{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:DXBHW66KDQS3MEM7J342PAO4EB","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"3c2a6560403ad6d93bf569616bf4b0a066d1c1d70c5b963b6d96e6f62f26d100","cross_cats_sorted":["math-ph","math.AG","math.MP"],"license":"","primary_cat":"math.QA","submitted_at":"2006-01-09T21:59:11Z","title_canon_sha256":"7976b2a0654fc2f9a5f294d4bbefa1c68fa4c982d8f15600214eebe7e6569950"},"schema_version":"1.0","source":{"id":"math/0601194","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0601194","created_at":"2026-07-04T14:52:47Z"},{"alias_kind":"arxiv_version","alias_value":"math/0601194v3","created_at":"2026-07-04T14:52:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0601194","created_at":"2026-07-04T14:52:47Z"},{"alias_kind":"pith_short_12","alias_value":"DXBHW66KDQS3","created_at":"2026-07-04T14:52:47Z"},{"alias_kind":"pith_short_16","alias_value":"DXBHW66KDQS3MEM7","created_at":"2026-07-04T14:52:47Z"},{"alias_kind":"pith_short_8","alias_value":"DXBHW66K","created_at":"2026-07-04T14:52:47Z"}],"graph_snapshots":[{"event_id":"sha256:b64843b13e11b6c704978bdfb9965d7f90ba187ffbccf0d09c11e81af04ffa64","target":"graph","created_at":"2026-07-04T14:52:47Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0601194/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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 ","authors_text":"Brad Safnuk (UC Davis), Motohico Mulase (UC Davis)","cross_cats":["math-ph","math.AG","math.MP"],"headline":"","license":"","primary_cat":"math.QA","submitted_at":"2006-01-09T21:59:11Z","title":"Mirzakhani's recursion relations, Virasoro constraints and the KdV hierarchy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0601194","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:16b91a9a95a8c39ad8dbb6efd329480cdfe7c75512498a17036c13e2981a623e","target":"record","created_at":"2026-07-04T14:52:47Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"3c2a6560403ad6d93bf569616bf4b0a066d1c1d70c5b963b6d96e6f62f26d100","cross_cats_sorted":["math-ph","math.AG","math.MP"],"license":"","primary_cat":"math.QA","submitted_at":"2006-01-09T21:59:11Z","title_canon_sha256":"7976b2a0654fc2f9a5f294d4bbefa1c68fa4c982d8f15600214eebe7e6569950"},"schema_version":"1.0","source":{"id":"math/0601194","kind":"arxiv","version":3}},"canonical_sha256":"1dc27b7bca1c25b6119f4ef9a781dc207bdeb80973b87bb897e357235dac64e1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1dc27b7bca1c25b6119f4ef9a781dc207bdeb80973b87bb897e357235dac64e1","first_computed_at":"2026-07-04T14:52:47.622409Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:52:47.622409Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qNuipk9dFfz/FDZDdfOu5DGnAjwfD23h+TCA24OAbQMHhOQjTX+UzO7BCA0O3eaXzC1xt94VYVzZiY7/CkB7BQ==","signature_status":"signed_v1","signed_at":"2026-07-04T14:52:47.623029Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0601194","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:16b91a9a95a8c39ad8dbb6efd329480cdfe7c75512498a17036c13e2981a623e","sha256:b64843b13e11b6c704978bdfb9965d7f90ba187ffbccf0d09c11e81af04ffa64"],"state_sha256":"b4369c77489f897fdf5d804c49cc14dd21a82da30b0fea074d9cab96bb42cc6a"}