{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:7726PBEFCXDYJBFNFC7MMDEI6C","short_pith_number":"pith:7726PBEF","schema_version":"1.0","canonical_sha256":"fff5e7848515c78484ad28bec60c88f081a4e7bb8b6235262fa8fa720b64419f","source":{"kind":"arxiv","id":"1309.0383","version":3},"attestation_state":"computed","paper":{"title":"Hyperbolic metrics, measured foliations and pants decompositions for non-orientable surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Athanase Papadopoulos (IRMA), Robert C. Penner","submitted_at":"2013-09-02T12:40:36Z","abstract_excerpt":"We provide analogues for non-orientable surfaces with or without boundary or punctures of several basic theorems in the setting of the Thurston theory of surfaces which were developed so far only in the case of orientable surfaces. Namely, we provide natural analogues for non-orientable surfaces of the Fenchel-Nielsen theorem on the parametrization of the Teichm\\\"uller space of the surface, the Dehn-Thurston theorem on the parametrization of measured foliations in the surface, and the Hatcher-Thurston theorem, which gives a complete minimal set of moves between pair of pants decompositions of "},"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":"1309.0383","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-09-02T12:40:36Z","cross_cats_sorted":[],"title_canon_sha256":"ba34b34d182347647f597ada2b277fceb5f9ab93aea4f2b0710b4a9af546e9d1","abstract_canon_sha256":"c35c626988f89a9cb3c001a192024f9734b1a44f58455fba85f6d44116a7fa9a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:11:46.087192Z","signature_b64":"IXhNQ4KXeU8j0zvblvSn4stxsJXFKL/+fv92J6BSf6ObFGa358J1qAzqgCo1CJgwiB3ifyK2qG4cEYBjfQBXCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fff5e7848515c78484ad28bec60c88f081a4e7bb8b6235262fa8fa720b64419f","last_reissued_at":"2026-05-18T03:11:46.086487Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:11:46.086487Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hyperbolic metrics, measured foliations and pants decompositions for non-orientable surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Athanase Papadopoulos (IRMA), Robert C. Penner","submitted_at":"2013-09-02T12:40:36Z","abstract_excerpt":"We provide analogues for non-orientable surfaces with or without boundary or punctures of several basic theorems in the setting of the Thurston theory of surfaces which were developed so far only in the case of orientable surfaces. Namely, we provide natural analogues for non-orientable surfaces of the Fenchel-Nielsen theorem on the parametrization of the Teichm\\\"uller space of the surface, the Dehn-Thurston theorem on the parametrization of measured foliations in the surface, and the Hatcher-Thurston theorem, which gives a complete minimal set of moves between pair of pants decompositions of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.0383","kind":"arxiv","version":3},"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":"1309.0383","created_at":"2026-05-18T03:11:46.086605+00:00"},{"alias_kind":"arxiv_version","alias_value":"1309.0383v3","created_at":"2026-05-18T03:11:46.086605+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.0383","created_at":"2026-05-18T03:11:46.086605+00:00"},{"alias_kind":"pith_short_12","alias_value":"7726PBEFCXDY","created_at":"2026-05-18T12:27:36.564083+00:00"},{"alias_kind":"pith_short_16","alias_value":"7726PBEFCXDYJBFN","created_at":"2026-05-18T12:27:36.564083+00:00"},{"alias_kind":"pith_short_8","alias_value":"7726PBEF","created_at":"2026-05-18T12:27:36.564083+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/7726PBEFCXDYJBFNFC7MMDEI6C","json":"https://pith.science/pith/7726PBEFCXDYJBFNFC7MMDEI6C.json","graph_json":"https://pith.science/api/pith-number/7726PBEFCXDYJBFNFC7MMDEI6C/graph.json","events_json":"https://pith.science/api/pith-number/7726PBEFCXDYJBFNFC7MMDEI6C/events.json","paper":"https://pith.science/paper/7726PBEF"},"agent_actions":{"view_html":"https://pith.science/pith/7726PBEFCXDYJBFNFC7MMDEI6C","download_json":"https://pith.science/pith/7726PBEFCXDYJBFNFC7MMDEI6C.json","view_paper":"https://pith.science/paper/7726PBEF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1309.0383&json=true","fetch_graph":"https://pith.science/api/pith-number/7726PBEFCXDYJBFNFC7MMDEI6C/graph.json","fetch_events":"https://pith.science/api/pith-number/7726PBEFCXDYJBFNFC7MMDEI6C/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7726PBEFCXDYJBFNFC7MMDEI6C/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7726PBEFCXDYJBFNFC7MMDEI6C/action/storage_attestation","attest_author":"https://pith.science/pith/7726PBEFCXDYJBFNFC7MMDEI6C/action/author_attestation","sign_citation":"https://pith.science/pith/7726PBEFCXDYJBFNFC7MMDEI6C/action/citation_signature","submit_replication":"https://pith.science/pith/7726PBEFCXDYJBFNFC7MMDEI6C/action/replication_record"}},"created_at":"2026-05-18T03:11:46.086605+00:00","updated_at":"2026-05-18T03:11:46.086605+00:00"}