{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2001:W6OFLOYCUMCMQLXXHCOGLYOBNQ","short_pith_number":"pith:W6OFLOYC","schema_version":"1.0","canonical_sha256":"b79c55bb02a304c82ef7389c65e1c16c115e86f1fd637dd9e1d5e84bd7e91018","source":{"kind":"arxiv","id":"gr-qc/0109093","version":3},"attestation_state":"computed","paper":{"title":"Isometric embeddings of black hole horizons in three-dimensional flat space","license":"","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Edward Seidel, Miguel Alcubierre, Mihai Bondarescu","submitted_at":"2001-09-28T08:25:45Z","abstract_excerpt":"The geometry of a two-dimensional surface in a curved space can be most easily visualized by using an isometric embedding in flat three-dimensional space. Here we present a new method for embedding surfaces with spherical topology in flat space when such a embedding exists. Our method is based on expanding the surface in spherical harmonics and minimizing for the differences between the metric on the original surface and the metric on the trial surface in the space of the expansion coefficients. We have applied this method to study the geometry of back hole horizons in the presence of strong, "},"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/0109093","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"gr-qc","submitted_at":"2001-09-28T08:25:45Z","cross_cats_sorted":[],"title_canon_sha256":"a9747eb8fed90963a9a89c730b0373b1ab6570dc1bc7c4772bbb46bf2cbc098c","abstract_canon_sha256":"f25e1328e4e02c119646a4291897ae4fed9d5b1b5a8416d569ce60753920beb5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:26:57.929221Z","signature_b64":"iDAqh5Azcps2/OBf7gROTS6wmryC/cPYoOwetsPujpFHs7EcsuIpcdwyHutW91RiaYFt1bxU4kwowZFyd/0iAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b79c55bb02a304c82ef7389c65e1c16c115e86f1fd637dd9e1d5e84bd7e91018","last_reissued_at":"2026-07-04T16:26:57.928848Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:26:57.928848Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Isometric embeddings of black hole horizons in three-dimensional flat space","license":"","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Edward Seidel, Miguel Alcubierre, Mihai Bondarescu","submitted_at":"2001-09-28T08:25:45Z","abstract_excerpt":"The geometry of a two-dimensional surface in a curved space can be most easily visualized by using an isometric embedding in flat three-dimensional space. Here we present a new method for embedding surfaces with spherical topology in flat space when such a embedding exists. Our method is based on expanding the surface in spherical harmonics and minimizing for the differences between the metric on the original surface and the metric on the trial surface in the space of the expansion coefficients. We have applied this method to study the geometry of back hole horizons in the presence of strong, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/0109093","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/0109093/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/0109093","created_at":"2026-07-04T16:26:57.928904+00:00"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/0109093v3","created_at":"2026-07-04T16:26:57.928904+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/0109093","created_at":"2026-07-04T16:26:57.928904+00:00"},{"alias_kind":"pith_short_12","alias_value":"W6OFLOYCUMCM","created_at":"2026-07-04T16:26:57.928904+00:00"},{"alias_kind":"pith_short_16","alias_value":"W6OFLOYCUMCMQLXX","created_at":"2026-07-04T16:26:57.928904+00:00"},{"alias_kind":"pith_short_8","alias_value":"W6OFLOYC","created_at":"2026-07-04T16:26:57.928904+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/W6OFLOYCUMCMQLXXHCOGLYOBNQ","json":"https://pith.science/pith/W6OFLOYCUMCMQLXXHCOGLYOBNQ.json","graph_json":"https://pith.science/api/pith-number/W6OFLOYCUMCMQLXXHCOGLYOBNQ/graph.json","events_json":"https://pith.science/api/pith-number/W6OFLOYCUMCMQLXXHCOGLYOBNQ/events.json","paper":"https://pith.science/paper/W6OFLOYC"},"agent_actions":{"view_html":"https://pith.science/pith/W6OFLOYCUMCMQLXXHCOGLYOBNQ","download_json":"https://pith.science/pith/W6OFLOYCUMCMQLXXHCOGLYOBNQ.json","view_paper":"https://pith.science/paper/W6OFLOYC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=gr-qc/0109093&json=true","fetch_graph":"https://pith.science/api/pith-number/W6OFLOYCUMCMQLXXHCOGLYOBNQ/graph.json","fetch_events":"https://pith.science/api/pith-number/W6OFLOYCUMCMQLXXHCOGLYOBNQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/W6OFLOYCUMCMQLXXHCOGLYOBNQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/W6OFLOYCUMCMQLXXHCOGLYOBNQ/action/storage_attestation","attest_author":"https://pith.science/pith/W6OFLOYCUMCMQLXXHCOGLYOBNQ/action/author_attestation","sign_citation":"https://pith.science/pith/W6OFLOYCUMCMQLXXHCOGLYOBNQ/action/citation_signature","submit_replication":"https://pith.science/pith/W6OFLOYCUMCMQLXXHCOGLYOBNQ/action/replication_record"}},"created_at":"2026-07-04T16:26:57.928904+00:00","updated_at":"2026-07-04T16:26:57.928904+00:00"}