{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:CZTTIMTOKEASXVYONO56RCFAIN","short_pith_number":"pith:CZTTIMTO","canonical_record":{"source":{"id":"1607.00634","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-07-03T12:51:41Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"f7f527d01d74b63a42d593c086680ba637ac050327fb8aaf0d46e418db144b31","abstract_canon_sha256":"7f4f66e5d67b765b5bb5cccdd5686bede39b1ae100100920029e0655ad9701d8"},"schema_version":"1.0"},"canonical_sha256":"166734326e51012bd70e6bbbe888a0437b54d85621cb2dc95f04be13d9cefe11","source":{"kind":"arxiv","id":"1607.00634","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.00634","created_at":"2026-05-17T23:53:34Z"},{"alias_kind":"arxiv_version","alias_value":"1607.00634v2","created_at":"2026-05-17T23:53:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.00634","created_at":"2026-05-17T23:53:34Z"},{"alias_kind":"pith_short_12","alias_value":"CZTTIMTOKEAS","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CZTTIMTOKEASXVYO","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CZTTIMTO","created_at":"2026-05-18T12:30:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:CZTTIMTOKEASXVYONO56RCFAIN","target":"record","payload":{"canonical_record":{"source":{"id":"1607.00634","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-07-03T12:51:41Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"f7f527d01d74b63a42d593c086680ba637ac050327fb8aaf0d46e418db144b31","abstract_canon_sha256":"7f4f66e5d67b765b5bb5cccdd5686bede39b1ae100100920029e0655ad9701d8"},"schema_version":"1.0"},"canonical_sha256":"166734326e51012bd70e6bbbe888a0437b54d85621cb2dc95f04be13d9cefe11","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:34.158414Z","signature_b64":"UMen6fXTp/0fldstM0BpOOLVR6IbkemcAFwFBLAdNQ4UlnW2aowZhU1zeoAryofqi9x+Ee/7tEWVsuNkAb19DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"166734326e51012bd70e6bbbe888a0437b54d85621cb2dc95f04be13d9cefe11","last_reissued_at":"2026-05-17T23:53:34.157772Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:34.157772Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1607.00634","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":"2026-05-17T23:53:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0nw2+dt+JtYnWUVNMipUCrX6sCJ7BHMCRqqlTrTjV9fSjnHJzWMwh7Ex9dabH9bUNu3Clsstbmepg4Mq5NvoDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T14:22:20.861732Z"},"content_sha256":"db7198e0c635297c58703bf8eebaef4e516c4b0a366168c6968f2e4b75a873cf","schema_version":"1.0","event_id":"sha256:db7198e0c635297c58703bf8eebaef4e516c4b0a366168c6968f2e4b75a873cf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:CZTTIMTOKEASXVYONO56RCFAIN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Holomorphic Legendrian curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.CV","authors_text":"Antonio Alarcon, Franc Forstneric, Francisco J. Lopez","submitted_at":"2016-07-03T12:51:41Z","abstract_excerpt":"In this paper we study holomorphic Legendrian curves in the standard holomorphic contact structure on $\\mathbb{C}^{2n+1}$ for any $n\\in\\mathbb{N}$. We provide several approximation and desingularization results which enable us to prove general existence theorems, settling some of the open problems in the subject. In particular, we show that every open Riemann surface $M$ admits a proper holomorphic Legendrian embedding $M\\hookrightarrow\\mathbb{C}^{2n+1}$, and we prove that for every compact bordered Riemann surface $M=\\mathring M\\cup bM$ there exists a topological embedding $M\\hookrightarrow \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.00634","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":"2026-05-17T23:53:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rHEKIXnprbJBXVy75W3/1L6f0UJSin2ERjN+gwlcmUxUZYsa+R2ml143g4E1nsuzF4fGZXYWtOGc5nUwooLCDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T14:22:20.862135Z"},"content_sha256":"e53d6f9a50faa5376ae49da70a82ff52c6db51d967516f7cc83c2fb8f635a70a","schema_version":"1.0","event_id":"sha256:e53d6f9a50faa5376ae49da70a82ff52c6db51d967516f7cc83c2fb8f635a70a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CZTTIMTOKEASXVYONO56RCFAIN/bundle.json","