{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:36F25KEAIB3QXMBZLQBEY7U3SI","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":"eca245d980a1a595facbbe4747db8868ae7d1d9bce8e319aeaf4354f53001e65","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-05-23T15:05:58Z","title_canon_sha256":"d143916f966a0013eb06a7404bcf7929db41bc647aef09f0bdc3f93a1bbef58a"},"schema_version":"1.0","source":{"id":"1806.02270","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.02270","created_at":"2026-05-17T23:40:14Z"},{"alias_kind":"arxiv_version","alias_value":"1806.02270v1","created_at":"2026-05-17T23:40:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.02270","created_at":"2026-05-17T23:40:14Z"},{"alias_kind":"pith_short_12","alias_value":"36F25KEAIB3Q","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"36F25KEAIB3QXMBZ","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"36F25KEA","created_at":"2026-05-18T12:32:02Z"}],"graph_snapshots":[{"event_id":"sha256:7d8b3f7c07fb2ea366a7e70e91fd6a90bebdd90df89b39babfbfe4fd8efae2fd","target":"graph","created_at":"2026-05-17T23:40:14Z","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 determine the precise bifurcation diagrams of the apparent contours of generic crosscaps, which contain the information of bifurcations with respect to the images of the singular sets of crosscaps: crosscap points and double point curves. Especially, three different kinds of equivalences play key roles.","authors_text":"Mart\\'in Barajas Sichac\\'a, Yutaro Kabata","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-05-23T15:05:58Z","title":"Projection of crosscap"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.02270","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:b85f7c880c1bf21698e31229cd235d1b3381ca291b0417b02a75df4653a98a99","target":"record","created_at":"2026-05-17T23:40:14Z","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":"eca245d980a1a595facbbe4747db8868ae7d1d9bce8e319aeaf4354f53001e65","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-05-23T15:05:58Z","title_canon_sha256":"d143916f966a0013eb06a7404bcf7929db41bc647aef09f0bdc3f93a1bbef58a"},"schema_version":"1.0","source":{"id":"1806.02270","kind":"arxiv","version":1}},"canonical_sha256":"df8baea88040770bb0395c024c7e9b92280bd6bc7c0bf63f69e417c009a07ad2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"df8baea88040770bb0395c024c7e9b92280bd6bc7c0bf63f69e417c009a07ad2","first_computed_at":"2026-05-17T23:40:14.154750Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:14.154750Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u03yf99cLP41ByIUNuA0BcEQfeNqhWBf6PjucA7UnII/mqmIqQXvdU4tg2nDhRCNPzqeBnCppIET81YFGAVNBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:14.155527Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.02270","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b85f7c880c1bf21698e31229cd235d1b3381ca291b0417b02a75df4653a98a99","sha256:7d8b3f7c07fb2ea366a7e70e91fd6a90bebdd90df89b39babfbfe4fd8efae2fd"],"state_sha256":"f003d140494695dfa7e395442ced6f9cd2741b7a61908f339feb8fef44262f55"}