{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:T672AOD6NEVSD42N5QFKM77KQB","short_pith_number":"pith:T672AOD6","canonical_record":{"source":{"id":"2010.00162","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2020-10-01T01:10:16Z","cross_cats_sorted":[],"title_canon_sha256":"96f905fb90c396b1219781aaa4f585a399dabbc7737f3adf83d0c623f6234e22","abstract_canon_sha256":"cdd66f8fa7e51f5f64da738756acb8336d211119bbf7145bf69234e55062d3d3"},"schema_version":"1.0"},"canonical_sha256":"9fbfa0387e692b21f34dec0aa67fea80540ae7d46137e68fbd54cc41aef7bf22","source":{"kind":"arxiv","id":"2010.00162","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2010.00162","created_at":"2026-07-05T02:43:09Z"},{"alias_kind":"arxiv_version","alias_value":"2010.00162v2","created_at":"2026-07-05T02:43:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2010.00162","created_at":"2026-07-05T02:43:09Z"},{"alias_kind":"pith_short_12","alias_value":"T672AOD6NEVS","created_at":"2026-07-05T02:43:09Z"},{"alias_kind":"pith_short_16","alias_value":"T672AOD6NEVSD42N","created_at":"2026-07-05T02:43:09Z"},{"alias_kind":"pith_short_8","alias_value":"T672AOD6","created_at":"2026-07-05T02:43:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:T672AOD6NEVSD42N5QFKM77KQB","target":"record","payload":{"canonical_record":{"source":{"id":"2010.00162","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2020-10-01T01:10:16Z","cross_cats_sorted":[],"title_canon_sha256":"96f905fb90c396b1219781aaa4f585a399dabbc7737f3adf83d0c623f6234e22","abstract_canon_sha256":"cdd66f8fa7e51f5f64da738756acb8336d211119bbf7145bf69234e55062d3d3"},"schema_version":"1.0"},"canonical_sha256":"9fbfa0387e692b21f34dec0aa67fea80540ae7d46137e68fbd54cc41aef7bf22","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:43:09.386488Z","signature_b64":"GTZRNn48VxfP08ATiaQ3zTbMNCshGLyTrs/ah/0c9jBo1X5XdafrgsF610GDmUzeGsyPhYtM6NucHfQ7yM6wBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9fbfa0387e692b21f34dec0aa67fea80540ae7d46137e68fbd54cc41aef7bf22","last_reissued_at":"2026-07-05T02:43:09.385985Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:43:09.385985Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2010.00162","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":"2026-07-05T02:43:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FzGphlDwsc/1VHSJnG5U1umPwkOwPXWiR/3rZB6z67jJPoojVQ/xS0sMIHoSVHUmSWmAxfT3RoLTlBe3bqoPDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T17:27:41.656168Z"},"content_sha256":"1b5d757bf3dbde3bfc504a6f60f53e28e94f644ec193d5f92e9279e38ea64011","schema_version":"1.0","event_id":"sha256:1b5d757bf3dbde3bfc504a6f60f53e28e94f644ec193d5f92e9279e38ea64011"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:T672AOD6NEVSD42N5QFKM77KQB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Numerical computation of second order vacuum perturbations of Kerr black holes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Elena Giorgi, Frans Pretorius, Justin L. Ripley, Nicholas Loutrel","submitted_at":"2020-10-01T01:10:16Z","abstract_excerpt":"Motivated by the desire to understand the leading order nonlinear gravitational wave interactions around arbitrarily rapidly rotating Kerr black holes, we describe a numerical code designed to compute second order vacuum perturbations on such spacetimes. A general discussion of the formalism we use is presented in (arXiv:2008.11770); here we show how we numerically implement that formalism with a particular choice of coordinates and tetrad conditions, and give example results for black holes with dimensionless spin parameters $a=0.7$ and $a=0.998$. We first solve the Teukolsky equation for the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.00162","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2010.00162/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T02:43:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VPF032VjublMh+JHQP1NRPKex/rLS1AhvjSUp487K/2YdTuZIAdBRr88UvVSdsT0OiD0AwN3qM75ndLWXdhgCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T17:27:41.656753Z"},"content_sha256":"7043d32e8448eb17156d91a5046c471e819f165cd6bc8ff96750ee1752cae54d","schema_version":"1.0","event_id":"sha256:7043d32e8448eb17156d91a5046c471e819f165cd6bc8ff96750ee1752cae54d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T672AOD6NEVSD42N5QFKM77KQB/bundle.json","state_url":"https://pith.science/pith/