{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:XWL6YOBEMVYHQI6TBF465AGADP","short_pith_number":"pith:XWL6YOBE","canonical_record":{"source":{"id":"1511.07579","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-11-24T06:05:41Z","cross_cats_sorted":[],"title_canon_sha256":"fe93799b9194f6dd404575397cad4e4324bfa92d1b4865f48c3b487284d2c8a9","abstract_canon_sha256":"56e98ed29cfc9b3c1ff98ed9ea287549fc9b8c78fdbe3419c0a5614f362c87ba"},"schema_version":"1.0"},"canonical_sha256":"bd97ec382465707823d30979ee80c01bf8dde7b5d3743d1eadd02642285559cb","source":{"kind":"arxiv","id":"1511.07579","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.07579","created_at":"2026-05-18T01:17:24Z"},{"alias_kind":"arxiv_version","alias_value":"1511.07579v2","created_at":"2026-05-18T01:17:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.07579","created_at":"2026-05-18T01:17:24Z"},{"alias_kind":"pith_short_12","alias_value":"XWL6YOBEMVYH","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"XWL6YOBEMVYHQI6T","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"XWL6YOBE","created_at":"2026-05-18T12:29:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:XWL6YOBEMVYHQI6TBF465AGADP","target":"record","payload":{"canonical_record":{"source":{"id":"1511.07579","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-11-24T06:05:41Z","cross_cats_sorted":[],"title_canon_sha256":"fe93799b9194f6dd404575397cad4e4324bfa92d1b4865f48c3b487284d2c8a9","abstract_canon_sha256":"56e98ed29cfc9b3c1ff98ed9ea287549fc9b8c78fdbe3419c0a5614f362c87ba"},"schema_version":"1.0"},"canonical_sha256":"bd97ec382465707823d30979ee80c01bf8dde7b5d3743d1eadd02642285559cb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:24.994267Z","signature_b64":"1Lbc2IP3XJczJZp679o5FYE1dZ7U30iveGADVTk3/lMyYThudWez/Gcsph3c8RiALrrFvkZN44VwtFgcN5WIDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bd97ec382465707823d30979ee80c01bf8dde7b5d3743d1eadd02642285559cb","last_reissued_at":"2026-05-18T01:17:24.993721Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:24.993721Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.07579","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":"2026-05-18T01:17:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zObfuMZ++4BL1cqWZxhS6QTw+854hSmMWBpT0jdE1iR7MFeYxt17CbZGBBRJ9DXet8Ktagw1OlF5qyJgUqG+AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T17:01:57.545082Z"},"content_sha256":"b4e2c0847317d02d358a3dbb7277ecd98662eba09964abdd6969c75dc266d561","schema_version":"1.0","event_id":"sha256:b4e2c0847317d02d358a3dbb7277ecd98662eba09964abdd6969c75dc266d561"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:XWL6YOBEMVYHQI6TBF465AGADP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A generalized Weierstrass representation of Lorentzian surfaces in $\\mathbb{R}^{2,2}$ and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Victor Patty","submitted_at":"2015-11-24T06:05:41Z","abstract_excerpt":"We give a generalized Weierstrass formula for a Lorentz surface conformally immersed in the four-dimensional space $\\mathbb{R}^{2,2}$ using spinors and Lorentz numbers. We also study the immersions of a Lorentzian surface in {\\bf the} Anti-de Sitter space (a pseudo-sphere in $\\mathbb{R}^{2,2}$): we give a new spinor representation formula and deduce the conformal description of a flat Lorentzian surface in that space."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.07579","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":""},"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":"2026-05-18T01:17:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KsNS15Ct9Dru3hzICLUVdYOTheLe5BVUcHkly3/JouA/nGfaGUrGNjR90DoyHPN/xZNkLJnjvHnXPEnnP5gvBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T17:01:57.545435Z"},"content_sha256":"b7a66d0e3153714750b633424fab84c3a31e090d11b1a7461eab5cca6c4b2f34","schema_version":"1.0","event_id":"sha256:b7a66d0e3153714750b633424fab84c3a31e090d11b1a7461eab5cca6c4b2f34"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XWL6YOBEMVYHQI6TBF465AGADP/bundle.json","