{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:F7HYL22RF64XAPJHMASVMLDDVM","short_pith_number":"pith:F7HYL22R","canonical_record":{"source":{"id":"1608.08788","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-08-31T09:42:50Z","cross_cats_sorted":[],"title_canon_sha256":"80edd815a017a54e1dfe83f19c9807109539810b67276887f071801c2a0c93c9","abstract_canon_sha256":"96fa61e32d02abd3c44d82388fdac4467cd66a5631103e80f6ceac947eb8311f"},"schema_version":"1.0"},"canonical_sha256":"2fcf85eb512fb9703d276025562c63ab1f6b4213c2fa49388fac0e0505502ac1","source":{"kind":"arxiv","id":"1608.08788","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.08788","created_at":"2026-05-18T00:52:44Z"},{"alias_kind":"arxiv_version","alias_value":"1608.08788v2","created_at":"2026-05-18T00:52:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.08788","created_at":"2026-05-18T00:52:44Z"},{"alias_kind":"pith_short_12","alias_value":"F7HYL22RF64X","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"F7HYL22RF64XAPJH","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"F7HYL22R","created_at":"2026-05-18T12:30:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:F7HYL22RF64XAPJHMASVMLDDVM","target":"record","payload":{"canonical_record":{"source":{"id":"1608.08788","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-08-31T09:42:50Z","cross_cats_sorted":[],"title_canon_sha256":"80edd815a017a54e1dfe83f19c9807109539810b67276887f071801c2a0c93c9","abstract_canon_sha256":"96fa61e32d02abd3c44d82388fdac4467cd66a5631103e80f6ceac947eb8311f"},"schema_version":"1.0"},"canonical_sha256":"2fcf85eb512fb9703d276025562c63ab1f6b4213c2fa49388fac0e0505502ac1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:44.116921Z","signature_b64":"R9V5pE9zq028TtkH941XOerjA4KVVzEfikli5OYCvFUN1yZw0u2v36NddvcxG05n/FO3/Obor3vOnFJci9LpCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2fcf85eb512fb9703d276025562c63ab1f6b4213c2fa49388fac0e0505502ac1","last_reissued_at":"2026-05-18T00:52:44.116357Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:44.116357Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.08788","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":"2026-05-18T00:52:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PSWINo9ErTd1JMzJ1IToIgZn/F6N0kn3+QtTI8pTAAFYlCeD4IGt9HEvGbYG47VSLSi5P6I5yqzE3kJj2xn9CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T13:11:10.751250Z"},"content_sha256":"e5b8c0d748f6d9027b22e5e4714799a497298e2314dd316181826b5607d08313","schema_version":"1.0","event_id":"sha256:e5b8c0d748f6d9027b22e5e4714799a497298e2314dd316181826b5607d08313"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:F7HYL22RF64XAPJHMASVMLDDVM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Existence of minimal flows on nonorientable surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"D. Peralta-Salas, G. Soler L\\'opez, J.G. Esp\\'in Buend\\'ia","submitted_at":"2016-08-31T09:42:50Z","abstract_excerpt":"Surfaces admitting flows all whose orbits are dense are called minimal. Minimal orientable surfaces were characterized by J.C. Beni\\`{e}re in 1998, leaving open the nonorientable case. This paper fills this gap providing a characterization of minimal nonorientable surfaces of finite genus. We also construct an example of a minimal nonorientable surface with infinite genus and conjecture that any nonorientable surface without combinatorial boundary is minimal."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.08788","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":"2026-05-18T00:52:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SKhRmMSW5W4vVz3Pw72LLfP3kmtMTifPGfYOWKrb1FkujCpWeuNXChgkp0AuG0cUo+lUyw5KWuHQjyB+jDj7Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T13:11:10.752121Z"},"content_sha256":"93dd5b583eea5376181231b4a5e2b7f88ed938f81aa1f725ef46c3767429006f","schema_version":"1.0","event_id":"sha256:93dd5b583eea5376181231b4a5e2b7f88ed938f81aa1f725ef46c3767429006f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F7HYL22RF64XAPJHMASVMLDDVM/bundle.json","state_url":"