{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:WI4DXGUPJGEFQA2KVVA4FOAUED","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":"7db4e893cf83c37df110b9479d47d3178116d4c0310bcaa8bed9f29f56a81820","cross_cats_sorted":[],"license":"","primary_cat":"gr-qc","submitted_at":"2007-07-31T16:41:06Z","title_canon_sha256":"e8df8388590e2fd92282e1ea6e42c157f8d07384e57b2ffe7cef748e23aa776e"},"schema_version":"1.0","source":{"id":"0707.4654","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0707.4654","created_at":"2026-07-04T15:30:31Z"},{"alias_kind":"arxiv_version","alias_value":"0707.4654v3","created_at":"2026-07-04T15:30:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0707.4654","created_at":"2026-07-04T15:30:31Z"},{"alias_kind":"pith_short_12","alias_value":"WI4DXGUPJGEF","created_at":"2026-07-04T15:30:31Z"},{"alias_kind":"pith_short_16","alias_value":"WI4DXGUPJGEFQA2K","created_at":"2026-07-04T15:30:31Z"},{"alias_kind":"pith_short_8","alias_value":"WI4DXGUP","created_at":"2026-07-04T15:30:31Z"}],"graph_snapshots":[{"event_id":"sha256:194351e6d2d40420933ea8a2c58f67a9cd9f85e9ffe32d1036f2eea5c99965ce","target":"graph","created_at":"2026-07-04T15:30:31Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/0707.4654/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present expressions for the energy, linear momentum and angular momentum carried away from an isolated system by gravitational radiation based on spin-weighted spherical harmonics decomposition of the Weyl scalar $\\Psi_4$. We also show that the expressions derived are equivalent to the common expressions obtained when using a framework based on perturbations of a Schwazschild background. The main idea is to collect together all the different expressions in a uniform and consistent way. The formulae presented here are directly applicable to the calculation of the radiated energy, linear mome","authors_text":"Dario Nunez, Miguel Alcubierre, Milton Ruiz, Ryoji Takahashi","cross_cats":[],"headline":"","license":"","primary_cat":"gr-qc","submitted_at":"2007-07-31T16:41:06Z","title":"Multipole expansions for energy and momenta carried by gravitational waves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0707.4654","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":"sha256:65b066273c2bd9eb7b6e2e0b8fb570121d47152dd432627ded9160da94ff26f5","target":"record","created_at":"2026-07-04T15:30:31Z","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":"7db4e893cf83c37df110b9479d47d3178116d4c0310bcaa8bed9f29f56a81820","cross_cats_sorted":[],"license":"","primary_cat":"gr-qc","submitted_at":"2007-07-31T16:41:06Z","title_canon_sha256":"e8df8388590e2fd92282e1ea6e42c157f8d07384e57b2ffe7cef748e23aa776e"},"schema_version":"1.0","source":{"id":"0707.4654","kind":"arxiv","version":3}},"canonical_sha256":"b2383b9a8f498858034aad41c2b81420ec33f7fe5a4d7c9ec0f9f81cc6022571","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b2383b9a8f498858034aad41c2b81420ec33f7fe5a4d7c9ec0f9f81cc6022571","first_computed_at":"2026-07-04T15:30:31.805101Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:30:31.805101Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+AafyI/ZAjA4oR0ATAqyO4Ah0R5dFUN6EcpBmS+WM1J6LRagXl3TGhG0qes5ErMpc6JTo9Y7j+0TF/FDt8o2Dw==","signature_status":"signed_v1","signed_at":"2026-07-04T15:30:31.805526Z","signed_message":"canonical_sha256_bytes"},"source_id":"0707.4654","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:65b066273c2bd9eb7b6e2e0b8fb570121d47152dd432627ded9160da94ff26f5","sha256:194351e6d2d40420933ea8a2c58f67a9cd9f85e9ffe32d1036f2eea5c99965ce"],"state_sha256":"e5be0f53143554286d957d08b4b0c99814ce04f05b610c959a6d274187acd9b4"}