{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:MZKRI5CBGKXMMATP3NT7YFL7U3","short_pith_number":"pith:MZKRI5CB","canonical_record":{"source":{"id":"1707.07396","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-07-24T04:12:57Z","cross_cats_sorted":[],"title_canon_sha256":"c0b963b246e58ed694f7d9b22c5ce74af0caa6b3bf5386f2d33ed4d7e98bc4f7","abstract_canon_sha256":"3783bd09612271454e499604699b8179b4732811c7911c79853b66c4201d9f07"},"schema_version":"1.0"},"canonical_sha256":"665514744132aec6026fdb67fc157fa6d2acf2e8dcc63f6d906a8b10ed501760","source":{"kind":"arxiv","id":"1707.07396","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.07396","created_at":"2026-05-18T00:39:42Z"},{"alias_kind":"arxiv_version","alias_value":"1707.07396v1","created_at":"2026-05-18T00:39:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.07396","created_at":"2026-05-18T00:39:42Z"},{"alias_kind":"pith_short_12","alias_value":"MZKRI5CBGKXM","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"MZKRI5CBGKXMMATP","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"MZKRI5CB","created_at":"2026-05-18T12:31:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:MZKRI5CBGKXMMATP3NT7YFL7U3","target":"record","payload":{"canonical_record":{"source":{"id":"1707.07396","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-07-24T04:12:57Z","cross_cats_sorted":[],"title_canon_sha256":"c0b963b246e58ed694f7d9b22c5ce74af0caa6b3bf5386f2d33ed4d7e98bc4f7","abstract_canon_sha256":"3783bd09612271454e499604699b8179b4732811c7911c79853b66c4201d9f07"},"schema_version":"1.0"},"canonical_sha256":"665514744132aec6026fdb67fc157fa6d2acf2e8dcc63f6d906a8b10ed501760","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:42.375475Z","signature_b64":"BcHVwMg32WCz7SQN+VUIrpAyyemtlJ85Pl8SFHYts4X3zi5KHS+p0z4YQGROVKVVvXaFZtX1DnFkIvbrazbZBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"665514744132aec6026fdb67fc157fa6d2acf2e8dcc63f6d906a8b10ed501760","last_reissued_at":"2026-05-18T00:39:42.374636Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:42.374636Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1707.07396","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":"2026-05-18T00:39:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O4+SPZGvvPdApzHlL7mNrH+qIiVbtcY/9nCboSx5lWdCYP9XZG+gWaF+BB8TyYvy8bNawPnV/3Do8ZE9NGinBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T21:36:58.690854Z"},"content_sha256":"1ba87418113dbf6920c4ea3ef07378eb062a8f03605f983a68214c10fee42049","schema_version":"1.0","event_id":"sha256:1ba87418113dbf6920c4ea3ef07378eb062a8f03605f983a68214c10fee42049"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:MZKRI5CBGKXMMATP3NT7YFL7U3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Surfaces with light-like points in Lorentz-Minkowski 3-space with applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Kotaro Yamada, Masaaki Umehara","submitted_at":"2017-07-24T04:12:57Z","abstract_excerpt":"With several concrete examples of zero mean curvature surfaces in $\\boldsymbol{R}^3_1$ containing a light-like line recently having been found, here we construct all real analytic germs of zero mean curvature surfaces by applying the Cauchy-Kovalevski theorem for partial differential equations. A point where the first fundamental form of a surface degenerates is said to be light-like. We also show a theorem on a property of light-like points of a surface in $\\boldsymbol{R}^3_1$ whose mean curvature vector is smoothly extendable. This explains why such surfaces will contain a light-like line wh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.07396","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:39:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cl8lPIYWtJbatPkSHkN04aS2KuuEjNc38gJ9q5tLRAyBVwC0k3UC6ELWkj+00zF+mJLlkZWGc+QMfRvBsoWjAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T21:36:58.691196Z"},"content_sha256":"4191066c82bce28f8a186401cb2232b9fb5c056b2096648f833413b4c1356485","schema_version":"1.0","event_id":"sha256:4191066c82bce28f8a186401cb2232b9fb5c056b2096648f833413b4c1356485"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MZKRI5CBGKXMMATP3NT7YFL7U3/bundle.json","state_url":"https://pith.science