{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:OPYUTJZ3I6POOGEG2YLYLKRAU3","short_pith_number":"pith:OPYUTJZ3","schema_version":"1.0","canonical_sha256":"73f149a73b479ee71886d61785aa20a6db7cc0edaeec75241c26e4ff2ddf8f84","source":{"kind":"arxiv","id":"1010.5857","version":1},"attestation_state":"computed","paper":{"title":"Linear chord diagrams on two intervals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Christian M. Reidys, J{\\o}rgen E. Andersen, Rita R. Wang, Robert C. Penner","submitted_at":"2010-10-28T04:28:34Z","abstract_excerpt":"Consider all possible ways of attaching disjoint chords to two ordered and oriented disjoint intervals so as to produce a connected graph. Taking the intervals to lie in the real axis with the induced orientation and the chords to lie in the upper half plane canonically determines a corresponding fatgraph which has some associated genus $g\\geq 0$, and we consider the natural generating function ${\\bf C}_g^{[2]}(z)=\\sum_{n\\geq 0} {\\bf c}^{[2]}_g(n)z^n$ for the number ${\\bf c}^{[2]}_g(n)$ of distinct such chord diagrams of fixed genus $g\\geq 0$ with a given number $n\\geq 0$ of chords. We prove h"},"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":"1010.5857","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-10-28T04:28:34Z","cross_cats_sorted":[],"title_canon_sha256":"ca1d111d48f29225cc1a61722ec168f8158acf2342b5a251fcc34c4121799e63","abstract_canon_sha256":"549996fbd550217448df03cb6b8293691791272b8755f05ecd8c5a5d4384f69a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:38:15.042129Z","signature_b64":"9WaRDaBDJOEeDDkziAcUmXwq0n0KXjUe2CrQsTYVN6RLdz1kc4dh47ayYH4UudeXZt279NVxxSqxY5Eza9TEAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"73f149a73b479ee71886d61785aa20a6db7cc0edaeec75241c26e4ff2ddf8f84","last_reissued_at":"2026-05-18T04:38:15.041613Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:38:15.041613Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Linear chord diagrams on two intervals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Christian M. Reidys, J{\\o}rgen E. Andersen, Rita R. Wang, Robert C. Penner","submitted_at":"2010-10-28T04:28:34Z","abstract_excerpt":"Consider all possible ways of attaching disjoint chords to two ordered and oriented disjoint intervals so as to produce a connected graph. Taking the intervals to lie in the real axis with the induced orientation and the chords to lie in the upper half plane canonically determines a corresponding fatgraph which has some associated genus $g\\geq 0$, and we consider the natural generating function ${\\bf C}_g^{[2]}(z)=\\sum_{n\\geq 0} {\\bf c}^{[2]}_g(n)z^n$ for the number ${\\bf c}^{[2]}_g(n)$ of distinct such chord diagrams of fixed genus $g\\geq 0$ with a given number $n\\geq 0$ of chords. We prove h"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.5857","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":"1010.5857","created_at":"2026-05-18T04:38:15.041720+00:00"},{"alias_kind":"arxiv_version","alias_value":"1010.5857v1","created_at":"2026-05-18T04:38:15.041720+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.5857","created_at":"2026-05-18T04:38:15.041720+00:00"},{"alias_kind":"pith_short_12","alias_value":"OPYUTJZ3I6PO","created_at":"2026-05-18T12:26:12.377268+00:00"},{"alias_kind":"pith_short_16","alias_value":"OPYUTJZ3I6POOGEG","created_at":"2026-05-18T12:26:12.377268+00:00"},{"alias_kind":"pith_short_8","alias_value":"OPYUTJZ3","created_at":"2026-05-18T12:26:12.377268+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/OPYUTJZ3I6POOGEG2YLYLKRAU3","json":"https://pith.science/pith/OPYUTJZ3I6POOGEG2YLYLKRAU3.json","graph_json":"https://pith.science/api/pith-number/OPYUTJZ3I6POOGEG2YLYLKRAU3/graph.json","events_json":"https://pith.science/api/pith-number/OPYUTJZ3I6POOGEG2YLYLKRAU3/events.json","paper":"https://pith.science/paper/OPYUTJZ3"},"agent_actions":{"view_html":"https://pith.science/pith/OPYUTJZ3I6POOGEG2YLYLKRAU3","download_json":"https://pith.science/pith/OPYUTJZ3I6POOGEG2YLYLKRAU3.json","view_paper":"https://pith.science/paper/OPYUTJZ3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1010.5857&json=true","fetch_graph":"https://pith.science/api/pith-number/OPYUTJZ3I6POOGEG2YLYLKRAU3/graph.json","fetch_events":"https://pith.science/api/pith-number/OPYUTJZ3I6POOGEG2YLYLKRAU3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OPYUTJZ3I6POOGEG2YLYLKRAU3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OPYUTJZ3I6POOGEG2YLYLKRAU3/action/storage_attestation","attest_author":"https://pith.science/pith/OPYUTJZ3I6POOGEG2YLYLKRAU3/action/author_attestation","sign_citation":"https://pith.science/pith/OPYUTJZ3I6POOGEG2YLYLKRAU3/action/citation_signature","submit_replication":"https://pith.science/pith/OPYUTJZ3I6POOGEG2YLYLKRAU3/action/replication_record"}},"created_at":"2026-05-18T04:38:15.041720+00:00","updated_at":"2026-05-18T04:38:15.041720+00:00"}