{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2003:FOM6GFZZH3WKULLN7EQ47R3XRO","short_pith_number":"pith:FOM6GFZZ","schema_version":"1.0","canonical_sha256":"2b99e317393eecaa2d6df921cfc7778b95696f443e6f64d2befa5a12f136f40a","source":{"kind":"arxiv","id":"gr-qc/0306056","version":3},"attestation_state":"computed","paper":{"title":"A Fast Apparent-Horizon Finder for 3-Dimensional Cartesian Grids in Numerical Relativity","license":"","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Jonathan Thornburg","submitted_at":"2003-06-12T21:47:40Z","abstract_excerpt":"In 3+1 numerical simulations of dynamic black hole spacetimes, it's useful to be able to find the apparent horizon(s) (AH) in each slice of a time evolution. A number of AH finders are available, but they often take many minutes to run, so they're too slow to be practically usable at each time step. Here I present a new AH finder,_AHFinderDirect_, which is very fast and accurate: at typical resolutions it takes only a few seconds to find an AH to $\\sim 10^{-5} m$ accuracy on a GHz-class processor.\n  I assume that an AH to be searched for is a Strahlk\\\"orper (star-shaped region) with respect to"},"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":"gr-qc/0306056","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"gr-qc","submitted_at":"2003-06-12T21:47:40Z","cross_cats_sorted":[],"title_canon_sha256":"dee9918293f0e602789b939f24d78c61f6cfe62f4b3f9ab1b4f4feb762f51dc9","abstract_canon_sha256":"e4d4c5607eb3cd4d99d05b79e70aa547eb49eef0fdc8085f23234d0d1e352ca0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:23:03.797373Z","signature_b64":"wXGYeOaj79XH8OLdvddq6mPdLxceV/e7uy0PqYHNinRZz3h2sRVtZW6tGXfmd3osIkYERdFm/LncNkTND9NbBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2b99e317393eecaa2d6df921cfc7778b95696f443e6f64d2befa5a12f136f40a","last_reissued_at":"2026-07-04T15:23:03.797020Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:23:03.797020Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Fast Apparent-Horizon Finder for 3-Dimensional Cartesian Grids in Numerical Relativity","license":"","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Jonathan Thornburg","submitted_at":"2003-06-12T21:47:40Z","abstract_excerpt":"In 3+1 numerical simulations of dynamic black hole spacetimes, it's useful to be able to find the apparent horizon(s) (AH) in each slice of a time evolution. A number of AH finders are available, but they often take many minutes to run, so they're too slow to be practically usable at each time step. Here I present a new AH finder,_AHFinderDirect_, which is very fast and accurate: at typical resolutions it takes only a few seconds to find an AH to $\\sim 10^{-5} m$ accuracy on a GHz-class processor.\n  I assume that an AH to be searched for is a Strahlk\\\"orper (star-shaped region) with respect to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/0306056","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/gr-qc/0306056/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":"gr-qc/0306056","created_at":"2026-07-04T15:23:03.797078+00:00"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/0306056v3","created_at":"2026-07-04T15:23:03.797078+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/0306056","created_at":"2026-07-04T15:23:03.797078+00:00"},{"alias_kind":"pith_short_12","alias_value":"FOM6GFZZH3WK","created_at":"2026-07-04T15:23:03.797078+00:00"},{"alias_kind":"pith_short_16","alias_value":"FOM6GFZZH3WKULLN","created_at":"2026-07-04T15:23:03.797078+00:00"},{"alias_kind":"pith_short_8","alias_value":"FOM6GFZZ","created_at":"2026-07-04T15:23:03.797078+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":9,"internal_anchor_count":6,"sample":[{"citing_arxiv_id":"2606.30865","citing_title":"Scalarization and descalarization in hyperbolic encounters of black holes","ref_index":124,"is_internal_anchor":true},{"citing_arxiv_id":"2605.20320","citing_title":"Ringdown and lensing of triple systems","ref_index":102,"is_internal_anchor":true},{"citing_arxiv_id":"2605.10874","citing_title":"Cusp Formation in Merging Black Hole Horizons","ref_index":59,"is_internal_anchor":true},{"citing_arxiv_id":"2507.22862","citing_title":"Parameter Estimation with Targeted Eccentric Numerical-Relativity Simulations for GW200208_22 and GW190620","ref_index":66,"is_internal_anchor":true},{"citing_arxiv_id":"2509.20450","citing_title":"Splitting the Gravitational Atom: Instabilities of Black Holes with Synchronized or Resonant Hair","ref_index":38,"is_internal_anchor":true},{"citing_arxiv_id":"2511.00307","citing_title":"Spin-up and mass-gain in hyperbolic encounters of spinning black holes","ref_index":104,"is_internal_anchor":true},{"citing_arxiv_id":"2604.26253","citing_title":"Trapping, Irregular Waveforms, and Efficient Radiation in Ultra-relativistic Black Hole Encounters","ref_index":57,"is_internal_anchor":false},{"citing_arxiv_id":"2605.10874","citing_title":"Cusp Formation in Merging Black Hole Horizons","ref_index":59,"is_internal_anchor":false},{"citing_arxiv_id":"2604.25582","citing_title":"Lessons from binary dynamics of inspiralling equal-mass boson-star mergers","ref_index":46,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FOM6GFZZH3WKULLN7EQ47R3XRO","json":"https://pith.science/pith/FOM6GFZZH3WKULLN7EQ47R3XRO.json","graph_json":"https://pith.science/api/pith-number/FOM6GFZZH3WKULLN7EQ47R3XRO/graph.json","events_json":"https://pith.science/api/pith-number/FOM6GFZZH3WKULLN7EQ47R3XRO/events.json","paper":"https://pith.science/paper/FOM6GFZZ"},"agent_actions":{"view_html":"https://pith.science/pith/FOM6GFZZH3WKULLN7EQ47R3XRO","download_json":"https://pith.science/pith/FOM6GFZZH3WKULLN7EQ47R3XRO.json","view_paper":"https://pith.science/paper/FOM6GFZZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=gr-qc/0306056&json=true","fetch_graph":"https://pith.science/api/pith-number/FOM6GFZZH3WKULLN7EQ47R3XRO/graph.json","fetch_events":"https://pith.science/api/pith-number/FOM6GFZZH3WKULLN7EQ47R3XRO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FOM6GFZZH3WKULLN7EQ47R3XRO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FOM6GFZZH3WKULLN7EQ47R3XRO/action/storage_attestation","attest_author":"https://pith.science/pith/FOM6GFZZH3WKULLN7EQ47R3XRO/action/author_attestation","sign_citation":"https://pith.science/pith/FOM6GFZZH3WKULLN7EQ47R3XRO/action/citation_signature","submit_replication":"https://pith.science/pith/FOM6GFZZH3WKULLN7EQ47R3XRO/action/replication_record"}},"created_at":"2026-07-04T15:23:03.797078+00:00","updated_at":"2026-07-04T15:23:03.797078+00:00"}