{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:C3UYAYVOG6CS23SQRDRC2ZR6KP","short_pith_number":"pith:C3UYAYVO","canonical_record":{"source":{"id":"1307.2152","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-07-08T16:36:46Z","cross_cats_sorted":[],"title_canon_sha256":"171d88d501b4cc386d26e38e6b86f71d752f179057f50404ad4a55164a59da44","abstract_canon_sha256":"0204999879a2adcf6206cca136c30b165687520fcdbae064e3c23922b94ded4b"},"schema_version":"1.0"},"canonical_sha256":"16e98062ae37852d6e5088e22d663e53d76185b032d677ffbbe5ba9a1c7fa958","source":{"kind":"arxiv","id":"1307.2152","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.2152","created_at":"2026-05-18T00:23:59Z"},{"alias_kind":"arxiv_version","alias_value":"1307.2152v1","created_at":"2026-05-18T00:23:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.2152","created_at":"2026-05-18T00:23:59Z"},{"alias_kind":"pith_short_12","alias_value":"C3UYAYVOG6CS","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"C3UYAYVOG6CS23SQ","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"C3UYAYVO","created_at":"2026-05-18T12:27:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:C3UYAYVOG6CS23SQRDRC2ZR6KP","target":"record","payload":{"canonical_record":{"source":{"id":"1307.2152","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-07-08T16:36:46Z","cross_cats_sorted":[],"title_canon_sha256":"171d88d501b4cc386d26e38e6b86f71d752f179057f50404ad4a55164a59da44","abstract_canon_sha256":"0204999879a2adcf6206cca136c30b165687520fcdbae064e3c23922b94ded4b"},"schema_version":"1.0"},"canonical_sha256":"16e98062ae37852d6e5088e22d663e53d76185b032d677ffbbe5ba9a1c7fa958","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:59.399498Z","signature_b64":"kgJiGkQcqxL8mhoeo06MGL5nHaeoIIhAFTKRdSaZHEIQhm+N9nF492WzzdY3UZNAZCiPD+wXPuGNAX2jdNO5AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"16e98062ae37852d6e5088e22d663e53d76185b032d677ffbbe5ba9a1c7fa958","last_reissued_at":"2026-05-18T00:23:59.398937Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:59.398937Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.2152","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":"2026-05-18T00:23:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"72A3m2e9ImNyqyHUjKs5rJYuX/Y0OU5ZYPUcofZLdGUoqXpqr6ae6uoXhTr+leeDfmcwCsVKv/R/KL67LjkBBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T13:58:41.804111Z"},"content_sha256":"31dd2f872bd0ebd8a72cc90649e2855d18b5ebb1288a9ba93087029f2010c009","schema_version":"1.0","event_id":"sha256:31dd2f872bd0ebd8a72cc90649e2855d18b5ebb1288a9ba93087029f2010c009"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:C3UYAYVOG6CS23SQRDRC2ZR6KP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A new construction of Lagrangians in the complex Euclidean plane in terms of planar curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Ana M. Lerma, Ildefonso Castro","submitted_at":"2013-07-08T16:36:46Z","abstract_excerpt":"We introduce a new method to construct a large family of Lagrangian surfaces in complex Euclidean plane by means of two planar curves making use of their usual product as complex functions and integrating the Hermitian product of their position and tangent vectors.\n  Among this family, we characterize minimal, constant mean curvature, Hamiltonian stationary, solitons for mean curvature flow and Willmore surfaces in terms of simple properties of the curvatures of the generating curves. As an application, we provide explicitly conformal parametrizations of known and new examples of these classes"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.2152","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":"2026-05-18T00:23:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cQfs71viu1QJt0zPREsaU5qLPY3bzDWJKI0QfbHGyOGKqI/KNekiUJ4BWXZr+AeHi87poKxJxnToIOaPCYLKCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T13:58:41.804695Z"},"content_sha256":"96d2adde78843d4b73dcd1cd995bd7954215dccb5645127286bb5afa077ab2e5","schema_version":"1.0","event_id":"sha256:96d2adde78843d4b73dcd1cd995bd7954215dccb5645127286bb5afa077ab2e5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C3UYAYVOG6CS23SQRDRC2ZR6KP/bundle.json","state_url":"https