{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:DXBHW66KDQS3MEM7J342PAO4EB","short_pith_number":"pith:DXBHW66K","schema_version":"1.0","canonical_sha256":"1dc27b7bca1c25b6119f4ef9a781dc207bdeb80973b87bb897e357235dac64e1","source":{"kind":"arxiv","id":"math/0601194","version":3},"attestation_state":"computed","paper":{"title":"Mirzakhani's recursion relations, Virasoro constraints and the KdV hierarchy","license":"","headline":"","cross_cats":["math-ph","math.AG","math.MP"],"primary_cat":"math.QA","authors_text":"Brad Safnuk (UC Davis), Motohico Mulase (UC Davis)","submitted_at":"2006-01-09T21:59:11Z","abstract_excerpt":"We present in this paper a differential version of Mirzakhani's recursion relation for the Weil-Petersson volumes of the moduli spaces of bordered Riemann surfaces. We discover that the differential relation, which is equivalent to the original integral formula of Mirzakhani, is a Virasoro constraint condition on a generating function for these volumes. We also show that the generating function for psi and kappa_1 intersections on the moduli space of stable algebraic curves is a 1-parameter solution to the KdV hierarchy. It recovers the Witten-Kontsevich generating function when the parameter "},"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":"math/0601194","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.QA","submitted_at":"2006-01-09T21:59:11Z","cross_cats_sorted":["math-ph","math.AG","math.MP"],"title_canon_sha256":"7976b2a0654fc2f9a5f294d4bbefa1c68fa4c982d8f15600214eebe7e6569950","abstract_canon_sha256":"3c2a6560403ad6d93bf569616bf4b0a066d1c1d70c5b963b6d96e6f62f26d100"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:52:47.623029Z","signature_b64":"qNuipk9dFfz/FDZDdfOu5DGnAjwfD23h+TCA24OAbQMHhOQjTX+UzO7BCA0O3eaXzC1xt94VYVzZiY7/CkB7BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1dc27b7bca1c25b6119f4ef9a781dc207bdeb80973b87bb897e357235dac64e1","last_reissued_at":"2026-07-04T14:52:47.622409Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:52:47.622409Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Mirzakhani's recursion relations, Virasoro constraints and the KdV hierarchy","license":"","headline":"","cross_cats":["math-ph","math.AG","math.MP"],"primary_cat":"math.QA","authors_text":"Brad Safnuk (UC Davis), Motohico Mulase (UC Davis)","submitted_at":"2006-01-09T21:59:11Z","abstract_excerpt":"We present in this paper a differential version of Mirzakhani's recursion relation for the Weil-Petersson volumes of the moduli spaces of bordered Riemann surfaces. We discover that the differential relation, which is equivalent to the original integral formula of Mirzakhani, is a Virasoro constraint condition on a generating function for these volumes. We also show that the generating function for psi and kappa_1 intersections on the moduli space of stable algebraic curves is a 1-parameter solution to the KdV hierarchy. It recovers the Witten-Kontsevich generating function when the parameter "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0601194","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0601194/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":"math/0601194","created_at":"2026-07-04T14:52:47.622475+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0601194v3","created_at":"2026-07-04T14:52:47.622475+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0601194","created_at":"2026-07-04T14:52:47.622475+00:00"},{"alias_kind":"pith_short_12","alias_value":"DXBHW66KDQS3","created_at":"2026-07-04T14:52:47.622475+00:00"},{"alias_kind":"pith_short_16","alias_value":"DXBHW66KDQS3MEM7","created_at":"2026-07-04T14:52:47.622475+00:00"},{"alias_kind":"pith_short_8","alias_value":"DXBHW66K","created_at":"2026-07-04T14:52:47.622475+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2505.16433","citing_title":"Non-perturbative effects in JT gravity from KdV equations","ref_index":25,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DXBHW66KDQS3MEM7J342PAO4EB","json":"https://pith.science/pith/DXBHW66KDQS3MEM7J342PAO4EB.json","graph_json":"https://pith.science/api/pith-number/DXBHW66KDQS3MEM7J342PAO4EB/graph.json","events_json":"https://pith.science/api/pith-number/DXBHW66KDQS3MEM7J342PAO4EB/events.json","paper":"https://pith.science/paper/DXBHW66K"},"agent_actions":{"view_html":"https://pith.science/pith/DXBHW66KDQS3MEM7J342PAO4EB","download_json":"https://pith.science/pith/DXBHW66KDQS3MEM7J342PAO4EB.json","view_paper":"https://pith.science/paper/DXBHW66K","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0601194&json=true","fetch_graph":"https://pith.science/api/pith-number/DXBHW66KDQS3MEM7J342PAO4EB/graph.json","fetch_events":"https://pith.science/api/pith-number/DXBHW66KDQS3MEM7J342PAO4EB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DXBHW66KDQS3MEM7J342PAO4EB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DXBHW66KDQS3MEM7J342PAO4EB/action/storage_attestation","attest_author":"https://pith.science/pith/DXBHW66KDQS3MEM7J342PAO4EB/action/author_attestation","sign_citation":"https://pith.science/pith/DXBHW66KDQS3MEM7J342PAO4EB/action/citation_signature","submit_replication":"https://pith.science/pith/DXBHW66KDQS3MEM7J342PAO4EB/action/replication_record"}},"created_at":"2026-07-04T14:52:47.622475+00:00","updated_at":"2026-07-04T14:52:47.622475+00:00"}