state_url":"https://pith.science/pith/XWL6YOBEMVYHQI6TBF465AGADP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XWL6YOBEMVYHQI6TBF465AGADP/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":"2026-06-24T17:01:57Z","links":{"resolver":"https://pith.science/pith/XWL6YOBEMVYHQI6TBF465AGADP","bundle":"https://pith.science/pith/XWL6YOBEMVYHQI6TBF465AGADP/bundle.json","state":"https://pith.science/pith/XWL6YOBEMVYHQI6TBF465AGADP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XWL6YOBEMVYHQI6TBF465AGADP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:XWL6YOBEMVYHQI6TBF465AGADP","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":"56e98ed29cfc9b3c1ff98ed9ea287549fc9b8c78fdbe3419c0a5614f362c87ba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-11-24T06:05:41Z","title_canon_sha256":"fe93799b9194f6dd404575397cad4e4324bfa92d1b4865f48c3b487284d2c8a9"},"schema_version":"1.0","source":{"id":"1511.07579","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.07579","created_at":"2026-05-18T01:17:24Z"},{"alias_kind":"arxiv_version","alias_value":"1511.07579v2","created_at":"2026-05-18T01:17:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.07579","created_at":"2026-05-18T01:17:24Z"},{"alias_kind":"pith_short_12","alias_value":"XWL6YOBEMVYH","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"XWL6YOBEMVYHQI6T","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"XWL6YOBE","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:b7a66d0e3153714750b633424fab84c3a31e090d11b1a7461eab5cca6c4b2f34","target":"graph","created_at":"2026-05-18T01:17:24Z","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"},"paper":{"abstract_excerpt":"We give a generalized Weierstrass formula for a Lorentz surface conformally immersed in the four-dimensional space $\\mathbb{R}^{2,2}$ using spinors and Lorentz numbers. We also study the immersions of a Lorentzian surface in {\\bf the} Anti-de Sitter space (a pseudo-sphere in $\\mathbb{R}^{2,2}$): we give a new spinor representation formula and deduce the conformal description of a flat Lorentzian surface in that space.","authors_text":"Victor Patty","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-11-24T06:05:41Z","title":"A generalized Weierstrass representation of Lorentzian surfaces in $\\mathbb{R}^{2,2}$ and applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.07579","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:b4e2c0847317d02d358a3dbb7277ecd98662eba09964abdd6969c75dc266d561","target":"record","created_at":"2026-05-18T01:17:24Z","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":"56e98ed29cfc9b3c1ff98ed9ea287549fc9b8c78fdbe3419c0a5614f362c87ba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-11-24T06:05:41Z","title_canon_sha256":"fe93799b9194f6dd404575397cad4e4324bfa92d1b4865f48c3b487284d2c8a9"},"schema_version":"1.0","source":{"id":"1511.07579","kind":"arxiv","version":2}},"canonical_sha256":"bd97ec382465707823d30979ee80c01bf8dde7b5d3743d1eadd02642285559cb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bd97ec382465707823d30979ee80c01bf8dde7b5d3743d1eadd02642285559cb","first_computed_at":"2026-05-18T01:17:24.993721Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:24.993721Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1Lbc2IP3XJczJZp679o5FYE1dZ7U30iveGADVTk3/lMyYThudWez/Gcsph3c8RiALrrFvkZN44VwtFgcN5WIDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:24.994267Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.07579","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b4e2c0847317d02d358a3dbb7277ecd98662eba09964abdd6969c75dc266d561","sha256:b7a66d0e3153714750b633424fab84c3a31e090d11b1a7461eab5cca6c4b2f34"],"state_sha256":"4990b7d744c5682f145bfa2a65e259fc59557cd32c352346d1274469f7547068"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HA3t4h3JMBIA0d+9MtG/GOUol4g+dhUo88soKI+yKa9O+Mp4PfqvEeg5P2cXXizqf57uD+TjcBZu70pEeBemCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T17:01:57.547354Z","bundle_sha256":"908785ce2704d5add972a4ec34800ef8e13c2d110577bbc625ffc39120a13d70"}}