{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:SBURWW6QV2S267XTALDZUNK2O5","short_pith_number":"pith:SBURWW6Q","schema_version":"1.0","canonical_sha256":"90691b5bd0aea5af7ef302c79a355a7776439562536532806cf7245c39e252af","source":{"kind":"arxiv","id":"1112.1617","version":2},"attestation_state":"computed","paper":{"title":"Simplicial Maps of the Complexes of Curves on Nonorientable Surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Elmas Irmak","submitted_at":"2011-12-07T16:35:10Z","abstract_excerpt":"Let $N$ be a compact, connected, nonorientable surface of genus $g$ with $n$ boundary components. Let $\\lambda$ be a simplicial map of the complex of curves, $\\mathcal{C}(N)$, on $N$ which satisfies the following: $[a]$ and $[b]$ are connected by an edge in $\\mathcal{C}(N)$ if and only if $\\lambda([a])$ and $\\lambda([b])$ are connected by an edge in $\\mathcal{C}(N)$ for every pair of vertices $[a], [b]$ in $\\mathcal{C}(N)$. We prove that $\\lambda$ is induced by a homeomorphism of $N$ if $(g, n) \\in \\{(1, 0), (1, 1), (2, 0)$, $(2, 1), (3, 0)\\}$ or $g + n \\geq 5$. Our result implies that superin"},"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":"1112.1617","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-12-07T16:35:10Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"1a7f931ad385b83c2521edfcab88c5d49a5d89b3889b0532911537fe5fc4def5","abstract_canon_sha256":"808ae8d1c6ab7a9b1ea56841a331532ffe0b6a068b224419deb4ad4be045d9b1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:58:36.712454Z","signature_b64":"6hx2mphpUagKiHqTu4qhSpbO75CPkb8+2p3vLy/16O8i1zO7Jxyqcnay7SsoE1E0/I6hVNEKyjhr6LldN7DSDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"90691b5bd0aea5af7ef302c79a355a7776439562536532806cf7245c39e252af","last_reissued_at":"2026-05-18T03:58:36.711967Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:58:36.711967Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Simplicial Maps of the Complexes of Curves on Nonorientable Surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Elmas Irmak","submitted_at":"2011-12-07T16:35:10Z","abstract_excerpt":"Let $N$ be a compact, connected, nonorientable surface of genus $g$ with $n$ boundary components. Let $\\lambda$ be a simplicial map of the complex of curves, $\\mathcal{C}(N)$, on $N$ which satisfies the following: $[a]$ and $[b]$ are connected by an edge in $\\mathcal{C}(N)$ if and only if $\\lambda([a])$ and $\\lambda([b])$ are connected by an edge in $\\mathcal{C}(N)$ for every pair of vertices $[a], [b]$ in $\\mathcal{C}(N)$. We prove that $\\lambda$ is induced by a homeomorphism of $N$ if $(g, n) \\in \\{(1, 0), (1, 1), (2, 0)$, $(2, 1), (3, 0)\\}$ or $g + n \\geq 5$. Our result implies that superin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.1617","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1112.1617","created_at":"2026-05-18T03:58:36.712026+00:00"},{"alias_kind":"arxiv_version","alias_value":"1112.1617v2","created_at":"2026-05-18T03:58:36.712026+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.1617","created_at":"2026-05-18T03:58:36.712026+00:00"},{"alias_kind":"pith_short_12","alias_value":"SBURWW6QV2S2","created_at":"2026-05-18T12:26:41.206345+00:00"},{"alias_kind":"pith_short_16","alias_value":"SBURWW6QV2S267XT","created_at":"2026-05-18T12:26:41.206345+00:00"},{"alias_kind":"pith_short_8","alias_value":"SBURWW6Q","created_at":"2026-05-18T12:26:41.206345+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/SBURWW6QV2S267XTALDZUNK2O5","json":"https://pith.science/pith/SBURWW6QV2S267XTALDZUNK2O5.json","graph_json":"https://pith.science/api/pith-number/SBURWW6QV2S267XTALDZUNK2O5/graph.json","events_json":"https://pith.science/api/pith-number/SBURWW6QV2S267XTALDZUNK2O5/events.json","paper":"https://pith.science/paper/SBURWW6Q"},"agent_actions":{"view_html":"https://pith.science/pith/SBURWW6QV2S267XTALDZUNK2O5","download_json":"https://pith.science/pith/SBURWW6QV2S267XTALDZUNK2O5.json","view_paper":"https://pith.science/paper/SBURWW6Q","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1112.1617&json=true","fetch_graph":"https://pith.science/api/pith-number/SBURWW6QV2S267XTALDZUNK2O5/graph.json","fetch_events":"https://pith.science/api/pith-number/SBURWW6QV2S267XTALDZUNK2O5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SBURWW6QV2S267XTALDZUNK2O5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SBURWW6QV2S267XTALDZUNK2O5/action/storage_attestation","attest_author":"https://pith.science/pith/SBURWW6QV2S267XTALDZUNK2O5/action/author_attestation","sign_citation":"https://pith.science/pith/SBURWW6QV2S267XTALDZUNK2O5/action/citation_signature","submit_replication":"https://pith.science/pith/SBURWW6QV2S267XTALDZUNK2O5/action/replication_record"}},"created_at":"2026-05-18T03:58:36.712026+00:00","updated_at":"2026-05-18T03:58:36.712026+00:00"}