{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:VQWBHI6UDKD6WWGLG4PEMA53DW","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":"e22ba40c93a2653ee15c8f69750b5e0856bfc4082123e407e9952fa8cc939674","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-08-31T01:12:16Z","title_canon_sha256":"96d692076035dd941d1540859d32ef9ebb2d1d6c129d69c685d80090a04115c6"},"schema_version":"1.0","source":{"id":"1309.0050","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.0050","created_at":"2026-05-18T00:27:30Z"},{"alias_kind":"arxiv_version","alias_value":"1309.0050v3","created_at":"2026-05-18T00:27:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.0050","created_at":"2026-05-18T00:27:30Z"},{"alias_kind":"pith_short_12","alias_value":"VQWBHI6UDKD6","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"VQWBHI6UDKD6WWGL","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"VQWBHI6U","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:81301c60133c691682fb5f6059a0ebacf525fc85b58a5c2b327786e49f18e766","target":"graph","created_at":"2026-05-18T00:27:30Z","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"},"paper":{"abstract_excerpt":"Motivated by the S-duality conjecture, we study the Donaldson-Thomas invariants of the 2 dimensional Gieseker stable sheaves on a threefold. These sheaves are supported on the fibers of a nonsingular threefold X fibered over a nonsingular curve. In the case where X is a K3 fibration, we express these invariants in terms of the Euler characteristic of the Hilbert scheme of points on the K3 fiber and the Noether-Lefschetz numbers of the fibration. We prove that a certain generating function of these invariants is a vector modular form of weight -3/2 as predicted in S-duality.","authors_text":"Amin Gholampour, Artan Sheshmani","cross_cats":["hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-08-31T01:12:16Z","title":"Donaldson-Thomas Invariants of 2-Dimensional sheaves inside threefolds and modular forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.0050","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":"sha256:8ab38053308589b3da65ba6209b5985c47bfe7cd7cfb53af6e02dda2c9bd2b81","target":"record","created_at":"2026-05-18T00:27:30Z","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":"e22ba40c93a2653ee15c8f69750b5e0856bfc4082123e407e9952fa8cc939674","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-08-31T01:12:16Z","title_canon_sha256":"96d692076035dd941d1540859d32ef9ebb2d1d6c129d69c685d80090a04115c6"},"schema_version":"1.0","source":{"id":"1309.0050","kind":"arxiv","version":3}},"canonical_sha256":"ac2c13a3d41a87eb58cb371e4603bb1dba6f984528fda8fa54bd59fdae45dea9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac2c13a3d41a87eb58cb371e4603bb1dba6f984528fda8fa54bd59fdae45dea9","first_computed_at":"2026-05-18T00:27:30.815571Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:27:30.815571Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lNYrpKm5bsnam5k0re43z9c7knDiaxcK4fzzVwe2HjbSibvLWWLG/5vbnSyFtlDiOLmd2C3/Wv3quwtLtxLYDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:27:30.816362Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.0050","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8ab38053308589b3da65ba6209b5985c47bfe7cd7cfb53af6e02dda2c9bd2b81","sha256:81301c60133c691682fb5f6059a0ebacf525fc85b58a5c2b327786e49f18e766"],"state_sha256":"f72d2e20fc048e34f07e1ed47bbb313364e9d8d991b1c9b7568c11670f90f186"}