{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:YMBOSSTIOYPFSTFPRTKPGTDOO3","short_pith_number":"pith:YMBOSSTI","schema_version":"1.0","canonical_sha256":"c302e94a68761e594caf8cd4f34c6e76c235c8ad0196717f693fcad5aef91f63","source":{"kind":"arxiv","id":"0906.0313","version":3},"attestation_state":"computed","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 "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"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"},"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"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"0906.0313","created_at":"2026-05-18T02:51:57.371268+00:00"},{"alias_kind":"arxiv_version","alias_value":"0906.0313v3","created_at":"2026-05-18T02:51:57.371268+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.0313","created_at":"2026-05-18T02:51:57.371268+00:00"},{"alias_kind":"pith_short_12","alias_value":"YMBOSSTIOYPF","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_16","alias_value":"YMBOSSTIOYPFSTFP","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_8","alias_value":"YMBOSSTI","created_at":"2026-05-18T12:26:02.257875+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":4,"internal_anchor_count":2,"sample":[{"citing_arxiv_id":"2412.20664","citing_title":"Enhancing Early Detection and Localization of Gravitational Waves via Eccentricity-Induced Higher Harmonic Modes with 2G Detector Networks","ref_index":27,"is_internal_anchor":true},{"citing_arxiv_id":"2605.13036","citing_title":"Inspiral gravitational waveforms from charged compact binaries with scalar hair","ref_index":49,"is_internal_anchor":true},{"citing_arxiv_id":"2605.05537","citing_title":"Implications of the LISA stochastic signal from eccentric stellar mass black hole binaries in vacuum","ref_index":54,"is_internal_anchor":false},{"citing_arxiv_id":"2604.21990","citing_title":"A New Spin on Dissipative Tides: First-Post-Newtonian Effects in Compact Binary Inspirals","ref_index":71,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YMBOSSTIOYPFSTFPRTKPGTDOO3","json":"https://pith.science/pith/YMBOSSTIOYPFSTFPRTKPGTDOO3.json","graph_json":"https://pith.science/api/pith-number/YMBOSSTIOYPFSTFPRTKPGTDOO3/graph.json","events_json":"https://pith.science/api/pith-number/YMBOSSTIOYPFSTFPRTKPGTDOO3/events.json","paper":"https://pith.science/paper/YMBOSSTI"},"agent_actions":{"view_html":"https://pith.science/pith/YMBOSSTIOYPFSTFPRTKPGTDOO3","download_json":"https://pith.science/pith/YMBOSSTIOYPFSTFPRTKPGTDOO3.json","view_paper":"https://pith.science/paper/YMBOSSTI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0906.0313&json=true","fetch_graph":"https://pith.science/api/pith-number/YMBOSSTIOYPFSTFPRTKPGTDOO3/graph.json","fetch_events":"https://pith.science/api/pith-number/YMBOSSTIOYPFSTFPRTKPGTDOO3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YMBOSSTIOYPFSTFPRTKPGTDOO3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YMBOSSTIOYPFSTFPRTKPGTDOO3/action/storage_attestation","attest_author":"https://pith.science/pith/YMBOSSTIOYPFSTFPRTKPGTDOO3/action/author_attestation","sign_citation":"https://pith.science/pith/YMBOSSTIOYPFSTFPRTKPGTDOO3/action/citation_signature","submit_replication":"https://pith.science/pith/YMBOSSTIOYPFSTFPRTKPGTDOO3/action/replication_record"}},"created_at":"2026-05-18T02:51:57.371268+00:00","updated_at":"2026-05-18T02:51:57.371268+00:00"}