40:16Z","links":{"resolver":"https://pith.science/pith/YMBOSSTIOYPFSTFPRTKPGTDOO3","bundle":"https://pith.science/pith/YMBOSSTIOYPFSTFPRTKPGTDOO3/bundle.json","state":"https://pith.science/pith/YMBOSSTIOYPFSTFPRTKPGTDOO3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YMBOSSTIOYPFSTFPRTKPGTDOO3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:YMBOSSTIOYPFSTFPRTKPGTDOO3","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":"4ddfeca6486c765ef3e0e1d1f6ebc43b8587208c21e1b65e1518a97ffef6282a","cross_cats_sorted":["astro-ph.CO","astro-ph.GA","astro-ph.HE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2009-06-01T16:56:25Z","title_canon_sha256":"3cac688089bfe78cb2df012788f26bfbfb7c7507d9aa7f9a97db99a75ed9c737"},"schema_version":"1.0","source":{"id":"0906.0313","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0906.0313","created_at":"2026-05-18T02:51:57Z"},{"alias_kind":"arxiv_version","alias_value":"0906.0313v3","created_at":"2026-05-18T02:51:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.0313","created_at":"2026-05-18T02:51:57Z"},{"alias_kind":"pith_short_12","alias_value":"YMBOSSTIOYPF","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"YMBOSSTIOYPFSTFP","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"YMBOSSTI","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:9dc14c34b55e1f5d4cdd1114b206144162ca13ae289b918148c14e23b51ee89c","target":"graph","created_at":"2026-05-18T02:51:57Z","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 lay the foundations for the construction of analytic expressions for Fourier-domain gravitational waveforms produced by eccentric, inspiraling compact binaries in a post-circular or small-eccentricity approximation. The time-dependent, \"plus\" and \"cross\" polarizations are expanded in Bessel functions, which are then self-consistently re-expanded in a power series about zero initial eccentricity to eighth order. The stationary phase approximation is then employed to obtain explicit analytic expressions for the Fourier transform of the post-circular expanded, time-domain signal. We exemplify ","authors_text":"Clifford M. Will, Emanuele Berti, K. G. Arun, Nicolas Yunes","cross_cats":["astro-ph.CO","astro-ph.GA","astro-ph.HE"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2009-06-01T16:56:25Z","title":"Post-Circular Expansion of Eccentric Binary Inspirals: Fourier-Domain Waveforms in the Stationary Phase Approximation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.0313","kind":"arxiv","version":3},"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:cb649496955fb189700d69cb472a2c15331da5e74a3d6c8ae0118b0b5aa715c9","target":"record","created_at":"2026-05-18T02:51:57Z","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":"4ddfeca6486c765ef3e0e1d1f6ebc43b8587208c21e1b65e1518a97ffef6282a","cross_cats_sorted":["astro-ph.CO","astro-ph.GA","astro-ph.HE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2009-06-01T16:56:25Z","title_canon_sha256":"3cac688089bfe78cb2df012788f26bfbfb7c7507d9aa7f9a97db99a75ed9c737"},"schema_version":"1.0","source":{"id":"0906.0313","kind":"arxiv","version":3}},"canonical_sha256":"c302e94a68761e594caf8cd4f34c6e76c235c8ad0196717f693fcad5aef91f63","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c302e94a68761e594caf8cd4f34c6e76c235c8ad0196717f693fcad5aef91f63","first_computed_at":"2026-05-18T02:51:57.371184Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:51:57.371184Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q22KGc2PBbkhDzU6u91i3g5hX412BZPxr+qpy/6EOdcdeVwNzkznpRfBvxlwGf84txZSmxtfyBPMQ95TjhHIAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:51:57.371723Z","signed_message":"canonical_sha256_bytes"},"source_id":"0906.0313","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cb649496955fb189700d69cb472a2c15331da5e74a3d6c8ae0118b0b5aa715c9","sha256:9dc14c34b55e1f5d4cdd1114b206144162ca13ae289b918148c14e23b51ee89c"],"state_sha256":"194d52404fb1df2b6ae70ee0e4e4e06791577072ba62cf435463edb8697ce3b2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yypbSNBzAbj6GLXYXUcD8MpjbLlGg5a3fgukz0AlZmCMRaLytAJdw6FsDeRzZhbqSFNirEGi6IheZKak6mPMAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T19:40:16.543442Z","bundle_sha256":"9cc1238b999654c9c34dd4439d5c9876bff3e564f77222bf18efbe68f04c3a16"}}