{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:X7G3LQQDNVXJCMDBLEKWSPIKLX","short_pith_number":"pith:X7G3LQQD","canonical_record":{"source":{"id":"1905.04089","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2019-05-10T11:51:54Z","cross_cats_sorted":[],"title_canon_sha256":"2f1328c76fb861fef6ab812b599144d8368bbc9ed89900f9c43d98f784e753f6","abstract_canon_sha256":"e86a82b4667a8bc57e64843939986f817a16afebc48bc38f0b0e4b0d6f8f66e1"},"schema_version":"1.0"},"canonical_sha256":"bfcdb5c2036d6e9130615915693d0a5dcd3842b234441340e2225f17ccb7eabd","source":{"kind":"arxiv","id":"1905.04089","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.04089","created_at":"2026-05-17T23:46:34Z"},{"alias_kind":"arxiv_version","alias_value":"1905.04089v1","created_at":"2026-05-17T23:46:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.04089","created_at":"2026-05-17T23:46:34Z"},{"alias_kind":"pith_short_12","alias_value":"X7G3LQQDNVXJ","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"X7G3LQQDNVXJCMDB","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"X7G3LQQD","created_at":"2026-05-18T12:33:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:X7G3LQQDNVXJCMDBLEKWSPIKLX","target":"record","payload":{"canonical_record":{"source":{"id":"1905.04089","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2019-05-10T11:51:54Z","cross_cats_sorted":[],"title_canon_sha256":"2f1328c76fb861fef6ab812b599144d8368bbc9ed89900f9c43d98f784e753f6","abstract_canon_sha256":"e86a82b4667a8bc57e64843939986f817a16afebc48bc38f0b0e4b0d6f8f66e1"},"schema_version":"1.0"},"canonical_sha256":"bfcdb5c2036d6e9130615915693d0a5dcd3842b234441340e2225f17ccb7eabd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:34.613066Z","signature_b64":"u8lnYL37mSng3xI/51nUEZNOvVlaVn4tkORowpUcOBwvKuPmAsyEgP04TNu7G8jsXHmd5UmxPmH13RCXP79QBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bfcdb5c2036d6e9130615915693d0a5dcd3842b234441340e2225f17ccb7eabd","last_reissued_at":"2026-05-17T23:46:34.612521Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:34.612521Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1905.04089","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":"2026-05-17T23:46:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EurGMfgNW9giVLQceRzJ7zAu0irHunBUhENoWFMR4iFrDdFWrge2XX8oiFRfxs+xbTuUvJFywFstrF/+sLOZDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T04:45:01.659672Z"},"content_sha256":"efcb1a6668c1089198922664aacea6929619adae4f3098ae62e368b9958c2290","schema_version":"1.0","event_id":"sha256:efcb1a6668c1089198922664aacea6929619adae4f3098ae62e368b9958c2290"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:X7G3LQQDNVXJCMDBLEKWSPIKLX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Parity in Knotoids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Louis Kauffman, Neslihan G\\\"ug\\\"umc\\\"u","submitted_at":"2019-05-10T11:51:54Z","abstract_excerpt":"This paper investigates the parity concept in knotoids in $S^2$ and in $\\mathbb{R}^2$ in relation with virtual knots. We show that the virtual closure map is not surjective and give specific examples of virtual knots that are not in the image. We introduce a planar version of the parity bracket polynomial for knotoids in $\\mathbb{R}^2$. By using the Nikonov/Manturov theorem on minimal diagrams of virtual knots we prove a conjecture of Turaev showing that minimal diagrams of knot-type knotoids have zero height."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.04089","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":"2026-05-17T23:46:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0rLy0hvgx7SbqAmRTUOY7sZDrRPl6oTPC0gBnCh7Ck6IoLD4DY/SnirfOnC/7QERQKzVHk36CvUBkE6zmG96Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T04:45:01.660017Z"},"content_sha256":"fad66a908458df43808eebd6ef4c580004310d415fcc677cc613a27c32152821","schema_version":"1.0","event_id":"sha256:fad66a908458df43808eebd6ef4c580004310d415fcc677cc613a27c32152821"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X7G3LQQDNVXJCMDBLEKWSPIKLX/bundle.json","state_url":"https://pith