{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:LZEMI3GXPPDPK42URSV3SG4SUX","short_pith_number":"pith:LZEMI3GX","canonical_record":{"source":{"id":"1312.0927","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-12-03T20:40:32Z","cross_cats_sorted":[],"title_canon_sha256":"b52ba37ff0d60bc20514653603c4cedd07cdeb4c6f275e6f8f04b4218a9c70f4","abstract_canon_sha256":"0c6281ce524c50ec686019e5abe28aff807ee21ee0fd813fa4a83e9e6d30f5f8"},"schema_version":"1.0"},"canonical_sha256":"5e48c46cd77bc6f573548cabb91b92a5f4bd900243d88b9e1dded8c22c1d51da","source":{"kind":"arxiv","id":"1312.0927","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.0927","created_at":"2026-05-18T01:36:15Z"},{"alias_kind":"arxiv_version","alias_value":"1312.0927v1","created_at":"2026-05-18T01:36:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.0927","created_at":"2026-05-18T01:36:15Z"},{"alias_kind":"pith_short_12","alias_value":"LZEMI3GXPPDP","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LZEMI3GXPPDPK42U","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LZEMI3GX","created_at":"2026-05-18T12:27:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:LZEMI3GXPPDPK42URSV3SG4SUX","target":"record","payload":{"canonical_record":{"source":{"id":"1312.0927","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-12-03T20:40:32Z","cross_cats_sorted":[],"title_canon_sha256":"b52ba37ff0d60bc20514653603c4cedd07cdeb4c6f275e6f8f04b4218a9c70f4","abstract_canon_sha256":"0c6281ce524c50ec686019e5abe28aff807ee21ee0fd813fa4a83e9e6d30f5f8"},"schema_version":"1.0"},"canonical_sha256":"5e48c46cd77bc6f573548cabb91b92a5f4bd900243d88b9e1dded8c22c1d51da","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:15.731923Z","signature_b64":"kSXWzi6z9cKMBOzJ6/K6fV1uQu0/WE6qZ4uawbfSDC3tqvUU7tDzxxFhMVkWEqVwa2zKssMJGLmBz1tjnNb5BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5e48c46cd77bc6f573548cabb91b92a5f4bd900243d88b9e1dded8c22c1d51da","last_reissued_at":"2026-05-18T01:36:15.731353Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:15.731353Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.0927","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":"2026-05-18T01:36:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QSe78BW9QAGKx+J278s5aaihuUiOAZBJMlDmTA6MdXgQsJIGS9JF42HsjGr6DavGGsFL6nhyx/EzWj08eLZBDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T20:11:50.576183Z"},"content_sha256":"0a2313f04f3876ae14d6cfb016b1a848651635cceb45bbb7592e878a9e060341","schema_version":"1.0","event_id":"sha256:0a2313f04f3876ae14d6cfb016b1a848651635cceb45bbb7592e878a9e060341"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:LZEMI3GXPPDPK42URSV3SG4SUX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Invariant sets near singularities of holomorphic foliations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"C\\'esar Camacho, Rudy Rosas","submitted_at":"2013-12-03T20:40:32Z","abstract_excerpt":"Consider a complex one dimensional foliation on a complex surface near a singularity $p$. If $\\mathcal{I}$ is a closed invariant set containing the singularity $p$, then $\\mathcal{I}$ contains either a separatrix at $p$ or an invariant real three dimensional manifold singular at $p$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.0927","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":"2026-05-18T01:36:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dmhAT5aby5z1Vc61u0mU3ZvSWAtTgPew0H1FVhT/OSlN2IhT1vpetxeOCOu89xy8cGeJY8YaHE1QHXF42bD5AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T20:11:50.576547Z"},"content_sha256":"7bed8f76c651095adb494ece341e7d63c6cbe9995f637589f7bf3abf31358243","schema_version":"1.0","event_id":"sha256:7bed8f76c651095adb494ece341e7d63c6cbe9995f637589f7bf3abf31358243"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LZEMI3GXPPDPK42URSV3SG4SUX/bundle.json","state_url":"https