{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:XS2RZHZLDGSSDGFQ72WFHHFDIP","short_pith_number":"pith:XS2RZHZL","schema_version":"1.0","canonical_sha256":"bcb51c9f2b19a52198b0feac539ca343cabc6e1e0224ab89bd0c3fb477894bd3","source":{"kind":"arxiv","id":"2212.13799","version":6},"attestation_state":"computed","paper":{"title":"Noncrossing partitions of a marked surface","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Nathan Reading","submitted_at":"2022-12-28T12:44:19Z","abstract_excerpt":"We define noncrossing partitions of a marked surface without punctures (interior marked points). We show that the natural partial order on noncrossing partitions is a graded lattice and describe its rank function topologically. Lower intervals in the lattice are isomorphic to products of noncrossing partition lattices of other surfaces. We similarly define noncrossing partitions of a symmetric marked surface with double points and prove some of the analogous results. The combination of symmetry and double points plays a role that one might have expected to be played by punctures."},"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":"2212.13799","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2022-12-28T12:44:19Z","cross_cats_sorted":[],"title_canon_sha256":"7ef0aad4da446f39bfddf4c0f8b7dc0314ccdedc7ad4e4dc31453f5f0a039616","abstract_canon_sha256":"c4c40cd084a68eb42248798e353b661693cc41ca1caff03af52db03dc4d80e84"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-22T01:03:13.280423Z","signature_b64":"5HPlQgteUgQRQ5hIkFDKaHovRkRmalFtuh++2p2/Bs/CvmqS3SnrdNT95bE/qCYUKDMQyU0umXDYpUSaeULQCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bcb51c9f2b19a52198b0feac539ca343cabc6e1e0224ab89bd0c3fb477894bd3","last_reissued_at":"2026-05-22T01:03:13.279491Z","signature_status":"signed_v1","first_computed_at":"2026-05-22T01:03:13.279491Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Noncrossing partitions of a marked surface","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Nathan Reading","submitted_at":"2022-12-28T12:44:19Z","abstract_excerpt":"We define noncrossing partitions of a marked surface without punctures (interior marked points). We show that the natural partial order on noncrossing partitions is a graded lattice and describe its rank function topologically. Lower intervals in the lattice are isomorphic to products of noncrossing partition lattices of other surfaces. We similarly define noncrossing partitions of a symmetric marked surface with double points and prove some of the analogous results. The combination of symmetry and double points plays a role that one might have expected to be played by punctures."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.13799","kind":"arxiv","version":6},"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/2212.13799/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":"2212.13799","created_at":"2026-05-22T01:03:13.279620+00:00"},{"alias_kind":"arxiv_version","alias_value":"2212.13799v6","created_at":"2026-05-22T01:03:13.279620+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.13799","created_at":"2026-05-22T01:03:13.279620+00:00"},{"alias_kind":"pith_short_12","alias_value":"XS2RZHZLDGSS","created_at":"2026-05-22T01:03:13.279620+00:00"},{"alias_kind":"pith_short_16","alias_value":"XS2RZHZLDGSSDGFQ","created_at":"2026-05-22T01:03:13.279620+00:00"},{"alias_kind":"pith_short_8","alias_value":"XS2RZHZL","created_at":"2026-05-22T01:03:13.279620+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":2,"sample":[{"citing_arxiv_id":"2312.17331","citing_title":"Symmetric noncrossing partitions of an annulus with double points","ref_index":12,"is_internal_anchor":true},{"citing_arxiv_id":"2212.14151","citing_title":"Noncrossing partitions of an annulus","ref_index":26,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XS2RZHZLDGSSDGFQ72WFHHFDIP","json":"https://pith.science/pith/XS2RZHZLDGSSDGFQ72WFHHFDIP.json","graph_json":"https://pith.science/api/pith-number/XS2RZHZLDGSSDGFQ72WFHHFDIP/graph.json","events_json":"https://pith.science/api/pith-number/XS2RZHZLDGSSDGFQ72WFHHFDIP/events.json","paper":"https://pith.science/paper/XS2RZHZL"},"agent_actions":{"view_html":"https://pith.science/pith/XS2RZHZLDGSSDGFQ72WFHHFDIP","download_json":"https://pith.science/pith/XS2RZHZLDGSSDGFQ72WFHHFDIP.json","view_paper":"https://pith.science/paper/XS2RZHZL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2212.13799&json=true","fetch_graph":"https://pith.science/api/pith-number/XS2RZHZLDGSSDGFQ72WFHHFDIP/graph.json","fetch_events":"https://pith.science/api/pith-number/XS2RZHZLDGSSDGFQ72WFHHFDIP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XS2RZHZLDGSSDGFQ72WFHHFDIP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XS2RZHZLDGSSDGFQ72WFHHFDIP/action/storage_attestation","attest_author":"https://pith.science/pith/XS2RZHZLDGSSDGFQ72WFHHFDIP/action/author_attestation","sign_citation":"https://pith.science/pith/XS2RZHZLDGSSDGFQ72WFHHFDIP/action/citation_signature","submit_replication":"https://pith.science/pith/XS2RZHZLDGSSDGFQ72WFHHFDIP/action/replication_record"}},"created_at":"2026-05-22T01:03:13.279620+00:00","updated_at":"2026-05-22T01:03:13.279620+00:00"}