://pith.science/pith/C3UYAYVOG6CS23SQRDRC2ZR6KP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C3UYAYVOG6CS23SQRDRC2ZR6KP/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":"2026-06-06T13:58:41Z","links":{"resolver":"https://pith.science/pith/C3UYAYVOG6CS23SQRDRC2ZR6KP","bundle":"https://pith.science/pith/C3UYAYVOG6CS23SQRDRC2ZR6KP/bundle.json","state":"https://pith.science/pith/C3UYAYVOG6CS23SQRDRC2ZR6KP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C3UYAYVOG6CS23SQRDRC2ZR6KP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:C3UYAYVOG6CS23SQRDRC2ZR6KP","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":"0204999879a2adcf6206cca136c30b165687520fcdbae064e3c23922b94ded4b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-07-08T16:36:46Z","title_canon_sha256":"171d88d501b4cc386d26e38e6b86f71d752f179057f50404ad4a55164a59da44"},"schema_version":"1.0","source":{"id":"1307.2152","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.2152","created_at":"2026-05-18T00:23:59Z"},{"alias_kind":"arxiv_version","alias_value":"1307.2152v1","created_at":"2026-05-18T00:23:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.2152","created_at":"2026-05-18T00:23:59Z"},{"alias_kind":"pith_short_12","alias_value":"C3UYAYVOG6CS","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"C3UYAYVOG6CS23SQ","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"C3UYAYVO","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:96d2adde78843d4b73dcd1cd995bd7954215dccb5645127286bb5afa077ab2e5","target":"graph","created_at":"2026-05-18T00:23:59Z","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 introduce a new method to construct a large family of Lagrangian surfaces in complex Euclidean plane by means of two planar curves making use of their usual product as complex functions and integrating the Hermitian product of their position and tangent vectors.\n  Among this family, we characterize minimal, constant mean curvature, Hamiltonian stationary, solitons for mean curvature flow and Willmore surfaces in terms of simple properties of the curvatures of the generating curves. As an application, we provide explicitly conformal parametrizations of known and new examples of these classes","authors_text":"Ana M. Lerma, Ildefonso Castro","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-07-08T16:36:46Z","title":"A new construction of Lagrangians in the complex Euclidean plane in terms of planar curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.2152","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":"sha256:31dd2f872bd0ebd8a72cc90649e2855d18b5ebb1288a9ba93087029f2010c009","target":"record","created_at":"2026-05-18T00:23:59Z","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":"0204999879a2adcf6206cca136c30b165687520fcdbae064e3c23922b94ded4b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-07-08T16:36:46Z","title_canon_sha256":"171d88d501b4cc386d26e38e6b86f71d752f179057f50404ad4a55164a59da44"},"schema_version":"1.0","source":{"id":"1307.2152","kind":"arxiv","version":1}},"canonical_sha256":"16e98062ae37852d6e5088e22d663e53d76185b032d677ffbbe5ba9a1c7fa958","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"16e98062ae37852d6e5088e22d663e53d76185b032d677ffbbe5ba9a1c7fa958","first_computed_at":"2026-05-18T00:23:59.398937Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:59.398937Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kgJiGkQcqxL8mhoeo06MGL5nHaeoIIhAFTKRdSaZHEIQhm+N9nF492WzzdY3UZNAZCiPD+wXPuGNAX2jdNO5AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:59.399498Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.2152","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:31dd2f872bd0ebd8a72cc90649e2855d18b5ebb1288a9ba93087029f2010c009","sha256:96d2adde78843d4b73dcd1cd995bd7954215dccb5645127286bb5afa077ab2e5"],"state_sha256":"1db001fad20e7da480109ed51c37db8db65756d2bc4adf8472c378b3ec063a67"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yWXOIDEwTok26em55aNUU+ETHLGowZoZkeP2gG6LONeFYTK3Tnm3sKnWk+AnBfFvJF06D9EuRfvqe0kKvDgsBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T13:58:41.808354Z","bundle_sha256":"3a44c80fb0de07ac49fa1ea1cdf601e1a0f4e35adcaa9e7da11ef5d4f81f641f"}}