/pith/MZKRI5CBGKXMMATP3NT7YFL7U3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MZKRI5CBGKXMMATP3NT7YFL7U3/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":"2026-06-02T21:36:58Z","links":{"resolver":"https://pith.science/pith/MZKRI5CBGKXMMATP3NT7YFL7U3","bundle":"https://pith.science/pith/MZKRI5CBGKXMMATP3NT7YFL7U3/bundle.json","state":"https://pith.science/pith/MZKRI5CBGKXMMATP3NT7YFL7U3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MZKRI5CBGKXMMATP3NT7YFL7U3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:MZKRI5CBGKXMMATP3NT7YFL7U3","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":"3783bd09612271454e499604699b8179b4732811c7911c79853b66c4201d9f07","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-07-24T04:12:57Z","title_canon_sha256":"c0b963b246e58ed694f7d9b22c5ce74af0caa6b3bf5386f2d33ed4d7e98bc4f7"},"schema_version":"1.0","source":{"id":"1707.07396","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.07396","created_at":"2026-05-18T00:39:42Z"},{"alias_kind":"arxiv_version","alias_value":"1707.07396v1","created_at":"2026-05-18T00:39:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.07396","created_at":"2026-05-18T00:39:42Z"},{"alias_kind":"pith_short_12","alias_value":"MZKRI5CBGKXM","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"MZKRI5CBGKXMMATP","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"MZKRI5CB","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:4191066c82bce28f8a186401cb2232b9fb5c056b2096648f833413b4c1356485","target":"graph","created_at":"2026-05-18T00:39:42Z","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":"With several concrete examples of zero mean curvature surfaces in $\\boldsymbol{R}^3_1$ containing a light-like line recently having been found, here we construct all real analytic germs of zero mean curvature surfaces by applying the Cauchy-Kovalevski theorem for partial differential equations. A point where the first fundamental form of a surface degenerates is said to be light-like. We also show a theorem on a property of light-like points of a surface in $\\boldsymbol{R}^3_1$ whose mean curvature vector is smoothly extendable. This explains why such surfaces will contain a light-like line wh","authors_text":"Kotaro Yamada, Masaaki Umehara","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-07-24T04:12:57Z","title":"Surfaces with light-like points in Lorentz-Minkowski 3-space with applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.07396","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":"sha256:1ba87418113dbf6920c4ea3ef07378eb062a8f03605f983a68214c10fee42049","target":"record","created_at":"2026-05-18T00:39:42Z","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":"3783bd09612271454e499604699b8179b4732811c7911c79853b66c4201d9f07","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-07-24T04:12:57Z","title_canon_sha256":"c0b963b246e58ed694f7d9b22c5ce74af0caa6b3bf5386f2d33ed4d7e98bc4f7"},"schema_version":"1.0","source":{"id":"1707.07396","kind":"arxiv","version":1}},"canonical_sha256":"665514744132aec6026fdb67fc157fa6d2acf2e8dcc63f6d906a8b10ed501760","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"665514744132aec6026fdb67fc157fa6d2acf2e8dcc63f6d906a8b10ed501760","first_computed_at":"2026-05-18T00:39:42.374636Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:39:42.374636Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BcHVwMg32WCz7SQN+VUIrpAyyemtlJ85Pl8SFHYts4X3zi5KHS+p0z4YQGROVKVVvXaFZtX1DnFkIvbrazbZBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:39:42.375475Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.07396","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1ba87418113dbf6920c4ea3ef07378eb062a8f03605f983a68214c10fee42049","sha256:4191066c82bce28f8a186401cb2232b9fb5c056b2096648f833413b4c1356485"],"state_sha256":"43520dbad853922141d7533e93358b8243f86c00adb61ba7afc1ed611fabe3ed"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qn2tnyt4vx3a3hNAP0e49BSBiRKqGY0jnWqN+grJcwwpNPpKuY8ie3DTOVC4Hf6Mj36DTVuXWMhUCxdKHmQqCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T21:36:58.693470Z","bundle_sha256":"4bf2e4e3fc68b7944c4e1cf81a684d2eb23794ba13bc94d9976d2c9d5cffa9d6"}}