{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:X2FVM6BFX2Z4ALMR7CRSBO6CME","short_pith_number":"pith:X2FVM6BF","canonical_record":{"source":{"id":"1009.3331","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"gr-qc","submitted_at":"2010-09-17T04:30:22Z","cross_cats_sorted":[],"title_canon_sha256":"0b66ab239a625e6945f7a7a4f05970c4fff0796ba58066d6dac86806707ebbfe","abstract_canon_sha256":"e6e8fc9e2db2ad774cf2fc3e5df8e5c073559f27025b44538da164bb0fe37b41"},"schema_version":"1.0"},"canonical_sha256":"be8b567825beb3c02d91f8a320bbc26124255ea27db3c4f1446b68f782f9813b","source":{"kind":"arxiv","id":"1009.3331","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.3331","created_at":"2026-05-18T04:23:02Z"},{"alias_kind":"arxiv_version","alias_value":"1009.3331v3","created_at":"2026-05-18T04:23:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.3331","created_at":"2026-05-18T04:23:02Z"},{"alias_kind":"pith_short_12","alias_value":"X2FVM6BFX2Z4","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"X2FVM6BFX2Z4ALMR","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"X2FVM6BF","created_at":"2026-05-18T12:26:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:X2FVM6BFX2Z4ALMR7CRSBO6CME","target":"record","payload":{"canonical_record":{"source":{"id":"1009.3331","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"gr-qc","submitted_at":"2010-09-17T04:30:22Z","cross_cats_sorted":[],"title_canon_sha256":"0b66ab239a625e6945f7a7a4f05970c4fff0796ba58066d6dac86806707ebbfe","abstract_canon_sha256":"e6e8fc9e2db2ad774cf2fc3e5df8e5c073559f27025b44538da164bb0fe37b41"},"schema_version":"1.0"},"canonical_sha256":"be8b567825beb3c02d91f8a320bbc26124255ea27db3c4f1446b68f782f9813b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:23:02.861737Z","signature_b64":"w81iXle4qwNBszj2L9rb8YRa4GqY4rdUMCcgi7GUVaC04qmeWuC58q/xSAGnG2VO9aaD/XA+dgaEJfFkLjTBDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"be8b567825beb3c02d91f8a320bbc26124255ea27db3c4f1446b68f782f9813b","last_reissued_at":"2026-05-18T04:23:02.861300Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:23:02.861300Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1009.3331","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":"2026-05-18T04:23:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TKLohmjpUqmmTRH2QvI8lKeNsKP5zYSl7uKNTYl1HJOzthx13YRR0YEiyTjy6YAPSyHtobuwONafVMYzR14mAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T15:10:18.633375Z"},"content_sha256":"aed37a6afeb836a9791204b9d33afde2ea40a06b927c279490f4c6709c77e60a","schema_version":"1.0","event_id":"sha256:aed37a6afeb836a9791204b9d33afde2ea40a06b927c279490f4c6709c77e60a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:X2FVM6BFX2Z4ALMR7CRSBO6CME","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gravitational radiation and angular momentum flux from a slow rotating dynamical black hole","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Chih-Hung Wang, Yu-Huei Wu","submitted_at":"2010-09-17T04:30:22Z","abstract_excerpt":"A four-dimensional asymptotic expansion scheme is used to study the next order effects of the nonlinearity near a spinning dynamical black hole. The angular momentum flux and energy flux formula are then obtained by constructing the reference frame in terms of the compatible constant spinors and the compatibility of the coupling leading order Newman-Penrose equations. By using the slow rotation and small-tide approximation for a spinning black hole, we chose the horizon cross-section is spherical symmetric. It turns out the flux formula is rather simple and can be compared with the known resul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.3331","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":"2026-05-18T04:23:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QEFVYcyDQPtXC4Vbxqs6tzGwsePVLqGey/B/VewfC3mPmELN9n0WCQ9uBM8qSK4Rmk5wI9aAVR3CAqYgmsaiAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T15:10:18.633735Z"},"content_sha256":"290071e86bc1933229fda9f624268df3ec1fa35013d958dde8b4d8aeef75a0cf","schema_version":"1.0","event_id":"sha256:290071e86bc1933229fda9f624268df3ec1fa35013d958dde8b4d8aeef75a0cf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X2FVM6BFX2Z4ALMR7CRSBO6CME/bundle.json","state_url":"https://pith.science