{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:QDQBJM2ZDBBZJM54SJPQG35VVA","short_pith_number":"pith:QDQBJM2Z","canonical_record":{"source":{"id":"1208.1650","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-08-08T12:28:09Z","cross_cats_sorted":[],"title_canon_sha256":"76c634e8c5fe00410c6524ba10882d611b71cae12e08719f510e5129bcc44560","abstract_canon_sha256":"81cfaeb3b026cc5c31cd4bc13af10455106d3540d6850e7a34be9a36739cf2b2"},"schema_version":"1.0"},"canonical_sha256":"80e014b359184394b3bc925f036fb5a815b718c9b82f43d4dbaa09f63729af26","source":{"kind":"arxiv","id":"1208.1650","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.1650","created_at":"2026-05-18T03:48:26Z"},{"alias_kind":"arxiv_version","alias_value":"1208.1650v3","created_at":"2026-05-18T03:48:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.1650","created_at":"2026-05-18T03:48:26Z"},{"alias_kind":"pith_short_12","alias_value":"QDQBJM2ZDBBZ","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"QDQBJM2ZDBBZJM54","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"QDQBJM2Z","created_at":"2026-05-18T12:27:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:QDQBJM2ZDBBZJM54SJPQG35VVA","target":"record","payload":{"canonical_record":{"source":{"id":"1208.1650","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-08-08T12:28:09Z","cross_cats_sorted":[],"title_canon_sha256":"76c634e8c5fe00410c6524ba10882d611b71cae12e08719f510e5129bcc44560","abstract_canon_sha256":"81cfaeb3b026cc5c31cd4bc13af10455106d3540d6850e7a34be9a36739cf2b2"},"schema_version":"1.0"},"canonical_sha256":"80e014b359184394b3bc925f036fb5a815b718c9b82f43d4dbaa09f63729af26","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:48:26.628294Z","signature_b64":"w6VcOTAn9RfyRnrtGF2E/XsPNrjHpW6SvYV1QCMEx1apqhWtlu502aJ4Y626nSrXpVs86AAgkGxrhFOjPX4cBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"80e014b359184394b3bc925f036fb5a815b718c9b82f43d4dbaa09f63729af26","last_reissued_at":"2026-05-18T03:48:26.627566Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:48:26.627566Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1208.1650","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:48:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QseOpPBsHiw0GOeLC47qCGsk94CgxSh9mkjA1vIi301LFIUC2h/qlwbXCIjIc45AoRyfgFrFllnzLqxNrGZkDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T14:56:02.803655Z"},"content_sha256":"cae274bce948e7602c7304a9dc326886ecf8eeaeca0b5b4a2b9784047c1dec5a","schema_version":"1.0","event_id":"sha256:cae274bce948e7602c7304a9dc326886ecf8eeaeca0b5b4a2b9784047c1dec5a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:QDQBJM2ZDBBZJM54SJPQG35VVA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A classification of minimal sets for surface homeomorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Alejandro Passeggi, Juliana Xavier","submitted_at":"2012-08-08T12:28:09Z","abstract_excerpt":"We classify minimal sets of (closed and oriented) hyperbolic surface homeomorphisms by studying the connected components of their complement. This extends the classification given by F. Kwakkel, T.J\\\"ager and A. Passeggi in the torus. The given classification is studied in the non-wandering setting and in light of the Nielsen-Thurston Theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.1650","kind":"arxiv","version":3},"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":"2026-05-18T03:48:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+RJpQfMuMP6biwfHbHmYMhIgPxKjI4zf9BkkvwbgcgaJJIuPinmS5yhVi3+xyJR+4EBm9C7E0CoTmL/aO2uKCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T14:56:02.803994Z"},"content_sha256":"30591421768e12344885459945a427081ba753a6bb5ce36dfd27c02983173b9c","schema_version":"1.0","event_id":"sha256:30591421768e12344885459945a427081ba753a6bb5ce36dfd27c02983173b9c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QDQBJM2ZDBBZJM54SJPQG35VVA/bundle.json","state_url":"https://pith