{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:FZYLLZROZOW2R4RGQVTMX3HKLP","short_pith_number":"pith:FZYLLZRO","schema_version":"1.0","canonical_sha256":"2e70b5e62ecbada8f2268566cbecea5bf0425bd019b7e32063dc7c035d2a78df","source":{"kind":"arxiv","id":"0706.0199","version":1},"attestation_state":"computed","paper":{"title":"Approximate Killing Vectors on S^2","license":"","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Bernard F. Whiting, Gregory B. Cook","submitted_at":"2007-06-01T19:01:14Z","abstract_excerpt":"We present a new method for computing the best approximation to a Killing vector on closed 2-surfaces that are topologically S^2. When solutions of Killing's equation do not exist, this method is shown to yield results superior to those produced by existing methods. In addition, this method appears to provide a new tool for studying the horizon geometry of distorted black holes."},"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":"0706.0199","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"gr-qc","submitted_at":"2007-06-01T19:01:14Z","cross_cats_sorted":[],"title_canon_sha256":"6986fc6591a889eac02132065ee5453f0203f2c4d0215c8ef7f1e91516ef0a13","abstract_canon_sha256":"8e48ef32069c1b35558331ee56b8f6dd7fca5b1128445f18f0bafb16d5a84ac6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:24:16.677384Z","signature_b64":"vZpHczc6LxewwJBtUFlR5Lq1amH4JNKtO9wPQ3cPFntI/GqlgHStC908zYkkvidYVlk5u+jsznEyEZ4QVdvjCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2e70b5e62ecbada8f2268566cbecea5bf0425bd019b7e32063dc7c035d2a78df","last_reissued_at":"2026-07-04T15:24:16.676957Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:24:16.676957Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Approximate Killing Vectors on S^2","license":"","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Bernard F. Whiting, Gregory B. Cook","submitted_at":"2007-06-01T19:01:14Z","abstract_excerpt":"We present a new method for computing the best approximation to a Killing vector on closed 2-surfaces that are topologically S^2. When solutions of Killing's equation do not exist, this method is shown to yield results superior to those produced by existing methods. In addition, this method appears to provide a new tool for studying the horizon geometry of distorted black holes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0706.0199","kind":"arxiv","version":1},"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/0706.0199/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"0706.0199","created_at":"2026-07-04T15:24:16.677019+00:00"},{"alias_kind":"arxiv_version","alias_value":"0706.0199v1","created_at":"2026-07-04T15:24:16.677019+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0706.0199","created_at":"2026-07-04T15:24:16.677019+00:00"},{"alias_kind":"pith_short_12","alias_value":"FZYLLZROZOW2","created_at":"2026-07-04T15:24:16.677019+00:00"},{"alias_kind":"pith_short_16","alias_value":"FZYLLZROZOW2R4RG","created_at":"2026-07-04T15:24:16.677019+00:00"},{"alias_kind":"pith_short_8","alias_value":"FZYLLZRO","created_at":"2026-07-04T15:24:16.677019+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2608.07985","citing_title":"Conformal-Mapping Method for Horizon Multipoles in Numerical Relativity: Implementation, Kerr Validation, and Applications Beyond Axisymmetry","ref_index":12,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FZYLLZROZOW2R4RGQVTMX3HKLP","json":"https://pith.science/pith/FZYLLZROZOW2R4RGQVTMX3HKLP.json","graph_json":"https://pith.science/api/pith-number/FZYLLZROZOW2R4RGQVTMX3HKLP/graph.json","events_json":"https://pith.science/api/pith-number/FZYLLZROZOW2R4RGQVTMX3HKLP/events.json","paper":"https://pith.science/paper/FZYLLZRO"},"agent_actions":{"view_html":"https://pith.science/pith/FZYLLZROZOW2R4RGQVTMX3HKLP","download_json":"https://pith.science/pith/FZYLLZROZOW2R4RGQVTMX3HKLP.json","view_paper":"https://pith.science/paper/FZYLLZRO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0706.0199&json=true","fetch_graph":"https://pith.science/api/pith-number/FZYLLZROZOW2R4RGQVTMX3HKLP/graph.json","fetch_events":"https://pith.science/api/pith-number/FZYLLZROZOW2R4RGQVTMX3HKLP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FZYLLZROZOW2R4RGQVTMX3HKLP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FZYLLZROZOW2R4RGQVTMX3HKLP/action/storage_attestation","attest_author":"https://pith.science/pith/FZYLLZROZOW2R4RGQVTMX3HKLP/action/author_attestation","sign_citation":"https://pith.science/pith/FZYLLZROZOW2R4RGQVTMX3HKLP/action/citation_signature","submit_replication":"https://pith.science/pith/FZYLLZROZOW2R4RGQVTMX3HKLP/action/replication_record"}},"created_at":"2026-07-04T15:24:16.677019+00:00","updated_at":"2026-07-04T15:24:16.677019+00:00"}