{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:SJGJCKUQQ6LZN6U4RASESZHH5R","short_pith_number":"pith:SJGJCKUQ","schema_version":"1.0","canonical_sha256":"924c912a90879796fa9c88244964e7ec636b4021b1a7ebfc1adbe6a8de166bb1","source":{"kind":"arxiv","id":"2605.24952","version":1},"attestation_state":"computed","paper":{"title":"Hurwitz numbers of a fixed partition (m, 1^{n-m}) via enumeration of unrooted hypermaps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Yi Song","submitted_at":"2026-05-24T09:05:59Z","abstract_excerpt":"This manuscript studies a special case of the Hurwitz enumeration problem: for branched covers from genus g compact Riemann surface to the Riemann sphere, with three branch points, and require the branching data at one of the branch points to be of the partition (m 1^{n-m}), obtain a formula of Hurwitz number. The Hurwitz enumeration problem can be transformed into enumeration of a class of unrooted hypermaps. We first provide a enumeration formula for rooted hypermaps, thereby obtaining the weighted Hurwitz numbers. Next give the quantitative relationship between the enumeration of unrooted 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":"2605.24952","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-24T09:05:59Z","cross_cats_sorted":[],"title_canon_sha256":"296bd2f223dae23656a4d755f7e50ae232763452c978e21f2ab37017954bc581","abstract_canon_sha256":"c0ad83d8bf3d7d41d500c873706f5be9c6b50219a96fac02b1d6332b182850a2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-26T01:04:07.378661Z","signature_b64":"ONm+ojQjwTuMawuUCZtLHAdqlFier4mdGzpK12sH0Jpl0zR8FIllFE1Sj+WPNnxgqoqTqTVJiTCFuYbQjZulCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"924c912a90879796fa9c88244964e7ec636b4021b1a7ebfc1adbe6a8de166bb1","last_reissued_at":"2026-05-26T01:04:07.378085Z","signature_status":"signed_v1","first_computed_at":"2026-05-26T01:04:07.378085Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hurwitz numbers of a fixed partition (m, 1^{n-m}) via enumeration of unrooted hypermaps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Yi Song","submitted_at":"2026-05-24T09:05:59Z","abstract_excerpt":"This manuscript studies a special case of the Hurwitz enumeration problem: for branched covers from genus g compact Riemann surface to the Riemann sphere, with three branch points, and require the branching data at one of the branch points to be of the partition (m 1^{n-m}), obtain a formula of Hurwitz number. The Hurwitz enumeration problem can be transformed into enumeration of a class of unrooted hypermaps. We first provide a enumeration formula for rooted hypermaps, thereby obtaining the weighted Hurwitz numbers. Next give the quantitative relationship between the enumeration of unrooted h"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.24952","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.24952/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":"2605.24952","created_at":"2026-05-26T01:04:07.378173+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.24952v1","created_at":"2026-05-26T01:04:07.378173+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.24952","created_at":"2026-05-26T01:04:07.378173+00:00"},{"alias_kind":"pith_short_12","alias_value":"SJGJCKUQQ6LZ","created_at":"2026-05-26T01:04:07.378173+00:00"},{"alias_kind":"pith_short_16","alias_value":"SJGJCKUQQ6LZN6U4","created_at":"2026-05-26T01:04:07.378173+00:00"},{"alias_kind":"pith_short_8","alias_value":"SJGJCKUQ","created_at":"2026-05-26T01:04:07.378173+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/SJGJCKUQQ6LZN6U4RASESZHH5R","json":"https://pith.science/pith/SJGJCKUQQ6LZN6U4RASESZHH5R.json","graph_json":"https://pith.science/api/pith-number/SJGJCKUQQ6LZN6U4RASESZHH5R/graph.json","events_json":"https://pith.science/api/pith-number/SJGJCKUQQ6LZN6U4RASESZHH5R/events.json","paper":"https://pith.science/paper/SJGJCKUQ"},"agent_actions":{"view_html":"https://pith.science/pith/SJGJCKUQQ6LZN6U4RASESZHH5R","download_json":"https://pith.science/pith/SJGJCKUQQ6LZN6U4RASESZHH5R.json","view_paper":"https://pith.science/paper/SJGJCKUQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.24952&json=true","fetch_graph":"https://pith.science/api/pith-number/SJGJCKUQQ6LZN6U4RASESZHH5R/graph.json","fetch_events":"https://pith.science/api/pith-number/SJGJCKUQQ6LZN6U4RASESZHH5R/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SJGJCKUQQ6LZN6U4RASESZHH5R/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SJGJCKUQQ6LZN6U4RASESZHH5R/action/storage_attestation","attest_author":"https://pith.science/pith/SJGJCKUQQ6LZN6U4RASESZHH5R/action/author_attestation","sign_citation":"https://pith.science/pith/SJGJCKUQQ6LZN6U4RASESZHH5R/action/citation_signature","submit_replication":"https://pith.science/pith/SJGJCKUQQ6LZN6U4RASESZHH5R/action/replication_record"}},"created_at":"2026-05-26T01:04:07.378173+00:00","updated_at":"2026-05-26T01:04:07.378173+00:00"}