{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:BOIZIZSXSQONFMPAIO5F3ALIJ3","short_pith_number":"pith:BOIZIZSX","canonical_record":{"source":{"id":"1908.01967","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-08-06T05:57:13Z","cross_cats_sorted":[],"title_canon_sha256":"ab65d45aad3c5bad685ea87bbf6a1c77f927ce505b5926e3e775be886b652788","abstract_canon_sha256":"aa1fb23cf3a210c8cc9121daec6c62f3d1200078ada145f8070e7a897e4fe422"},"schema_version":"1.0"},"canonical_sha256":"0b91946657941cd2b1e043ba5d81684ed13c9c196a5c269fa252d99e63ed4f2c","source":{"kind":"arxiv","id":"1908.01967","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.01967","created_at":"2026-07-04T23:51:49Z"},{"alias_kind":"arxiv_version","alias_value":"1908.01967v1","created_at":"2026-07-04T23:51:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.01967","created_at":"2026-07-04T23:51:49Z"},{"alias_kind":"pith_short_12","alias_value":"BOIZIZSXSQON","created_at":"2026-07-04T23:51:49Z"},{"alias_kind":"pith_short_16","alias_value":"BOIZIZSXSQONFMPA","created_at":"2026-07-04T23:51:49Z"},{"alias_kind":"pith_short_8","alias_value":"BOIZIZSX","created_at":"2026-07-04T23:51:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:BOIZIZSXSQONFMPAIO5F3ALIJ3","target":"record","payload":{"canonical_record":{"source":{"id":"1908.01967","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-08-06T05:57:13Z","cross_cats_sorted":[],"title_canon_sha256":"ab65d45aad3c5bad685ea87bbf6a1c77f927ce505b5926e3e775be886b652788","abstract_canon_sha256":"aa1fb23cf3a210c8cc9121daec6c62f3d1200078ada145f8070e7a897e4fe422"},"schema_version":"1.0"},"canonical_sha256":"0b91946657941cd2b1e043ba5d81684ed13c9c196a5c269fa252d99e63ed4f2c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:51:49.824845Z","signature_b64":"eHYrT6LG5EYeaGe0Tn9QS/9Jk846DpK7cDk59PPmziCnDyKYb2CkvrOafVblyZuSBfba2fokiRN05RvRKJvGBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0b91946657941cd2b1e043ba5d81684ed13c9c196a5c269fa252d99e63ed4f2c","last_reissued_at":"2026-07-04T23:51:49.824501Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:51:49.824501Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.01967","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T23:51:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9APUK5IhBZhi9XFLYC+VrsUd2Bib2xsk0AFxeAabfYrRrpby6ajM524zWFuU+uYIzsFpIK+na++FOn1UGmBWBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T04:46:30.715902Z"},"content_sha256":"ab8524aa1426c5f26d26911244340d3f7c19878f533aa492ad893b06c8976116","schema_version":"1.0","event_id":"sha256:ab8524aa1426c5f26d26911244340d3f7c19878f533aa492ad893b06c8976116"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:BOIZIZSXSQONFMPAIO5F3ALIJ3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Isometric deformations of mixed type surfaces in Lorentz-Minkowski space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Atsufumi Honda","submitted_at":"2019-08-06T05:57:13Z","abstract_excerpt":"A connected regular surface in Lorentz-Minkowski 3-space is called a mixed type surface if the spacelike, timelike and lightlike point sets are all non-empty. Lightlike points on mixed type surfaces may be regarded as singular points of the induced metrics. In this paper, we introduce the L-Gauss map around non-degenerate lightlike points, and show the fundamental theorem of surface theory for mixed type surfaces at non-degenerate lightlike points. As an application, we prove that a real analytic mixed type surface admits non-trivial isometric deformations around generic lightlike points."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.01967","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/1908.01967/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T23:51:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+bZ6tjGwIdFVSYjvtvM4BIKnvg3fBbgwHWQ8oLetA1F2JVueuhV94iO/pzCTR/OIT+zK/spzUQy2Zsh/Q0A6Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T04:46:30.716653Z"},"content_sha256":"0d8888a4f149fcd98fc67723c521bb070ca2c3aa61625ef7d621c6b60036696a","schema_version":"1.0","event_id":"sha256:0d8888a4f149fcd98fc67723c521bb070ca2c3aa61625ef7d621c6b60036696a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BOIZIZSXSQONFMPAIO5F3ALIJ3/bundle.json","state_url":"https://pith.science/pith/BOIZIZSXSQONFMPAIO5F3ALIJ3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BOIZIZSXSQONFMPAIO5F3ALIJ3/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":"2026-08-16T04:46:30Z","links":{"resolver":"https://pith.science/pith/BOIZIZSXSQONFMPAIO5F3ALIJ3","bundle":"https://pith.science/pith/BOIZIZSXSQONFMPAIO5F3ALIJ3/bundle.json","state":"https://pith.science/pith/BOIZIZSXSQONFMPAIO5F3ALIJ3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BOIZIZSXSQONFMPAIO5F3ALIJ3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:BOIZIZSXSQONFMPAIO5F3ALIJ3","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":"aa1fb23cf3a210c8cc9121daec6c62f3d1200078ada145f8070e7a897e4fe422","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-08-06T05:57:13Z","title_canon_sha256":"ab65d45aad3c5bad685ea87bbf6a1c77f927ce505b5926e3e775be886b652788"},"schema_version":"1.0","source":{"id":"1908.01967","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.01967","created_at":"2026-07-04T23:51:49Z"},{"alias_kind":"arxiv_version","alias_value":"1908.01967v1","created_at":"2026-07-04T23:51:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.01967","created_at":"2026-07-04T23:51:49Z"},{"alias_kind":"pith_short_12","alias_value":"BOIZIZSXSQON","created_at":"2026-07-04T23:51:49Z"},{"alias_kind":"pith_short_16","alias_value":"BOIZIZSXSQONFMPA","created_at":"2026-07-04T23:51:49Z"},{"alias_kind":"pith_short_8","alias_value":"BOIZIZSX","created_at":"2026-07-04T23:51:49Z"}],"graph_snapshots":[{"event_id":"sha256:0d8888a4f149fcd98fc67723c521bb070ca2c3aa61625ef7d621c6b60036696a","target":"graph","created_at":"2026-07-04T23:51:49Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.01967/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A connected regular surface in Lorentz-Minkowski 3-space is called a mixed type surface if the spacelike, timelike and lightlike point sets are all non-empty. Lightlike points on mixed type surfaces may be regarded as singular points of the induced metrics. In this paper, we introduce the L-Gauss map around non-degenerate lightlike points, and show the fundamental theorem of surface theory for mixed type surfaces at non-degenerate lightlike points. As an application, we prove that a real analytic mixed type surface admits non-trivial isometric deformations around generic lightlike points.","authors_text":"Atsufumi Honda","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-08-06T05:57:13Z","title":"Isometric deformations of mixed type surfaces in Lorentz-Minkowski space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.01967","kind":"arxiv","version":1},"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:ab8524aa1426c5f26d26911244340d3f7c19878f533aa492ad893b06c8976116","target":"record","created_at":"2026-07-04T23:51:49Z","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":"aa1fb23cf3a210c8cc9121daec6c62f3d1200078ada145f8070e7a897e4fe422","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-08-06T05:57:13Z","title_canon_sha256":"ab65d45aad3c5bad685ea87bbf6a1c77f927ce505b5926e3e775be886b652788"},"schema_version":"1.0","source":{"id":"1908.01967","kind":"arxiv","version":1}},"canonical_sha256":"0b91946657941cd2b1e043ba5d81684ed13c9c196a5c269fa252d99e63ed4f2c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0b91946657941cd2b1e043ba5d81684ed13c9c196a5c269fa252d99e63ed4f2c","first_computed_at":"2026-07-04T23:51:49.824501Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:51:49.824501Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eHYrT6LG5EYeaGe0Tn9QS/9Jk846DpK7cDk59PPmziCnDyKYb2CkvrOafVblyZuSBfba2fokiRN05RvRKJvGBA==","signature_status":"signed_v1","signed_at":"2026-07-04T23:51:49.824845Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.01967","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ab8524aa1426c5f26d26911244340d3f7c19878f533aa492ad893b06c8976116","sha256:0d8888a4f149fcd98fc67723c521bb070ca2c3aa61625ef7d621c6b60036696a"],"state_sha256":"0ec129b0c76f933698ee4901b0c36bd6a85c76461b444033d6ac77269e0ba570"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ruumfNGaFpmDrfsb7KljfJCC/Xiex3+kYG9Y9nw0fYh9bCMOh+nno5YLfUo64/B76g6i8Ww4g44mtmXbnDQxBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T04:46:30.722973Z","bundle_sha256":"b27fa501b2e6ded46a1f31b6bb11fe881a8105fbacd88dd5ff2180d595f25d59"}}