T672AOD6NEVSD42N5QFKM77KQB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T672AOD6NEVSD42N5QFKM77KQB/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":"2026-08-03T17:27:41Z","links":{"resolver":"https://pith.science/pith/T672AOD6NEVSD42N5QFKM77KQB","bundle":"https://pith.science/pith/T672AOD6NEVSD42N5QFKM77KQB/bundle.json","state":"https://pith.science/pith/T672AOD6NEVSD42N5QFKM77KQB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T672AOD6NEVSD42N5QFKM77KQB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:T672AOD6NEVSD42N5QFKM77KQB","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":"cdd66f8fa7e51f5f64da738756acb8336d211119bbf7145bf69234e55062d3d3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2020-10-01T01:10:16Z","title_canon_sha256":"96f905fb90c396b1219781aaa4f585a399dabbc7737f3adf83d0c623f6234e22"},"schema_version":"1.0","source":{"id":"2010.00162","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2010.00162","created_at":"2026-07-05T02:43:09Z"},{"alias_kind":"arxiv_version","alias_value":"2010.00162v2","created_at":"2026-07-05T02:43:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2010.00162","created_at":"2026-07-05T02:43:09Z"},{"alias_kind":"pith_short_12","alias_value":"T672AOD6NEVS","created_at":"2026-07-05T02:43:09Z"},{"alias_kind":"pith_short_16","alias_value":"T672AOD6NEVSD42N","created_at":"2026-07-05T02:43:09Z"},{"alias_kind":"pith_short_8","alias_value":"T672AOD6","created_at":"2026-07-05T02:43:09Z"}],"graph_snapshots":[{"event_id":"sha256:7043d32e8448eb17156d91a5046c471e819f165cd6bc8ff96750ee1752cae54d","target":"graph","created_at":"2026-07-05T02:43:09Z","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/2010.00162/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Motivated by the desire to understand the leading order nonlinear gravitational wave interactions around arbitrarily rapidly rotating Kerr black holes, we describe a numerical code designed to compute second order vacuum perturbations on such spacetimes. A general discussion of the formalism we use is presented in (arXiv:2008.11770); here we show how we numerically implement that formalism with a particular choice of coordinates and tetrad conditions, and give example results for black holes with dimensionless spin parameters $a=0.7$ and $a=0.998$. We first solve the Teukolsky equation for the","authors_text":"Elena Giorgi, Frans Pretorius, Justin L. Ripley, Nicholas Loutrel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2020-10-01T01:10:16Z","title":"Numerical computation of second order vacuum perturbations of Kerr black holes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.00162","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":"sha256:1b5d757bf3dbde3bfc504a6f60f53e28e94f644ec193d5f92e9279e38ea64011","target":"record","created_at":"2026-07-05T02:43:09Z","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":"cdd66f8fa7e51f5f64da738756acb8336d211119bbf7145bf69234e55062d3d3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2020-10-01T01:10:16Z","title_canon_sha256":"96f905fb90c396b1219781aaa4f585a399dabbc7737f3adf83d0c623f6234e22"},"schema_version":"1.0","source":{"id":"2010.00162","kind":"arxiv","version":2}},"canonical_sha256":"9fbfa0387e692b21f34dec0aa67fea80540ae7d46137e68fbd54cc41aef7bf22","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9fbfa0387e692b21f34dec0aa67fea80540ae7d46137e68fbd54cc41aef7bf22","first_computed_at":"2026-07-05T02:43:09.385985Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:43:09.385985Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GTZRNn48VxfP08ATiaQ3zTbMNCshGLyTrs/ah/0c9jBo1X5XdafrgsF610GDmUzeGsyPhYtM6NucHfQ7yM6wBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T02:43:09.386488Z","signed_message":"canonical_sha256_bytes"},"source_id":"2010.00162","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1b5d757bf3dbde3bfc504a6f60f53e28e94f644ec193d5f92e9279e38ea64011","sha256:7043d32e8448eb17156d91a5046c471e819f165cd6bc8ff96750ee1752cae54d"],"state_sha256":"d038d0edb49656f8aa72446a3de6e16054d7bdeaab6b024a5d2dadbb22d17c61"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i2tkySXhBa2r8tBS918DDr0TV58AkwxjCOt0bjZbs5AZlBFDwk9Ss/d02RXjt4E1jW4+pL28Nqwj+k3x6B0iDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T17:27:41.662490Z","bundle_sha256":"2453bb97cc46f1714c386b083d778a12b69eb51bc17ca9535aabfd333bca9ecb"}}