{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2000:D74H44RQFF5DAARYBTUTESG5KK","short_pith_number":"pith:D74H44RQ","canonical_record":{"source":{"id":"gr-qc/0002043","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"gr-qc","submitted_at":"2000-02-11T22:22:38Z","cross_cats_sorted":["astro-ph"],"title_canon_sha256":"8e45d60424e3e4530e0df1c101f5a915444dba95a0902c6761d64a6d3b07e484","abstract_canon_sha256":"daab6136ff785a77ea3141935c1f3eb28299b3b38ec8119b8c867563e169e7b1"},"schema_version":"1.0"},"canonical_sha256":"1ff87e7230297a3002380ce93248dd528914f43695a1c643facd1235f331a6f7","source":{"kind":"arxiv","id":"gr-qc/0002043","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"gr-qc/0002043","created_at":"2026-05-18T02:37:36Z"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/0002043v2","created_at":"2026-05-18T02:37:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/0002043","created_at":"2026-05-18T02:37:36Z"},{"alias_kind":"pith_short_12","alias_value":"D74H44RQFF5D","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"D74H44RQFF5DAARY","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"D74H44RQ","created_at":"2026-05-18T12:25:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2000:D74H44RQFF5DAARYBTUTESG5KK","target":"record","payload":{"canonical_record":{"source":{"id":"gr-qc/0002043","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"gr-qc","submitted_at":"2000-02-11T22:22:38Z","cross_cats_sorted":["astro-ph"],"title_canon_sha256":"8e45d60424e3e4530e0df1c101f5a915444dba95a0902c6761d64a6d3b07e484","abstract_canon_sha256":"daab6136ff785a77ea3141935c1f3eb28299b3b38ec8119b8c867563e169e7b1"},"schema_version":"1.0"},"canonical_sha256":"1ff87e7230297a3002380ce93248dd528914f43695a1c643facd1235f331a6f7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:37:36.540270Z","signature_b64":"kXViKAKjlBTtX4IP16UerZ5PBl596odghGzUQlAV/FDZuRlBB2FUfzCb2vieRJlJjx9sN5st//M9o3N47jo5CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1ff87e7230297a3002380ce93248dd528914f43695a1c643facd1235f331a6f7","last_reissued_at":"2026-05-18T02:37:36.539898Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:37:36.539898Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"gr-qc/0002043","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":"2026-05-18T02:37:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UC6eJ12Hrx0O7o9WVB4WoI17QgCd3z+Xo4cPL6Atpv9eeUdjCcNG2R3yutSUqiFz23JEleoov8t4k9bl22rBDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T17:15:57.864178Z"},"content_sha256":"8172e5691c006d7a418ab2d094036e31440a109cf0c1379d0e9c9e794afc1e50","schema_version":"1.0","event_id":"sha256:8172e5691c006d7a418ab2d094036e31440a109cf0c1379d0e9c9e794afc1e50"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2000:D74H44RQFF5DAARYBTUTESG5KK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Computing radiation from Kerr black holes: Generalization of the Sasaki-Nakamura equation","license":"","headline":"","cross_cats":["astro-ph"],"primary_cat":"gr-qc","authors_text":"Scott A. Hughes","submitted_at":"2000-02-11T22:22:38Z","abstract_excerpt":"As shown by Teukolsky, the master equation governing the propagation of weak radiation in a black hole spacetime can be separated into four ordinary differential equations, one for each spacetime coordinate. (``Weak'' means the radiation's amplitude is small enough that its own gravitation may be neglected.) Unfortunately, it is difficult to accurately compute solutions to the separated radial equation (the Teukolsky equation), particularly in a numerical implementation. The fundamental reason for this is that the Teukolsky equation's potentials are long ranged. For non-spinning black holes, o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/0002043","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":"2026-05-18T02:37:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gCR8qcCz/4P6a0zhQnbE+nIr72CXmSQ7rleJdBrs+rF5gAiUWHGZiCQSMcq5WtnaprQV6vyOFcMMfscShulaCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T17:15:57.864937Z"},"content_sha256":"9f80693a0a1a448bdbf4dd7a479af60b19e6be4975be70c33c1152cdf0eca285","schema_version":"1.0","event_id":"sha256:9f80693a0a1a448bdbf4dd7a479af60b19e6be4975be70c33c1152cdf0eca285"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D74H44RQFF5DAARYBTUTESG5KK/bundle.json","state_url":"