.science/pith/X7G3LQQDNVXJCMDBLEKWSPIKLX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X7G3LQQDNVXJCMDBLEKWSPIKLX/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":"2026-06-03T04:45:01Z","links":{"resolver":"https://pith.science/pith/X7G3LQQDNVXJCMDBLEKWSPIKLX","bundle":"https://pith.science/pith/X7G3LQQDNVXJCMDBLEKWSPIKLX/bundle.json","state":"https://pith.science/pith/X7G3LQQDNVXJCMDBLEKWSPIKLX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X7G3LQQDNVXJCMDBLEKWSPIKLX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:X7G3LQQDNVXJCMDBLEKWSPIKLX","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":"e86a82b4667a8bc57e64843939986f817a16afebc48bc38f0b0e4b0d6f8f66e1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2019-05-10T11:51:54Z","title_canon_sha256":"2f1328c76fb861fef6ab812b599144d8368bbc9ed89900f9c43d98f784e753f6"},"schema_version":"1.0","source":{"id":"1905.04089","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.04089","created_at":"2026-05-17T23:46:34Z"},{"alias_kind":"arxiv_version","alias_value":"1905.04089v1","created_at":"2026-05-17T23:46:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.04089","created_at":"2026-05-17T23:46:34Z"},{"alias_kind":"pith_short_12","alias_value":"X7G3LQQDNVXJ","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"X7G3LQQDNVXJCMDB","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"X7G3LQQD","created_at":"2026-05-18T12:33:33Z"}],"graph_snapshots":[{"event_id":"sha256:fad66a908458df43808eebd6ef4c580004310d415fcc677cc613a27c32152821","target":"graph","created_at":"2026-05-17T23:46:34Z","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":"This paper investigates the parity concept in knotoids in $S^2$ and in $\\mathbb{R}^2$ in relation with virtual knots. We show that the virtual closure map is not surjective and give specific examples of virtual knots that are not in the image. We introduce a planar version of the parity bracket polynomial for knotoids in $\\mathbb{R}^2$. By using the Nikonov/Manturov theorem on minimal diagrams of virtual knots we prove a conjecture of Turaev showing that minimal diagrams of knot-type knotoids have zero height.","authors_text":"Louis Kauffman, Neslihan G\\\"ug\\\"umc\\\"u","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2019-05-10T11:51:54Z","title":"Parity in Knotoids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.04089","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:efcb1a6668c1089198922664aacea6929619adae4f3098ae62e368b9958c2290","target":"record","created_at":"2026-05-17T23:46:34Z","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":"e86a82b4667a8bc57e64843939986f817a16afebc48bc38f0b0e4b0d6f8f66e1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2019-05-10T11:51:54Z","title_canon_sha256":"2f1328c76fb861fef6ab812b599144d8368bbc9ed89900f9c43d98f784e753f6"},"schema_version":"1.0","source":{"id":"1905.04089","kind":"arxiv","version":1}},"canonical_sha256":"bfcdb5c2036d6e9130615915693d0a5dcd3842b234441340e2225f17ccb7eabd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bfcdb5c2036d6e9130615915693d0a5dcd3842b234441340e2225f17ccb7eabd","first_computed_at":"2026-05-17T23:46:34.612521Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:34.612521Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u8lnYL37mSng3xI/51nUEZNOvVlaVn4tkORowpUcOBwvKuPmAsyEgP04TNu7G8jsXHmd5UmxPmH13RCXP79QBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:34.613066Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.04089","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:efcb1a6668c1089198922664aacea6929619adae4f3098ae62e368b9958c2290","sha256:fad66a908458df43808eebd6ef4c580004310d415fcc677cc613a27c32152821"],"state_sha256":"0d410604c73ed2cd3d712da75f98c6cd4d9cb4e0470a02ed6887b20dde57c6e8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G301tqO8wmYc3kOFBXpUaYJg56086n3Sx9OkOOMbj+4WIZ+F5KkX6vj/lO2zjk6WLTsEydYI6GvjCOOBOzgbCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T04:45:01.661990Z","bundle_sha256":"f6d0bf94fbb09fd685145912d2f23bc9f40585dfb749ea72e4df575c1ece9522"}}