{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1998:32P4M6P4J3RHHRXLHF7XFQYEOS","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":"9c51ac57a2cb1e6255c608afa7f4efed3467cc8e4f74d28e73cd2f0f93be47a4","cross_cats_sorted":["hep-th"],"license":"","primary_cat":"math.AG","submitted_at":"1998-06-19T22:44:37Z","title_canon_sha256":"142b3b616ef2fc577cc5c9de62363961fa29ced26d48e9c86065a770b55b3469"},"schema_version":"1.0","source":{"id":"math/9806111","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9806111","created_at":"2026-07-04T14:40:42Z"},{"alias_kind":"arxiv_version","alias_value":"math/9806111v4","created_at":"2026-07-04T14:40:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9806111","created_at":"2026-07-04T14:40:42Z"},{"alias_kind":"pith_short_12","alias_value":"32P4M6P4J3RH","created_at":"2026-07-04T14:40:42Z"},{"alias_kind":"pith_short_16","alias_value":"32P4M6P4J3RHHRXL","created_at":"2026-07-04T14:40:42Z"},{"alias_kind":"pith_short_8","alias_value":"32P4M6P4","created_at":"2026-07-04T14:40:42Z"}],"graph_snapshots":[{"event_id":"sha256:55a828e0041ad82a392cacd3884856ffb1fd7631513a790b4acd304937f38efe","target":"graph","created_at":"2026-07-04T14:40:42Z","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/9806111/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"R. P. Thomas","cross_cats":["hep-th"],"headline":"","license":"","primary_cat":"math.AG","submitted_at":"1998-06-19T22:44:37Z","title":"A holomorphic Casson invariant for Calabi-Yau 3-folds, and bundles on K3 fibrations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9806111","kind":"arxiv","version":4},"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":"sha256:6ff8d754e57d4ab0626b106c72c0b26c92b9c869361b1a194eb638bfc8755728","target":"record","created_at":"2026-07-04T14:40:42Z","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":"9c51ac57a2cb1e6255c608afa7f4efed3467cc8e4f74d28e73cd2f0f93be47a4","cross_cats_sorted":["hep-th"],"license":"","primary_cat":"math.AG","submitted_at":"1998-06-19T22:44:37Z","title_canon_sha256":"142b3b616ef2fc577cc5c9de62363961fa29ced26d48e9c86065a770b55b3469"},"schema_version":"1.0","source":{"id":"math/9806111","kind":"arxiv","version":4}},"canonical_sha256":"de9fc679fc4ee273c6eb397f72c304749a6eb9cb2a0dfde40b39de52f77987b3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"de9fc679fc4ee273c6eb397f72c304749a6eb9cb2a0dfde40b39de52f77987b3","first_computed_at":"2026-07-04T14:40:42.057238Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:40:42.057238Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KseywGScsX4QkQ+ZGtFgP+lSxREs3CrF1ZZtUf7dBIwUz/44ufwrqXuIUJ9MoxU6ku14j4JeNSllTvu4y9G7CQ==","signature_status":"signed_v1","signed_at":"2026-07-04T14:40:42.057648Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9806111","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6ff8d754e57d4ab0626b106c72c0b26c92b9c869361b1a194eb638bfc8755728","sha256:55a828e0041ad82a392cacd3884856ffb1fd7631513a790b4acd304937f38efe"],"state_sha256":"686f36bc35ff4ce0af80ed84e3ce866a4a1d7dfb1b29e24b9f8e21470b8e142a"}