{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:INLK5UEIX45N643HX7TYZ7PVGY","short_pith_number":"pith:INLK5UEI","schema_version":"1.0","canonical_sha256":"4356aed088bf3adf7367bfe78cfdf5362076df748be6ca596dadc8c4c8e65258","source":{"kind":"arxiv","id":"1708.03925","version":1},"attestation_state":"computed","paper":{"title":"More intrinsically knotted graphs with 22 edges and the restoring method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Hyoungjun Kim, Seungsang Oh, Thomas Mattman","submitted_at":"2017-08-13T16:19:28Z","abstract_excerpt":"A graph is called intrinsically knotted if every embedding of the graph contains a knotted cycle. Johnson, Kidwell and Michael, and, independently, Mattman showed that intrinsically knotted graphs have at least 21 edges. Recently Lee, Kim, Lee and Oh, and, independently, Barsotti and Mattman, showed that $K_7$ and the 13 graphs obtained from $K_7$ by $\\nabla Y$ moves are the only intrinsically knotted graphs with 21 edges. Also Kim, Lee, Lee, Mattman and Oh showed that there are exactly three triangle-free intrinsically knotted graphs with 22 edges having at least two vertices of degree 5. Fur"},"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":"1708.03925","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-08-13T16:19:28Z","cross_cats_sorted":[],"title_canon_sha256":"db93bd0d6bf4e95abb47f21c13905884acdd8c27487d3a1e03d5cf974417ec53","abstract_canon_sha256":"498b556431f4f5c803e503536ce6ed7f6840631f6f3c3af27d7bd4a123a2f399"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:07.496754Z","signature_b64":"XXNYl4FvM8/pCZNzomLHd+lc/qLERnhgWQEP1zE1cThAjww/BmgHsTn8dcDkbeUFqEedZyh1Uow0an9r7dnxCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4356aed088bf3adf7367bfe78cfdf5362076df748be6ca596dadc8c4c8e65258","last_reissued_at":"2026-05-18T00:38:07.496247Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:07.496247Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"More intrinsically knotted graphs with 22 edges and the restoring method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Hyoungjun Kim, Seungsang Oh, Thomas Mattman","submitted_at":"2017-08-13T16:19:28Z","abstract_excerpt":"A graph is called intrinsically knotted if every embedding of the graph contains a knotted cycle. Johnson, Kidwell and Michael, and, independently, Mattman showed that intrinsically knotted graphs have at least 21 edges. Recently Lee, Kim, Lee and Oh, and, independently, Barsotti and Mattman, showed that $K_7$ and the 13 graphs obtained from $K_7$ by $\\nabla Y$ moves are the only intrinsically knotted graphs with 21 edges. Also Kim, Lee, Lee, Mattman and Oh showed that there are exactly three triangle-free intrinsically knotted graphs with 22 edges having at least two vertices of degree 5. Fur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.03925","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1708.03925","created_at":"2026-05-18T00:38:07.496334+00:00"},{"alias_kind":"arxiv_version","alias_value":"1708.03925v1","created_at":"2026-05-18T00:38:07.496334+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.03925","created_at":"2026-05-18T00:38:07.496334+00:00"},{"alias_kind":"pith_short_12","alias_value":"INLK5UEIX45N","created_at":"2026-05-18T12:31:21.493067+00:00"},{"alias_kind":"pith_short_16","alias_value":"INLK5UEIX45N643H","created_at":"2026-05-18T12:31:21.493067+00:00"},{"alias_kind":"pith_short_8","alias_value":"INLK5UEI","created_at":"2026-05-18T12:31:21.493067+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/INLK5UEIX45N643HX7TYZ7PVGY","json":"https://pith.science/pith/INLK5UEIX45N643HX7TYZ7PVGY.json","graph_json":"https://pith.science/api/pith-number/INLK5UEIX45N643HX7TYZ7PVGY/graph.json","events_json":"https://pith.science/api/pith-number/INLK5UEIX45N643HX7TYZ7PVGY/events.json","paper":"https://pith.science/paper/INLK5UEI"},"agent_actions":{"view_html":"https://pith.science/pith/INLK5UEIX45N643HX7TYZ7PVGY","download_json":"https://pith.science/pith/INLK5UEIX45N643HX7TYZ7PVGY.json","view_paper":"https://pith.science/paper/INLK5UEI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1708.03925&json=true","fetch_graph":"https://pith.science/api/pith-number/INLK5UEIX45N643HX7TYZ7PVGY/graph.json","fetch_events":"https://pith.science/api/pith-number/INLK5UEIX45N643HX7TYZ7PVGY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/INLK5UEIX45N643HX7TYZ7PVGY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/INLK5UEIX45N643HX7TYZ7PVGY/action/storage_attestation","attest_author":"https://pith.science/pith/INLK5UEIX45N643HX7TYZ7PVGY/action/author_attestation","sign_citation":"https://pith.science/pith/INLK5UEIX45N643HX7TYZ7PVGY/action/citation_signature","submit_replication":"https://pith.science/pith/INLK5UEIX45N643HX7TYZ7PVGY/action/replication_record"}},"created_at":"2026-05-18T00:38:07.496334+00:00","updated_at":"2026-05-18T00:38:07.496334+00:00"}