https://pith.science/pith/F7HYL22RF64XAPJHMASVMLDDVM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F7HYL22RF64XAPJHMASVMLDDVM/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":"2026-06-06T13:11:10Z","links":{"resolver":"https://pith.science/pith/F7HYL22RF64XAPJHMASVMLDDVM","bundle":"https://pith.science/pith/F7HYL22RF64XAPJHMASVMLDDVM/bundle.json","state":"https://pith.science/pith/F7HYL22RF64XAPJHMASVMLDDVM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F7HYL22RF64XAPJHMASVMLDDVM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:F7HYL22RF64XAPJHMASVMLDDVM","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":"96fa61e32d02abd3c44d82388fdac4467cd66a5631103e80f6ceac947eb8311f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-08-31T09:42:50Z","title_canon_sha256":"80edd815a017a54e1dfe83f19c9807109539810b67276887f071801c2a0c93c9"},"schema_version":"1.0","source":{"id":"1608.08788","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.08788","created_at":"2026-05-18T00:52:44Z"},{"alias_kind":"arxiv_version","alias_value":"1608.08788v2","created_at":"2026-05-18T00:52:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.08788","created_at":"2026-05-18T00:52:44Z"},{"alias_kind":"pith_short_12","alias_value":"F7HYL22RF64X","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"F7HYL22RF64XAPJH","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"F7HYL22R","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:93dd5b583eea5376181231b4a5e2b7f88ed938f81aa1f725ef46c3767429006f","target":"graph","created_at":"2026-05-18T00:52:44Z","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":"Surfaces admitting flows all whose orbits are dense are called minimal. Minimal orientable surfaces were characterized by J.C. Beni\\`{e}re in 1998, leaving open the nonorientable case. This paper fills this gap providing a characterization of minimal nonorientable surfaces of finite genus. We also construct an example of a minimal nonorientable surface with infinite genus and conjecture that any nonorientable surface without combinatorial boundary is minimal.","authors_text":"D. Peralta-Salas, G. Soler L\\'opez, J.G. Esp\\'in Buend\\'ia","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-08-31T09:42:50Z","title":"Existence of minimal flows on nonorientable surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.08788","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:e5b8c0d748f6d9027b22e5e4714799a497298e2314dd316181826b5607d08313","target":"record","created_at":"2026-05-18T00:52:44Z","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":"96fa61e32d02abd3c44d82388fdac4467cd66a5631103e80f6ceac947eb8311f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-08-31T09:42:50Z","title_canon_sha256":"80edd815a017a54e1dfe83f19c9807109539810b67276887f071801c2a0c93c9"},"schema_version":"1.0","source":{"id":"1608.08788","kind":"arxiv","version":2}},"canonical_sha256":"2fcf85eb512fb9703d276025562c63ab1f6b4213c2fa49388fac0e0505502ac1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2fcf85eb512fb9703d276025562c63ab1f6b4213c2fa49388fac0e0505502ac1","first_computed_at":"2026-05-18T00:52:44.116357Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:44.116357Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"R9V5pE9zq028TtkH941XOerjA4KVVzEfikli5OYCvFUN1yZw0u2v36NddvcxG05n/FO3/Obor3vOnFJci9LpCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:44.116921Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.08788","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e5b8c0d748f6d9027b22e5e4714799a497298e2314dd316181826b5607d08313","sha256:93dd5b583eea5376181231b4a5e2b7f88ed938f81aa1f725ef46c3767429006f"],"state_sha256":"48d423b2cb4737b1e47154cea4e89a6a27e34db7933ae89f28015a8563080e95"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jtHn6JzVeWooFuH5OL5pcbxd3Lp++HWKEoCAx11CUF0DZOVTO0dm1pOgjVAPjXJN+I1hM8mdc/zbX42lzuQSDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T13:11:10.755142Z","bundle_sha256":"f97c3d43179494ea88c7e196fb7b7993f2017013f3970dba460da0d4a9c60929"}}