{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:UEGRNC7RQ64LPCSV4HD25GQLR4","short_pith_number":"pith:UEGRNC7R","schema_version":"1.0","canonical_sha256":"a10d168bf187b8b78a55e1c7ae9a0b8f2f32de98f60b02b63e9617b3928cd62f","source":{"kind":"arxiv","id":"1908.05382","version":1},"attestation_state":"computed","paper":{"title":"Gordian complexes of knots and virtual knots given by region crossing changes and arc shift moves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Amrendra Gill, Andrei Vesnin, Madeti Prabhakar","submitted_at":"2019-08-15T00:50:03Z","abstract_excerpt":"Gordian complex of knots was defined by Hirasawa and Uchida as the simplicial complex whose vertices are knot isotopy classes in $\\mathbb{S}^3$. Later Horiuchi and Ohyama defined Gordian complex of virtual knots using $v$-move and forbidden moves. In this paper we discuss Gordian complex of knots by region crossing change and Gordian complex of virtual knots by arc shift move. Arc shift move is a local move in the virtual knot diagram which results in reversing orientation locally between two consecutive crossings. We show the existence of an arbitrarily high dimensional simplex in both the Go"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1908.05382","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2019-08-15T00:50:03Z","cross_cats_sorted":[],"title_canon_sha256":"d9aac08bf65b5772353028f5a77b8794f7c21d59803501afde6dd077599156d1","abstract_canon_sha256":"0878898905c2f65df073546be2b8aaa00d3cc18d32da6f8756c3058ec4548e62"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:49:35.064952Z","signature_b64":"qLDGjImRLTzOETXCMaAW3E7SJZhwwYOawd3X5L4u1HReoMjzAsx+xInOSPa3qh6w3Dab/bfUczfl5DxJ2aAgDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a10d168bf187b8b78a55e1c7ae9a0b8f2f32de98f60b02b63e9617b3928cd62f","last_reissued_at":"2026-07-05T01:49:35.064388Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:49:35.064388Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Gordian complexes of knots and virtual knots given by region crossing changes and arc shift moves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Amrendra Gill, Andrei Vesnin, Madeti Prabhakar","submitted_at":"2019-08-15T00:50:03Z","abstract_excerpt":"Gordian complex of knots was defined by Hirasawa and Uchida as the simplicial complex whose vertices are knot isotopy classes in $\\mathbb{S}^3$. Later Horiuchi and Ohyama defined Gordian complex of virtual knots using $v$-move and forbidden moves. In this paper we discuss Gordian complex of knots by region crossing change and Gordian complex of virtual knots by arc shift move. Arc shift move is a local move in the virtual knot diagram which results in reversing orientation locally between two consecutive crossings. We show the existence of an arbitrarily high dimensional simplex in both the Go"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.05382","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.05382/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1908.05382","created_at":"2026-07-05T01:49:35.064444+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.05382v1","created_at":"2026-07-05T01:49:35.064444+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.05382","created_at":"2026-07-05T01:49:35.064444+00:00"},{"alias_kind":"pith_short_12","alias_value":"UEGRNC7RQ64L","created_at":"2026-07-05T01:49:35.064444+00:00"},{"alias_kind":"pith_short_16","alias_value":"UEGRNC7RQ64LPCSV","created_at":"2026-07-05T01:49:35.064444+00:00"},{"alias_kind":"pith_short_8","alias_value":"UEGRNC7R","created_at":"2026-07-05T01:49:35.064444+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/UEGRNC7RQ64LPCSV4HD25GQLR4","json":"https://pith.science/pith/UEGRNC7RQ64LPCSV4HD25GQLR4.json","graph_json":"https://pith.science/api/pith-number/UEGRNC7RQ64LPCSV4HD25GQLR4/graph.json","events_json":"https://pith.science/api/pith-number/UEGRNC7RQ64LPCSV4HD25GQLR4/events.json","paper":"https://pith.science/paper/UEGRNC7R"},"agent_actions":{"view_html":"https://pith.science/pith/UEGRNC7RQ64LPCSV4HD25GQLR4","download_json":"https://pith.science/pith/UEGRNC7RQ64LPCSV4HD25GQLR4.json","view_paper":"https://pith.science/paper/UEGRNC7R","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.05382&json=true","fetch_graph":"https://pith.science/api/pith-number/UEGRNC7RQ64LPCSV4HD25GQLR4/graph.json","fetch_events":"https://pith.science/api/pith-number/UEGRNC7RQ64LPCSV4HD25GQLR4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UEGRNC7RQ64LPCSV4HD25GQLR4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UEGRNC7RQ64LPCSV4HD25GQLR4/action/storage_attestation","attest_author":"https://pith.science/pith/UEGRNC7RQ64LPCSV4HD25GQLR4/action/author_attestation","sign_citation":"https://pith.science/pith/UEGRNC7RQ64LPCSV4HD25GQLR4/action/citation_signature","submit_replication":"https://pith.science/pith/UEGRNC7RQ64LPCSV4HD25GQLR4/action/replication_record"}},"created_at":"2026-07-05T01:49:35.064444+00:00","updated_at":"2026-07-05T01:49:35.064444+00:00"}