.science/pith/QDQBJM2ZDBBZJM54SJPQG35VVA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QDQBJM2ZDBBZJM54SJPQG35VVA/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":"2026-06-23T14:56:02Z","links":{"resolver":"https://pith.science/pith/QDQBJM2ZDBBZJM54SJPQG35VVA","bundle":"https://pith.science/pith/QDQBJM2ZDBBZJM54SJPQG35VVA/bundle.json","state":"https://pith.science/pith/QDQBJM2ZDBBZJM54SJPQG35VVA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QDQBJM2ZDBBZJM54SJPQG35VVA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:QDQBJM2ZDBBZJM54SJPQG35VVA","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":"81cfaeb3b026cc5c31cd4bc13af10455106d3540d6850e7a34be9a36739cf2b2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-08-08T12:28:09Z","title_canon_sha256":"76c634e8c5fe00410c6524ba10882d611b71cae12e08719f510e5129bcc44560"},"schema_version":"1.0","source":{"id":"1208.1650","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.1650","created_at":"2026-05-18T03:48:26Z"},{"alias_kind":"arxiv_version","alias_value":"1208.1650v3","created_at":"2026-05-18T03:48:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.1650","created_at":"2026-05-18T03:48:26Z"},{"alias_kind":"pith_short_12","alias_value":"QDQBJM2ZDBBZ","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"QDQBJM2ZDBBZJM54","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"QDQBJM2Z","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:30591421768e12344885459945a427081ba753a6bb5ce36dfd27c02983173b9c","target":"graph","created_at":"2026-05-18T03:48:26Z","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 classify minimal sets of (closed and oriented) hyperbolic surface homeomorphisms by studying the connected components of their complement. This extends the classification given by F. Kwakkel, T.J\\\"ager and A. Passeggi in the torus. The given classification is studied in the non-wandering setting and in light of the Nielsen-Thurston Theory.","authors_text":"Alejandro Passeggi, Juliana Xavier","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-08-08T12:28:09Z","title":"A classification of minimal sets for surface homeomorphisms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.1650","kind":"arxiv","version":3},"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:cae274bce948e7602c7304a9dc326886ecf8eeaeca0b5b4a2b9784047c1dec5a","target":"record","created_at":"2026-05-18T03:48:26Z","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":"81cfaeb3b026cc5c31cd4bc13af10455106d3540d6850e7a34be9a36739cf2b2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-08-08T12:28:09Z","title_canon_sha256":"76c634e8c5fe00410c6524ba10882d611b71cae12e08719f510e5129bcc44560"},"schema_version":"1.0","source":{"id":"1208.1650","kind":"arxiv","version":3}},"canonical_sha256":"80e014b359184394b3bc925f036fb5a815b718c9b82f43d4dbaa09f63729af26","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"80e014b359184394b3bc925f036fb5a815b718c9b82f43d4dbaa09f63729af26","first_computed_at":"2026-05-18T03:48:26.627566Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:48:26.627566Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"w6VcOTAn9RfyRnrtGF2E/XsPNrjHpW6SvYV1QCMEx1apqhWtlu502aJ4Y626nSrXpVs86AAgkGxrhFOjPX4cBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:48:26.628294Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.1650","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cae274bce948e7602c7304a9dc326886ecf8eeaeca0b5b4a2b9784047c1dec5a","sha256:30591421768e12344885459945a427081ba753a6bb5ce36dfd27c02983173b9c"],"state_sha256":"a6aa9dbb3daaf80b74f65f687ed111296406c25d2c16ccaf69b2fbebdfbaf953"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jqx1OK+z2sSK54lFbS0J+m7sOnRtCIVL5WkW8N5u0IgdpVJ715EQpb9Qo/mrhNjWIkmL/OSS8Jzn5asI06o1DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T14:56:02.805879Z","bundle_sha256":"63f45e8f15aa1870251f7611ba081e786b6c996c591b88bd5176a2a690f1e0c9"}}