{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:2U4EVL4WXIGEZRJYUNDD5QSETB","short_pith_number":"pith:2U4EVL4W","schema_version":"1.0","canonical_sha256":"d5384aaf96ba0c4cc538a3463ec24498436dcd64118ccbf39c96bbe014ec593c","source":{"kind":"arxiv","id":"1712.03662","version":4},"attestation_state":"computed","paper":{"title":"A new cohomology class on the moduli space of curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AG","authors_text":"Paul Norbury","submitted_at":"2017-12-11T07:25:57Z","abstract_excerpt":"We define a collection $\\Theta_{g,n}\\in H^{4g-4+2n}(\\overline{\\cal M}_{g,n},\\mathbb{Q})$ for $2g-2+n>0$ of cohomology classes that restrict naturally to boundary divisors. We prove that the intersection numbers $\\int_{\\overline{\\cal M}_{g,n}}\\Theta_{g,n}\\prod_{i=1}^n\\psi_i^{m_i}$ can be recursively calculated. We conjecture that a generating function for these intersection numbers is a tau function of the KdV hierarchy. This is analogous to the conjecture of Witten proven by Kontsevich that a generating function for the intersection numbers $\\int_{\\overline{\\cal M}_{g,n}}\\prod_{i=1}^n\\psi_i^{m"},"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":"1712.03662","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-12-11T07:25:57Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"4831a43cf1c41548081eed30f182fdb173260171f2f03c1ec524ebb345ed078e","abstract_canon_sha256":"1b35f53b9127d7af25be6d65875fbf8f9efeb9f5c75cd503cb08c87944cea9ab"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:54:10.071434Z","signature_b64":"tj5peleHtPaklt4d9N+6Y920wf8OCVooW2+Yiov+60s6774srIjRIFUsQZb+XPdZREA5WzJtWNfOn6RXvgR5CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d5384aaf96ba0c4cc538a3463ec24498436dcd64118ccbf39c96bbe014ec593c","last_reissued_at":"2026-07-05T06:54:10.070974Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:54:10.070974Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A new cohomology class on the moduli space of curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AG","authors_text":"Paul Norbury","submitted_at":"2017-12-11T07:25:57Z","abstract_excerpt":"We define a collection $\\Theta_{g,n}\\in H^{4g-4+2n}(\\overline{\\cal M}_{g,n},\\mathbb{Q})$ for $2g-2+n>0$ of cohomology classes that restrict naturally to boundary divisors. We prove that the intersection numbers $\\int_{\\overline{\\cal M}_{g,n}}\\Theta_{g,n}\\prod_{i=1}^n\\psi_i^{m_i}$ can be recursively calculated. We conjecture that a generating function for these intersection numbers is a tau function of the KdV hierarchy. This is analogous to the conjecture of Witten proven by Kontsevich that a generating function for the intersection numbers $\\int_{\\overline{\\cal M}_{g,n}}\\prod_{i=1}^n\\psi_i^{m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.03662","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1712.03662/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1712.03662","created_at":"2026-07-05T06:54:10.071031+00:00"},{"alias_kind":"arxiv_version","alias_value":"1712.03662v4","created_at":"2026-07-05T06:54:10.071031+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.03662","created_at":"2026-07-05T06:54:10.071031+00:00"},{"alias_kind":"pith_short_12","alias_value":"2U4EVL4WXIGE","created_at":"2026-07-05T06:54:10.071031+00:00"},{"alias_kind":"pith_short_16","alias_value":"2U4EVL4WXIGEZRJY","created_at":"2026-07-05T06:54:10.071031+00:00"},{"alias_kind":"pith_short_8","alias_value":"2U4EVL4W","created_at":"2026-07-05T06:54:10.071031+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":3,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.20796","citing_title":"$N=1$ Supersymmetry, Weil-Petersson Volume Recursion, and a Spectral Curve","ref_index":10,"is_internal_anchor":false},{"citing_arxiv_id":"2604.26038","citing_title":"The Super Virasoro Minimal String from 3d Supergravity","ref_index":36,"is_internal_anchor":false},{"citing_arxiv_id":"2604.11902","citing_title":"Universal formulae for correlators of a broad class of models","ref_index":65,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2U4EVL4WXIGEZRJYUNDD5QSETB","json":"https://pith.science/pith/2U4EVL4WXIGEZRJYUNDD5QSETB.json","graph_json":"https://pith.science/api/pith-number/2U4EVL4WXIGEZRJYUNDD5QSETB/graph.json","events_json":"https://pith.science/api/pith-number/2U4EVL4WXIGEZRJYUNDD5QSETB/events.json","paper":"https://pith.science/paper/2U4EVL4W"},"agent_actions":{"view_html":"https://pith.science/pith/2U4EVL4WXIGEZRJYUNDD5QSETB","download_json":"https://pith.science/pith/2U4EVL4WXIGEZRJYUNDD5QSETB.json","view_paper":"https://pith.science/paper/2U4EVL4W","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1712.03662&json=true","fetch_graph":"https://pith.science/api/pith-number/2U4EVL4WXIGEZRJYUNDD5QSETB/graph.json","fetch_events":"https://pith.science/api/pith-number/2U4EVL4WXIGEZRJYUNDD5QSETB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2U4EVL4WXIGEZRJYUNDD5QSETB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2U4EVL4WXIGEZRJYUNDD5QSETB/action/storage_attestation","attest_author":"https://pith.science/pith/2U4EVL4WXIGEZRJYUNDD5QSETB/action/author_attestation","sign_citation":"https://pith.science/pith/2U4EVL4WXIGEZRJYUNDD5QSETB/action/citation_signature","submit_replication":"https://pith.science/pith/2U4EVL4WXIGEZRJYUNDD5QSETB/action/replication_record"}},"created_at":"2026-07-05T06:54:10.071031+00:00","updated_at":"2026-07-05T06:54:10.071031+00:00"}