{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1998:32P4M6P4J3RHHRXLHF7XFQYEOS","short_pith_number":"pith:32P4M6P4","schema_version":"1.0","canonical_sha256":"de9fc679fc4ee273c6eb397f72c304749a6eb9cb2a0dfde40b39de52f77987b3","source":{"kind":"arxiv","id":"math/9806111","version":4},"attestation_state":"computed","paper":{"title":"A holomorphic Casson invariant for Calabi-Yau 3-folds, and bundles on K3 fibrations","license":"","headline":"","cross_cats":["hep-th"],"primary_cat":"math.AG","authors_text":"R. P. Thomas","submitted_at":"1998-06-19T22:44:37Z","abstract_excerpt":"We briefly review the formal picture in which a Calabi-Yau $n$-fold is the complex analogue of an oriented real $n$-manifold, and a Fano with a fixed smooth anticanonical divisor is the analogue of a manifold with boundary, motivating a holomorphic Casson invariant counting bundles on a Calabi-Yau 3-fold. We develop the deformation theory necessary to obtain the virtual moduli cycles of \\cite{LT}, \\cite{BF} in moduli spaces of stable sheaves whose higher obstruction groups vanish. This gives, for instance, virtual moduli cycles in Hilbert schemes of curves in $\\Pee^3$, and Donaldson-- and Grom"},"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/9806111","kind":"arxiv","version":4},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"1998-06-19T22:44:37Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"142b3b616ef2fc577cc5c9de62363961fa29ced26d48e9c86065a770b55b3469","abstract_canon_sha256":"9c51ac57a2cb1e6255c608afa7f4efed3467cc8e4f74d28e73cd2f0f93be47a4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:40:42.057648Z","signature_b64":"KseywGScsX4QkQ+ZGtFgP+lSxREs3CrF1ZZtUf7dBIwUz/44ufwrqXuIUJ9MoxU6ku14j4JeNSllTvu4y9G7CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"de9fc679fc4ee273c6eb397f72c304749a6eb9cb2a0dfde40b39de52f77987b3","last_reissued_at":"2026-07-04T14:40:42.057238Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:40:42.057238Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A holomorphic Casson invariant for Calabi-Yau 3-folds, and bundles on K3 fibrations","license":"","headline":"","cross_cats":["hep-th"],"primary_cat":"math.AG","authors_text":"R. P. Thomas","submitted_at":"1998-06-19T22:44:37Z","abstract_excerpt":"We briefly review the formal picture in which a Calabi-Yau $n$-fold is the complex analogue of an oriented real $n$-manifold, and a Fano with a fixed smooth anticanonical divisor is the analogue of a manifold with boundary, motivating a holomorphic Casson invariant counting bundles on a Calabi-Yau 3-fold. We develop the deformation theory necessary to obtain the virtual moduli cycles of \\cite{LT}, \\cite{BF} in moduli spaces of stable sheaves whose higher obstruction groups vanish. This gives, for instance, virtual moduli cycles in Hilbert schemes of curves in $\\Pee^3$, and Donaldson-- and Grom"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9806111","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/math/9806111/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/9806111","created_at":"2026-07-04T14:40:42.057296+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/9806111v4","created_at":"2026-07-04T14:40:42.057296+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9806111","created_at":"2026-07-04T14:40:42.057296+00:00"},{"alias_kind":"pith_short_12","alias_value":"32P4M6P4J3RH","created_at":"2026-07-04T14:40:42.057296+00:00"},{"alias_kind":"pith_short_16","alias_value":"32P4M6P4J3RHHRXL","created_at":"2026-07-04T14:40:42.057296+00:00"},{"alias_kind":"pith_short_8","alias_value":"32P4M6P4","created_at":"2026-07-04T14:40:42.057296+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":4,"internal_anchor_count":4,"sample":[{"citing_arxiv_id":"2606.30172","citing_title":"Virtual K-theoretic invariants of the nested Hilbert scheme on $\\mathbb{C}^2$","ref_index":44,"is_internal_anchor":true},{"citing_arxiv_id":"2605.19552","citing_title":"Large Order Enumerative Geometry, Black Holes and Black Rings","ref_index":9,"is_internal_anchor":true},{"citing_arxiv_id":"2605.19552","citing_title":"Large Order Enumerative Geometry, Black Holes and Black Rings","ref_index":9,"is_internal_anchor":true},{"citing_arxiv_id":"2512.21606","citing_title":"Shell formulas for instantons and gauge origami","ref_index":50,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/32P4M6P4J3RHHRXLHF7XFQYEOS","json":"https://pith.science/pith/32P4M6P4J3RHHRXLHF7XFQYEOS.json","graph_json":"https://pith.science/api/pith-number/32P4M6P4J3RHHRXLHF7XFQYEOS/graph.json","events_json":"https://pith.science/api/pith-number/32P4M6P4J3RHHRXLHF7XFQYEOS/events.json","paper":"https://pith.science/paper/32P4M6P4"},"agent_actions":{"view_html":"https://pith.science/pith/32P4M6P4J3RHHRXLHF7XFQYEOS","download_json":"https://pith.science/pith/32P4M6P4J3RHHRXLHF7XFQYEOS.json","view_paper":"https://pith.science/paper/32P4M6P4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/9806111&json=true","fetch_graph":"https://pith.science/api/pith-number/32P4M6P4J3RHHRXLHF7XFQYEOS/graph.json","fetch_events":"https://pith.science/api/pith-number/32P4M6P4J3RHHRXLHF7XFQYEOS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/32P4M6P4J3RHHRXLHF7XFQYEOS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/32P4M6P4J3RHHRXLHF7XFQYEOS/action/storage_attestation","attest_author":"https://pith.science/pith/32P4M6P4J3RHHRXLHF7XFQYEOS/action/author_attestation","sign_citation":"https://pith.science/pith/32P4M6P4J3RHHRXLHF7XFQYEOS/action/citation_signature","submit_replication":"https://pith.science/pith/32P4M6P4J3RHHRXLHF7XFQYEOS/action/replication_record"}},"created_at":"2026-07-04T14:40:42.057296+00:00","updated_at":"2026-07-04T14:40:42.057296+00:00"}