{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:LT75TISS4RSVR7QKRSWODDFQ2W","short_pith_number":"pith:LT75TISS","schema_version":"1.0","canonical_sha256":"5cffd9a252e46558fe0a8cace18cb0d594ab33ff9e160df9f3e9da55fb8292b1","source":{"kind":"arxiv","id":"0907.5224","version":3},"attestation_state":"computed","paper":{"title":"The Laplace transform of the cut-and-join equation and the Bouchard-Marino conjecture on Hurwitz numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CO","math.MP"],"primary_cat":"math.AG","authors_text":"Bertrand Eynard, Brad Safnuk, Motohico Mulase","submitted_at":"2009-07-29T21:34:17Z","abstract_excerpt":"We calculate the Laplace transform of the cut-and-join equation of Goulden, Jackson and Vakil. The result is a polynomial equation that has the topological structure identical to the Mirzakhani recursion formula for the Weil-Petersson volume of the moduli space of bordered hyperbolic surfaces. We find that the direct image of this Laplace transformed equation via the inverse of the Lambert W-function is the topological recursion formula for Hurwitz numbers conjectured by Bouchard and Marino using topological string theory."},"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":"0907.5224","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-07-29T21:34:17Z","cross_cats_sorted":["math-ph","math.CO","math.MP"],"title_canon_sha256":"2b582d2f0546c6068b405ad003096d5844166b2e0ce9980fb69a35c76fc5feb3","abstract_canon_sha256":"4db139cddcd19c42ffe76cdf575fbcfe2c57decb2c2021c6fd5ab2ab7d99f50f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:44.843278Z","signature_b64":"Jj6WuNlHnRLdhwn/f2f/pBfHQk04jjohnWGXwyrBgebaYLKRZ6QAxAjSutB6bDcNMGLrR7AjvWZ+EsRUsMRwBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5cffd9a252e46558fe0a8cace18cb0d594ab33ff9e160df9f3e9da55fb8292b1","last_reissued_at":"2026-05-18T02:38:44.842605Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:44.842605Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Laplace transform of the cut-and-join equation and the Bouchard-Marino conjecture on Hurwitz numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CO","math.MP"],"primary_cat":"math.AG","authors_text":"Bertrand Eynard, Brad Safnuk, Motohico Mulase","submitted_at":"2009-07-29T21:34:17Z","abstract_excerpt":"We calculate the Laplace transform of the cut-and-join equation of Goulden, Jackson and Vakil. The result is a polynomial equation that has the topological structure identical to the Mirzakhani recursion formula for the Weil-Petersson volume of the moduli space of bordered hyperbolic surfaces. We find that the direct image of this Laplace transformed equation via the inverse of the Lambert W-function is the topological recursion formula for Hurwitz numbers conjectured by Bouchard and Marino using topological string theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.5224","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":"0907.5224","created_at":"2026-05-18T02:38:44.842708+00:00"},{"alias_kind":"arxiv_version","alias_value":"0907.5224v3","created_at":"2026-05-18T02:38:44.842708+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.5224","created_at":"2026-05-18T02:38:44.842708+00:00"},{"alias_kind":"pith_short_12","alias_value":"LT75TISS4RSV","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_16","alias_value":"LT75TISS4RSVR7QK","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_8","alias_value":"LT75TISS","created_at":"2026-05-18T12:26:00.592388+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/LT75TISS4RSVR7QKRSWODDFQ2W","json":"https://pith.science/pith/LT75TISS4RSVR7QKRSWODDFQ2W.json","graph_json":"https://pith.science/api/pith-number/LT75TISS4RSVR7QKRSWODDFQ2W/graph.json","events_json":"https://pith.science/api/pith-number/LT75TISS4RSVR7QKRSWODDFQ2W/events.json","paper":"https://pith.science/paper/LT75TISS"},"agent_actions":{"view_html":"https://pith.science/pith/LT75TISS4RSVR7QKRSWODDFQ2W","download_json":"https://pith.science/pith/LT75TISS4RSVR7QKRSWODDFQ2W.json","view_paper":"https://pith.science/paper/LT75TISS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0907.5224&json=true","fetch_graph":"https://pith.science/api/pith-number/LT75TISS4RSVR7QKRSWODDFQ2W/graph.json","fetch_events":"https://pith.science/api/pith-number/LT75TISS4RSVR7QKRSWODDFQ2W/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LT75TISS4RSVR7QKRSWODDFQ2W/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LT75TISS4RSVR7QKRSWODDFQ2W/action/storage_attestation","attest_author":"https://pith.science/pith/LT75TISS4RSVR7QKRSWODDFQ2W/action/author_attestation","sign_citation":"https://pith.science/pith/LT75TISS4RSVR7QKRSWODDFQ2W/action/citation_signature","submit_replication":"https://pith.science/pith/LT75TISS4RSVR7QKRSWODDFQ2W/action/replication_record"}},"created_at":"2026-05-18T02:38:44.842708+00:00","updated_at":"2026-05-18T02:38:44.842708+00:00"}