{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:MIQCUEECW3Y45U5RXKJKS3C77R","short_pith_number":"pith:MIQCUEEC","schema_version":"1.0","canonical_sha256":"62202a1082b6f1ced3b1ba92a96c5ffc699252e7896dd60c78c0b79f86ed475d","source":{"kind":"arxiv","id":"1309.4914","version":1},"attestation_state":"computed","paper":{"title":"Cohomology of large semiprojective hyperkaehler varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Fernando Rodriguez Villegas, Tamas Hausel","submitted_at":"2013-09-19T09:50:25Z","abstract_excerpt":"In this paper we survey geometric and arithmetic techniques to study the cohomology of semiprojective hyperkaehler manifolds including toric hyperkaehler varieties, Nakajima quiver varieties and moduli spaces of Higgs bundles on Riemann surfaces. The resulting formulae for their Poincare polynomials are combinatorial and representation theoretical in nature. In particular we will look at their Betti numbers and will establish some results and expectations on their asymptotic shape."},"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":"1309.4914","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-09-19T09:50:25Z","cross_cats_sorted":[],"title_canon_sha256":"3d81a53f951f4d69c6599cfd7dc1c7ca90cd4a53ab990a46da13357274b841a2","abstract_canon_sha256":"7d97265bb25d922893cb33b4ed30bfbe87a3df0b9f1ef95098c63b9bdab7d486"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:56.922353Z","signature_b64":"I29ueQDgsnXYeGEoDssVX4q+P+ETdBMC4wzPGTrlCVJ37UdAXhPZQL+zIANbniOF5aWGLTFqivXBkj25j4PnDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"62202a1082b6f1ced3b1ba92a96c5ffc699252e7896dd60c78c0b79f86ed475d","last_reissued_at":"2026-05-18T03:12:56.921456Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:56.921456Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cohomology of large semiprojective hyperkaehler varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Fernando Rodriguez Villegas, Tamas Hausel","submitted_at":"2013-09-19T09:50:25Z","abstract_excerpt":"In this paper we survey geometric and arithmetic techniques to study the cohomology of semiprojective hyperkaehler manifolds including toric hyperkaehler varieties, Nakajima quiver varieties and moduli spaces of Higgs bundles on Riemann surfaces. The resulting formulae for their Poincare polynomials are combinatorial and representation theoretical in nature. In particular we will look at their Betti numbers and will establish some results and expectations on their asymptotic shape."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.4914","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":""},"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":"1309.4914","created_at":"2026-05-18T03:12:56.921586+00:00"},{"alias_kind":"arxiv_version","alias_value":"1309.4914v1","created_at":"2026-05-18T03:12:56.921586+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.4914","created_at":"2026-05-18T03:12:56.921586+00:00"},{"alias_kind":"pith_short_12","alias_value":"MIQCUEECW3Y4","created_at":"2026-05-18T12:27:52.871228+00:00"},{"alias_kind":"pith_short_16","alias_value":"MIQCUEECW3Y45U5R","created_at":"2026-05-18T12:27:52.871228+00:00"},{"alias_kind":"pith_short_8","alias_value":"MIQCUEEC","created_at":"2026-05-18T12:27:52.871228+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2512.06527","citing_title":"Betti numbers of the moduli space of Higgs bundles over a real curve","ref_index":9,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MIQCUEECW3Y45U5RXKJKS3C77R","json":"https://pith.science/pith/MIQCUEECW3Y45U5RXKJKS3C77R.json","graph_json":"https://pith.science/api/pith-number/MIQCUEECW3Y45U5RXKJKS3C77R/graph.json","events_json":"https://pith.science/api/pith-number/MIQCUEECW3Y45U5RXKJKS3C77R/events.json","paper":"https://pith.science/paper/MIQCUEEC"},"agent_actions":{"view_html":"https://pith.science/pith/MIQCUEECW3Y45U5RXKJKS3C77R","download_json":"https://pith.science/pith/MIQCUEECW3Y45U5RXKJKS3C77R.json","view_paper":"https://pith.science/paper/MIQCUEEC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1309.4914&json=true","fetch_graph":"https://pith.science/api/pith-number/MIQCUEECW3Y45U5RXKJKS3C77R/graph.json","fetch_events":"https://pith.science/api/pith-number/MIQCUEECW3Y45U5RXKJKS3C77R/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MIQCUEECW3Y45U5RXKJKS3C77R/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MIQCUEECW3Y45U5RXKJKS3C77R/action/storage_attestation","attest_author":"https://pith.science/pith/MIQCUEECW3Y45U5RXKJKS3C77R/action/author_attestation","sign_citation":"https://pith.science/pith/MIQCUEECW3Y45U5RXKJKS3C77R/action/citation_signature","submit_replication":"https://pith.science/pith/MIQCUEECW3Y45U5RXKJKS3C77R/action/replication_record"}},"created_at":"2026-05-18T03:12:56.921586+00:00","updated_at":"2026-05-18T03:12:56.921586+00:00"}