https://pith.science/pith/D74H44RQFF5DAARYBTUTESG5KK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D74H44RQFF5DAARYBTUTESG5KK/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":"2026-05-24T17:15:57Z","links":{"resolver":"https://pith.science/pith/D74H44RQFF5DAARYBTUTESG5KK","bundle":"https://pith.science/pith/D74H44RQFF5DAARYBTUTESG5KK/bundle.json","state":"https://pith.science/pith/D74H44RQFF5DAARYBTUTESG5KK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D74H44RQFF5DAARYBTUTESG5KK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2000:D74H44RQFF5DAARYBTUTESG5KK","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":"daab6136ff785a77ea3141935c1f3eb28299b3b38ec8119b8c867563e169e7b1","cross_cats_sorted":["astro-ph"],"license":"","primary_cat":"gr-qc","submitted_at":"2000-02-11T22:22:38Z","title_canon_sha256":"8e45d60424e3e4530e0df1c101f5a915444dba95a0902c6761d64a6d3b07e484"},"schema_version":"1.0","source":{"id":"gr-qc/0002043","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"gr-qc/0002043","created_at":"2026-05-18T02:37:36Z"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/0002043v2","created_at":"2026-05-18T02:37:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/0002043","created_at":"2026-05-18T02:37:36Z"},{"alias_kind":"pith_short_12","alias_value":"D74H44RQFF5D","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"D74H44RQFF5DAARY","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"D74H44RQ","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:9f80693a0a1a448bdbf4dd7a479af60b19e6be4975be70c33c1152cdf0eca285","target":"graph","created_at":"2026-05-18T02:37:36Z","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":"As shown by Teukolsky, the master equation governing the propagation of weak radiation in a black hole spacetime can be separated into four ordinary differential equations, one for each spacetime coordinate. (``Weak'' means the radiation's amplitude is small enough that its own gravitation may be neglected.) Unfortunately, it is difficult to accurately compute solutions to the separated radial equation (the Teukolsky equation), particularly in a numerical implementation. The fundamental reason for this is that the Teukolsky equation's potentials are long ranged. For non-spinning black holes, o","authors_text":"Scott A. Hughes","cross_cats":["astro-ph"],"headline":"","license":"","primary_cat":"gr-qc","submitted_at":"2000-02-11T22:22:38Z","title":"Computing radiation from Kerr black holes: Generalization of the Sasaki-Nakamura equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/0002043","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":"sha256:8172e5691c006d7a418ab2d094036e31440a109cf0c1379d0e9c9e794afc1e50","target":"record","created_at":"2026-05-18T02:37:36Z","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":"daab6136ff785a77ea3141935c1f3eb28299b3b38ec8119b8c867563e169e7b1","cross_cats_sorted":["astro-ph"],"license":"","primary_cat":"gr-qc","submitted_at":"2000-02-11T22:22:38Z","title_canon_sha256":"8e45d60424e3e4530e0df1c101f5a915444dba95a0902c6761d64a6d3b07e484"},"schema_version":"1.0","source":{"id":"gr-qc/0002043","kind":"arxiv","version":2}},"canonical_sha256":"1ff87e7230297a3002380ce93248dd528914f43695a1c643facd1235f331a6f7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1ff87e7230297a3002380ce93248dd528914f43695a1c643facd1235f331a6f7","first_computed_at":"2026-05-18T02:37:36.539898Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:37:36.539898Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kXViKAKjlBTtX4IP16UerZ5PBl596odghGzUQlAV/FDZuRlBB2FUfzCb2vieRJlJjx9sN5st//M9o3N47jo5CA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:37:36.540270Z","signed_message":"canonical_sha256_bytes"},"source_id":"gr-qc/0002043","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8172e5691c006d7a418ab2d094036e31440a109cf0c1379d0e9c9e794afc1e50","sha256:9f80693a0a1a448bdbf4dd7a479af60b19e6be4975be70c33c1152cdf0eca285"],"state_sha256":"685ee77fb476db406ff7c884aec23b7d7bc938d89fbf1cb96cac13720fdbf881"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3GQl0rIBePoXtk9SLmEShoNihYiaCgoSZyhC1zjROMLTlCPqasd3KMFIKt1y/yTn93Q5TxDMD1vno94uX21mCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-24T17:15:57.869529Z","bundle_sha256":"17107578c08257d338e060a3bee3d3b0a06c2aba7a6d16d6125084693d8e6421"}}