{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:HCGTMAEJMVBHBRP6V2DE7IXNRW","short_pith_number":"pith:HCGTMAEJ","schema_version":"1.0","canonical_sha256":"388d360089654270c5feae864fa2ed8d890aa24955ab26753cfcd5b530666e34","source":{"kind":"arxiv","id":"1211.4939","version":1},"attestation_state":"computed","paper":{"title":"Genus Ranges of 4-Regular Rigid Vertex Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GT","authors_text":"Dorothy Buck, Egor Dolzhenko, Karin Valencia, Masahico Saito, Natasha Jonoska","submitted_at":"2012-11-21T05:27:21Z","abstract_excerpt":"We introduce a notion of genus range as a set of values of genera over all surfaces into which a graph is embedded cellularly, and we study the genus ranges of a special family of four-regular graphs with rigid vertices that has been used in modeling homologous DNA recombination. We show that the genus ranges are sets of consecutive integers. For any positive integer $n$, there are graphs with $2n $ vertices that have genus range ${m,m+1,...,m'}$ for all $0\\le m<m'\\le n$, and there are graphs with $2n-1$ vertices with genus range ${m,m+1,...,m'}$ for all $0\\le m<m' <n$ or $0<m<m'\\le n$. Furthe"},"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":"1211.4939","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-11-21T05:27:21Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"cf1c7463f7facf8033656ca3996c286764baa7b3a3a7c448b0c1c46198325205","abstract_canon_sha256":"eb30dd2257c5a5c779fc25769222fec61b5d10851bc4a19695860573b42049bf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:40:15.463607Z","signature_b64":"faPOQzrFtfFVWyx9l2d37UMF6+AYiwA4qOJD5mymYxA8sBipWyazHtz7uDwTstD3Hi+L6u/3s+2sCWgTa/PDCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"388d360089654270c5feae864fa2ed8d890aa24955ab26753cfcd5b530666e34","last_reissued_at":"2026-05-18T03:40:15.462969Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:40:15.462969Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Genus Ranges of 4-Regular Rigid Vertex Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GT","authors_text":"Dorothy Buck, Egor Dolzhenko, Karin Valencia, Masahico Saito, Natasha Jonoska","submitted_at":"2012-11-21T05:27:21Z","abstract_excerpt":"We introduce a notion of genus range as a set of values of genera over all surfaces into which a graph is embedded cellularly, and we study the genus ranges of a special family of four-regular graphs with rigid vertices that has been used in modeling homologous DNA recombination. We show that the genus ranges are sets of consecutive integers. For any positive integer $n$, there are graphs with $2n $ vertices that have genus range ${m,m+1,...,m'}$ for all $0\\le m<m'\\le n$, and there are graphs with $2n-1$ vertices with genus range ${m,m+1,...,m'}$ for all $0\\le m<m' <n$ or $0<m<m'\\le n$. Furthe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.4939","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":"1211.4939","created_at":"2026-05-18T03:40:15.463075+00:00"},{"alias_kind":"arxiv_version","alias_value":"1211.4939v1","created_at":"2026-05-18T03:40:15.463075+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.4939","created_at":"2026-05-18T03:40:15.463075+00:00"},{"alias_kind":"pith_short_12","alias_value":"HCGTMAEJMVBH","created_at":"2026-05-18T12:27:09.501522+00:00"},{"alias_kind":"pith_short_16","alias_value":"HCGTMAEJMVBHBRP6","created_at":"2026-05-18T12:27:09.501522+00:00"},{"alias_kind":"pith_short_8","alias_value":"HCGTMAEJ","created_at":"2026-05-18T12:27:09.501522+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/HCGTMAEJMVBHBRP6V2DE7IXNRW","json":"https://pith.science/pith/HCGTMAEJMVBHBRP6V2DE7IXNRW.json","graph_json":"https://pith.science/api/pith-number/HCGTMAEJMVBHBRP6V2DE7IXNRW/graph.json","events_json":"https://pith.science/api/pith-number/HCGTMAEJMVBHBRP6V2DE7IXNRW/events.json","paper":"https://pith.science/paper/HCGTMAEJ"},"agent_actions":{"view_html":"https://pith.science/pith/HCGTMAEJMVBHBRP6V2DE7IXNRW","download_json":"https://pith.science/pith/HCGTMAEJMVBHBRP6V2DE7IXNRW.json","view_paper":"https://pith.science/paper/HCGTMAEJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1211.4939&json=true","fetch_graph":"https://pith.science/api/pith-number/HCGTMAEJMVBHBRP6V2DE7IXNRW/graph.json","fetch_events":"https://pith.science/api/pith-number/HCGTMAEJMVBHBRP6V2DE7IXNRW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HCGTMAEJMVBHBRP6V2DE7IXNRW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HCGTMAEJMVBHBRP6V2DE7IXNRW/action/storage_attestation","attest_author":"https://pith.science/pith/HCGTMAEJMVBHBRP6V2DE7IXNRW/action/author_attestation","sign_citation":"https://pith.science/pith/HCGTMAEJMVBHBRP6V2DE7IXNRW/action/citation_signature","submit_replication":"https://pith.science/pith/HCGTMAEJMVBHBRP6V2DE7IXNRW/action/replication_record"}},"created_at":"2026-05-18T03:40:15.463075+00:00","updated_at":"2026-05-18T03:40:15.463075+00:00"}