/pith/X2FVM6BFX2Z4ALMR7CRSBO6CME/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X2FVM6BFX2Z4ALMR7CRSBO6CME/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":"2026-06-03T15:10:18Z","links":{"resolver":"https://pith.science/pith/X2FVM6BFX2Z4ALMR7CRSBO6CME","bundle":"https://pith.science/pith/X2FVM6BFX2Z4ALMR7CRSBO6CME/bundle.json","state":"https://pith.science/pith/X2FVM6BFX2Z4ALMR7CRSBO6CME/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X2FVM6BFX2Z4ALMR7CRSBO6CME/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:X2FVM6BFX2Z4ALMR7CRSBO6CME","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":"e6e8fc9e2db2ad774cf2fc3e5df8e5c073559f27025b44538da164bb0fe37b41","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"gr-qc","submitted_at":"2010-09-17T04:30:22Z","title_canon_sha256":"0b66ab239a625e6945f7a7a4f05970c4fff0796ba58066d6dac86806707ebbfe"},"schema_version":"1.0","source":{"id":"1009.3331","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.3331","created_at":"2026-05-18T04:23:02Z"},{"alias_kind":"arxiv_version","alias_value":"1009.3331v3","created_at":"2026-05-18T04:23:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.3331","created_at":"2026-05-18T04:23:02Z"},{"alias_kind":"pith_short_12","alias_value":"X2FVM6BFX2Z4","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"X2FVM6BFX2Z4ALMR","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"X2FVM6BF","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:290071e86bc1933229fda9f624268df3ec1fa35013d958dde8b4d8aeef75a0cf","target":"graph","created_at":"2026-05-18T04:23:02Z","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":"A four-dimensional asymptotic expansion scheme is used to study the next order effects of the nonlinearity near a spinning dynamical black hole. The angular momentum flux and energy flux formula are then obtained by constructing the reference frame in terms of the compatible constant spinors and the compatibility of the coupling leading order Newman-Penrose equations. By using the slow rotation and small-tide approximation for a spinning black hole, we chose the horizon cross-section is spherical symmetric. It turns out the flux formula is rather simple and can be compared with the known resul","authors_text":"Chih-Hung Wang, Yu-Huei Wu","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"gr-qc","submitted_at":"2010-09-17T04:30:22Z","title":"Gravitational radiation and angular momentum flux from a slow rotating dynamical black hole"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.3331","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:aed37a6afeb836a9791204b9d33afde2ea40a06b927c279490f4c6709c77e60a","target":"record","created_at":"2026-05-18T04:23:02Z","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":"e6e8fc9e2db2ad774cf2fc3e5df8e5c073559f27025b44538da164bb0fe37b41","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"gr-qc","submitted_at":"2010-09-17T04:30:22Z","title_canon_sha256":"0b66ab239a625e6945f7a7a4f05970c4fff0796ba58066d6dac86806707ebbfe"},"schema_version":"1.0","source":{"id":"1009.3331","kind":"arxiv","version":3}},"canonical_sha256":"be8b567825beb3c02d91f8a320bbc26124255ea27db3c4f1446b68f782f9813b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"be8b567825beb3c02d91f8a320bbc26124255ea27db3c4f1446b68f782f9813b","first_computed_at":"2026-05-18T04:23:02.861300Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:23:02.861300Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"w81iXle4qwNBszj2L9rb8YRa4GqY4rdUMCcgi7GUVaC04qmeWuC58q/xSAGnG2VO9aaD/XA+dgaEJfFkLjTBDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:23:02.861737Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.3331","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aed37a6afeb836a9791204b9d33afde2ea40a06b927c279490f4c6709c77e60a","sha256:290071e86bc1933229fda9f624268df3ec1fa35013d958dde8b4d8aeef75a0cf"],"state_sha256":"9be2c6b426dd3a425447758fa150e81ed0d6c7b6eb3efdd0d4bf97911cfad7f9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hL1TLqrbSDZ2MRQRGlFiRL5J5Vje5NC95ILyt73knyhvkyqD6XogZd5McBHqdIzOIS3F3PGBXN1JpR5GtL5lCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T15:10:18.635749Z","bundle_sha256":"06cd47f31bb96893ec44040c56822067a3b5f28d84aabf850e87dea46f003574"}}