{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:FB3WD6N765Q2IPJYDX2ASM4ISO","short_pith_number":"pith:FB3WD6N7","schema_version":"1.0","canonical_sha256":"287761f9bff761a43d381df409338893801bee5a35dee769e718141a64544672","source":{"kind":"arxiv","id":"1705.00610","version":1},"attestation_state":"computed","paper":{"title":"Timelike surfaces into 4-dimensional Minkowski space via spinors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Victor H. Patty-Yujra","submitted_at":"2017-04-28T18:17:19Z","abstract_excerpt":"We prove that an isometric immersion of a timelike surface in four-dimensional Minkowski space is equivalent to a normalized spinor field which is a solution of a Dirac equation on the surface. Using the quaternions and the complex numbers, we obtain a spinor representation formula that relates the spinor field and the isometric immersion. Applying the representation formula, we deduce a new spinor representation of a timelike surface in three-dimensional De Sitter space; we give a formula for the Laplacian of the Gauss map of a minimal timelike surface in four-dimensional Minkowski space in t"},"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":"1705.00610","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-04-28T18:17:19Z","cross_cats_sorted":[],"title_canon_sha256":"7acbecf06231bc36f412591af1c21671d5a5c81e2e4b2835d4328beb5ccadc3d","abstract_canon_sha256":"cad31115c9de21deadc8c0095b104262adf116e4df8244ae0ff83b37926cd9b0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:10.333241Z","signature_b64":"7svmLjl1zcmv6b21tixAXYBzNf0usAHIY8LBEgM87PS6uuziUM8xB+0lh6sgucuoBmsy1AWltO3gGxFfKQ/zCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"287761f9bff761a43d381df409338893801bee5a35dee769e718141a64544672","last_reissued_at":"2026-05-18T00:45:10.332608Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:10.332608Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Timelike surfaces into 4-dimensional Minkowski space via spinors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Victor H. Patty-Yujra","submitted_at":"2017-04-28T18:17:19Z","abstract_excerpt":"We prove that an isometric immersion of a timelike surface in four-dimensional Minkowski space is equivalent to a normalized spinor field which is a solution of a Dirac equation on the surface. Using the quaternions and the complex numbers, we obtain a spinor representation formula that relates the spinor field and the isometric immersion. Applying the representation formula, we deduce a new spinor representation of a timelike surface in three-dimensional De Sitter space; we give a formula for the Laplacian of the Gauss map of a minimal timelike surface in four-dimensional Minkowski space in t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.00610","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":""},"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":"1705.00610","created_at":"2026-05-18T00:45:10.332713+00:00"},{"alias_kind":"arxiv_version","alias_value":"1705.00610v1","created_at":"2026-05-18T00:45:10.332713+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.00610","created_at":"2026-05-18T00:45:10.332713+00:00"},{"alias_kind":"pith_short_12","alias_value":"FB3WD6N765Q2","created_at":"2026-05-18T12:31:15.632608+00:00"},{"alias_kind":"pith_short_16","alias_value":"FB3WD6N765Q2IPJY","created_at":"2026-05-18T12:31:15.632608+00:00"},{"alias_kind":"pith_short_8","alias_value":"FB3WD6N7","created_at":"2026-05-18T12:31:15.632608+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/FB3WD6N765Q2IPJYDX2ASM4ISO","json":"https://pith.science/pith/FB3WD6N765Q2IPJYDX2ASM4ISO.json","graph_json":"https://pith.science/api/pith-number/FB3WD6N765Q2IPJYDX2ASM4ISO/graph.json","events_json":"https://pith.science/api/pith-number/FB3WD6N765Q2IPJYDX2ASM4ISO/events.json","paper":"https://pith.science/paper/FB3WD6N7"},"agent_actions":{"view_html":"https://pith.science/pith/FB3WD6N765Q2IPJYDX2ASM4ISO","download_json":"https://pith.science/pith/FB3WD6N765Q2IPJYDX2ASM4ISO.json","view_paper":"https://pith.science/paper/FB3WD6N7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1705.00610&json=true","fetch_graph":"https://pith.science/api/pith-number/FB3WD6N765Q2IPJYDX2ASM4ISO/graph.json","fetch_events":"https://pith.science/api/pith-number/FB3WD6N765Q2IPJYDX2ASM4ISO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FB3WD6N765Q2IPJYDX2ASM4ISO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FB3WD6N765Q2IPJYDX2ASM4ISO/action/storage_attestation","attest_author":"https://pith.science/pith/FB3WD6N765Q2IPJYDX2ASM4ISO/action/author_attestation","sign_citation":"https://pith.science/pith/FB3WD6N765Q2IPJYDX2ASM4ISO/action/citation_signature","submit_replication":"https://pith.science/pith/FB3WD6N765Q2IPJYDX2ASM4ISO/action/replication_record"}},"created_at":"2026-05-18T00:45:10.332713+00:00","updated_at":"2026-05-18T00:45:10.332713+00:00"}