state_url":"https://pith.science/pith/CZTTIMTOKEASXVYONO56RCFAIN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CZTTIMTOKEASXVYONO56RCFAIN/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":"2026-05-25T14:22:20Z","links":{"resolver":"https://pith.science/pith/CZTTIMTOKEASXVYONO56RCFAIN","bundle":"https://pith.science/pith/CZTTIMTOKEASXVYONO56RCFAIN/bundle.json","state":"https://pith.science/pith/CZTTIMTOKEASXVYONO56RCFAIN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CZTTIMTOKEASXVYONO56RCFAIN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:CZTTIMTOKEASXVYONO56RCFAIN","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":"7f4f66e5d67b765b5bb5cccdd5686bede39b1ae100100920029e0655ad9701d8","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-07-03T12:51:41Z","title_canon_sha256":"f7f527d01d74b63a42d593c086680ba637ac050327fb8aaf0d46e418db144b31"},"schema_version":"1.0","source":{"id":"1607.00634","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.00634","created_at":"2026-05-17T23:53:34Z"},{"alias_kind":"arxiv_version","alias_value":"1607.00634v2","created_at":"2026-05-17T23:53:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.00634","created_at":"2026-05-17T23:53:34Z"},{"alias_kind":"pith_short_12","alias_value":"CZTTIMTOKEAS","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CZTTIMTOKEASXVYO","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CZTTIMTO","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:e53d6f9a50faa5376ae49da70a82ff52c6db51d967516f7cc83c2fb8f635a70a","target":"graph","created_at":"2026-05-17T23:53:34Z","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":"In this paper we study holomorphic Legendrian curves in the standard holomorphic contact structure on $\\mathbb{C}^{2n+1}$ for any $n\\in\\mathbb{N}$. We provide several approximation and desingularization results which enable us to prove general existence theorems, settling some of the open problems in the subject. In particular, we show that every open Riemann surface $M$ admits a proper holomorphic Legendrian embedding $M\\hookrightarrow\\mathbb{C}^{2n+1}$, and we prove that for every compact bordered Riemann surface $M=\\mathring M\\cup bM$ there exists a topological embedding $M\\hookrightarrow \\","authors_text":"Antonio Alarcon, Franc Forstneric, Francisco J. Lopez","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-07-03T12:51:41Z","title":"Holomorphic Legendrian curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.00634","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:db7198e0c635297c58703bf8eebaef4e516c4b0a366168c6968f2e4b75a873cf","target":"record","created_at":"2026-05-17T23:53:34Z","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":"7f4f66e5d67b765b5bb5cccdd5686bede39b1ae100100920029e0655ad9701d8","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-07-03T12:51:41Z","title_canon_sha256":"f7f527d01d74b63a42d593c086680ba637ac050327fb8aaf0d46e418db144b31"},"schema_version":"1.0","source":{"id":"1607.00634","kind":"arxiv","version":2}},"canonical_sha256":"166734326e51012bd70e6bbbe888a0437b54d85621cb2dc95f04be13d9cefe11","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"166734326e51012bd70e6bbbe888a0437b54d85621cb2dc95f04be13d9cefe11","first_computed_at":"2026-05-17T23:53:34.157772Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:34.157772Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UMen6fXTp/0fldstM0BpOOLVR6IbkemcAFwFBLAdNQ4UlnW2aowZhU1zeoAryofqi9x+Ee/7tEWVsuNkAb19DA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:34.158414Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.00634","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:db7198e0c635297c58703bf8eebaef4e516c4b0a366168c6968f2e4b75a873cf","sha256:e53d6f9a50faa5376ae49da70a82ff52c6db51d967516f7cc83c2fb8f635a70a"],"state_sha256":"3c82d71f8445517691314f1e63aed73966f0c4c5a02f01ab36ad92c153b70ec9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q9m8wKvtjwBlsNGF/2buJ1WV/eXm43OhEACSzySaR3aETvUkN+4sTBcCBxxFmQTw3M6P5YNL9YAhq9pPskT1BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T14:22:20.865494Z","bundle_sha256":"ee190e0ac1050f37ebf2500d40d26c2faa8a333255d6179e72abcdf133f08d4b"}}