{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:4C4WPNZW2ZJDP54YBFNJLW5VNZ","short_pith_number":"pith:4C4WPNZW","canonical_record":{"source":{"id":"1608.07855","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2016-08-28T21:22:05Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"1c2471f90ba8880ba6e421188016512cbb8e3badbc55e6d63f5bfd29a74e136f","abstract_canon_sha256":"50ec13e2038fbbb477ed8cfd76de2bb164880d53932ca272f7ca1598626c9620"},"schema_version":"1.0"},"canonical_sha256":"e0b967b736d65237f798095a95dbb56e762d7b0a8aa8804ed5272266cc9fa6e5","source":{"kind":"arxiv","id":"1608.07855","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.07855","created_at":"2026-05-18T01:07:19Z"},{"alias_kind":"arxiv_version","alias_value":"1608.07855v2","created_at":"2026-05-18T01:07:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.07855","created_at":"2026-05-18T01:07:19Z"},{"alias_kind":"pith_short_12","alias_value":"4C4WPNZW2ZJD","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4C4WPNZW2ZJDP54Y","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4C4WPNZW","created_at":"2026-05-18T12:29:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:4C4WPNZW2ZJDP54YBFNJLW5VNZ","target":"record","payload":{"canonical_record":{"source":{"id":"1608.07855","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2016-08-28T21:22:05Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"1c2471f90ba8880ba6e421188016512cbb8e3badbc55e6d63f5bfd29a74e136f","abstract_canon_sha256":"50ec13e2038fbbb477ed8cfd76de2bb164880d53932ca272f7ca1598626c9620"},"schema_version":"1.0"},"canonical_sha256":"e0b967b736d65237f798095a95dbb56e762d7b0a8aa8804ed5272266cc9fa6e5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:07:19.947296Z","signature_b64":"c7tZQgwabSYunCVhgL3EXmfJgijrcwjtTSCB/Fjc60yCp+RrYgd6qjDrzCu3Gze1S8soJcnkjCJaifoUOOe7DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e0b967b736d65237f798095a95dbb56e762d7b0a8aa8804ed5272266cc9fa6e5","last_reissued_at":"2026-05-18T01:07:19.946694Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:07:19.946694Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.07855","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":"2026-05-18T01:07:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7UqAjI3HhDXaAd7Z6oMClUk7yMvpdxeqBnWMz4ENVPXAx6kPy2YEzJnSFt7sHVr8BApn45bUk+Dq1Z5PpgaKCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T17:06:15.312493Z"},"content_sha256":"8a3ac36f2db4923f89e6a249153be1ff5db9422216ae3e08fc6f5a41178dea06","schema_version":"1.0","event_id":"sha256:8a3ac36f2db4923f89e6a249153be1ff5db9422216ae3e08fc6f5a41178dea06"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:4C4WPNZW2ZJDP54YBFNJLW5VNZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Direct Proof of the Strong Hanani-Tutte Theorem on the Projective Plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.CG","authors_text":"\\'Eric Colin de Verdi\\`ere, Martin Tancer, Pavel Pat\\'ak, Vojt\\v{e}ch Kalu\\v{z}a, Zuzana Pat\\'akov\\'a","submitted_at":"2016-08-28T21:22:05Z","abstract_excerpt":"We reprove the strong Hanani-Tutte theorem on the projective plane. In contrast to the previous proof by Pelsmajer, Schaefer and Stasi, our method is constructive and does not rely on the characterization of forbidden minors, which gives hope to extend it to other surfaces. Moreover, our approach can be used to provide an efficient algorithm turning a Hanani-Tutte drawing on the projective plane into an embedding."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.07855","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":"2026-05-18T01:07:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ug62AhkGj5aErXsGpcPBYlj9e8Gv2W50wm2NAJpr2/2wcPzliaBqKHBHXjMiXu/EMhvAflvINaV48QfwO4FEDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T17:06:15.313190Z"},"content_sha256":"ba7c8b9a9162cc9b4ca1d5ae0ec5d79ea16b4203fad6a1c089673fa1c9571176","schema_version":"1.0","event_id":"sha256:ba7c8b9a9162cc9b4ca1d5ae0ec5d79ea16b4203fad6a1c089673fa1c9571176"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4C4WPNZW2ZJDP54YBFNJLW5VNZ/bundle.json","state