://pith.science/pith/LZEMI3GXPPDPK42URSV3SG4SUX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LZEMI3GXPPDPK42URSV3SG4SUX/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":"2026-06-25T20:11:50Z","links":{"resolver":"https://pith.science/pith/LZEMI3GXPPDPK42URSV3SG4SUX","bundle":"https://pith.science/pith/LZEMI3GXPPDPK42URSV3SG4SUX/bundle.json","state":"https://pith.science/pith/LZEMI3GXPPDPK42URSV3SG4SUX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LZEMI3GXPPDPK42URSV3SG4SUX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:LZEMI3GXPPDPK42URSV3SG4SUX","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":"0c6281ce524c50ec686019e5abe28aff807ee21ee0fd813fa4a83e9e6d30f5f8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-12-03T20:40:32Z","title_canon_sha256":"b52ba37ff0d60bc20514653603c4cedd07cdeb4c6f275e6f8f04b4218a9c70f4"},"schema_version":"1.0","source":{"id":"1312.0927","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.0927","created_at":"2026-05-18T01:36:15Z"},{"alias_kind":"arxiv_version","alias_value":"1312.0927v1","created_at":"2026-05-18T01:36:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.0927","created_at":"2026-05-18T01:36:15Z"},{"alias_kind":"pith_short_12","alias_value":"LZEMI3GXPPDP","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LZEMI3GXPPDPK42U","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LZEMI3GX","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:7bed8f76c651095adb494ece341e7d63c6cbe9995f637589f7bf3abf31358243","target":"graph","created_at":"2026-05-18T01:36:15Z","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":"Consider a complex one dimensional foliation on a complex surface near a singularity $p$. If $\\mathcal{I}$ is a closed invariant set containing the singularity $p$, then $\\mathcal{I}$ contains either a separatrix at $p$ or an invariant real three dimensional manifold singular at $p$.","authors_text":"C\\'esar Camacho, Rudy Rosas","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-12-03T20:40:32Z","title":"Invariant sets near singularities of holomorphic foliations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.0927","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":"sha256:0a2313f04f3876ae14d6cfb016b1a848651635cceb45bbb7592e878a9e060341","target":"record","created_at":"2026-05-18T01:36:15Z","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":"0c6281ce524c50ec686019e5abe28aff807ee21ee0fd813fa4a83e9e6d30f5f8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-12-03T20:40:32Z","title_canon_sha256":"b52ba37ff0d60bc20514653603c4cedd07cdeb4c6f275e6f8f04b4218a9c70f4"},"schema_version":"1.0","source":{"id":"1312.0927","kind":"arxiv","version":1}},"canonical_sha256":"5e48c46cd77bc6f573548cabb91b92a5f4bd900243d88b9e1dded8c22c1d51da","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5e48c46cd77bc6f573548cabb91b92a5f4bd900243d88b9e1dded8c22c1d51da","first_computed_at":"2026-05-18T01:36:15.731353Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:15.731353Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kSXWzi6z9cKMBOzJ6/K6fV1uQu0/WE6qZ4uawbfSDC3tqvUU7tDzxxFhMVkWEqVwa2zKssMJGLmBz1tjnNb5BA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:15.731923Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.0927","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0a2313f04f3876ae14d6cfb016b1a848651635cceb45bbb7592e878a9e060341","sha256:7bed8f76c651095adb494ece341e7d63c6cbe9995f637589f7bf3abf31358243"],"state_sha256":"fbffa13b0680c5116d94c9018170e4040e4b0d8fff88b2a36cc2287795a5d134"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DUvCuhr7dfzwXH1vSjMvt6yl3k/IlM4qvj0FFXQlCXgTts2fAUJFeslNo5MYLgAJPivwuljeuf+gSjv1L/7pDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T20:11:50.578449Z","bundle_sha256":"2725a160e500415830fad22b78405ca35b2b5601964c4a1cf619b7487f12bb69"}}