_url":"https://pith.science/pith/4C4WPNZW2ZJDP54YBFNJLW5VNZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4C4WPNZW2ZJDP54YBFNJLW5VNZ/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":"2026-05-29T17:06:15Z","links":{"resolver":"https://pith.science/pith/4C4WPNZW2ZJDP54YBFNJLW5VNZ","bundle":"https://pith.science/pith/4C4WPNZW2ZJDP54YBFNJLW5VNZ/bundle.json","state":"https://pith.science/pith/4C4WPNZW2ZJDP54YBFNJLW5VNZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4C4WPNZW2ZJDP54YBFNJLW5VNZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:4C4WPNZW2ZJDP54YBFNJLW5VNZ","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":"50ec13e2038fbbb477ed8cfd76de2bb164880d53932ca272f7ca1598626c9620","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2016-08-28T21:22:05Z","title_canon_sha256":"1c2471f90ba8880ba6e421188016512cbb8e3badbc55e6d63f5bfd29a74e136f"},"schema_version":"1.0","source":{"id":"1608.07855","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.07855","created_at":"2026-05-18T01:07:19Z"},{"alias_kind":"arxiv_version","alias_value":"1608.07855v2","created_at":"2026-05-18T01:07:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.07855","created_at":"2026-05-18T01:07:19Z"},{"alias_kind":"pith_short_12","alias_value":"4C4WPNZW2ZJD","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4C4WPNZW2ZJDP54Y","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4C4WPNZW","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:ba7c8b9a9162cc9b4ca1d5ae0ec5d79ea16b4203fad6a1c089673fa1c9571176","target":"graph","created_at":"2026-05-18T01:07:19Z","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 reprove the strong Hanani-Tutte theorem on the projective plane. In contrast to the previous proof by Pelsmajer, Schaefer and Stasi, our method is constructive and does not rely on the characterization of forbidden minors, which gives hope to extend it to other surfaces. Moreover, our approach can be used to provide an efficient algorithm turning a Hanani-Tutte drawing on the projective plane into an embedding.","authors_text":"\\'Eric Colin de Verdi\\`ere, Martin Tancer, Pavel Pat\\'ak, Vojt\\v{e}ch Kalu\\v{z}a, Zuzana Pat\\'akov\\'a","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2016-08-28T21:22:05Z","title":"A Direct Proof of the Strong Hanani-Tutte Theorem on the Projective Plane"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.07855","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":"sha256:8a3ac36f2db4923f89e6a249153be1ff5db9422216ae3e08fc6f5a41178dea06","target":"record","created_at":"2026-05-18T01:07:19Z","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":"50ec13e2038fbbb477ed8cfd76de2bb164880d53932ca272f7ca1598626c9620","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2016-08-28T21:22:05Z","title_canon_sha256":"1c2471f90ba8880ba6e421188016512cbb8e3badbc55e6d63f5bfd29a74e136f"},"schema_version":"1.0","source":{"id":"1608.07855","kind":"arxiv","version":2}},"canonical_sha256":"e0b967b736d65237f798095a95dbb56e762d7b0a8aa8804ed5272266cc9fa6e5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e0b967b736d65237f798095a95dbb56e762d7b0a8aa8804ed5272266cc9fa6e5","first_computed_at":"2026-05-18T01:07:19.946694Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:07:19.946694Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"c7tZQgwabSYunCVhgL3EXmfJgijrcwjtTSCB/Fjc60yCp+RrYgd6qjDrzCu3Gze1S8soJcnkjCJaifoUOOe7DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:07:19.947296Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.07855","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8a3ac36f2db4923f89e6a249153be1ff5db9422216ae3e08fc6f5a41178dea06","sha256:ba7c8b9a9162cc9b4ca1d5ae0ec5d79ea16b4203fad6a1c089673fa1c9571176"],"state_sha256":"dec010d150fce6df15ebb8c10195d3986d920ad2468c61048268cc47f4e80cbe"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Uo46RHrpE1rPX8IdWMx8MBR0XqrZSIrbf7DZ09GWhwJH0/cZ6dNo8d7kcAZi5P6uu8ciy/GLvw2cdEel3O4kDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T17:06:15.316893Z","bundle_sha256":"131f10ae728b77932b6d42fcb85b2e272b56e81541370bf68c4e90547f970713"}}