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For a fixed primitive curve class in $S$ of square $2h-2$, their conjecture predicts that the corresponding partition functions are given by meromorphic Jacobi forms of weight $-10$ and index $h-1$. We calculate the partition functions for primitive classes of square -2 and of square 0.\n  Our computation uses reduced Donaldson-Thomas invariants which are defined as the Behrend functi"},"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":"1504.02920","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-04-11T22:28:22Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"d4600e3ed233211b811ba41821bacb5f6f8b626990e4a28526982d4a4ba1350d","abstract_canon_sha256":"d8af4bbc40611e7a285010fcef974030ffa9c107724aa3d9d5e076268eeb6e66"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:30:09.585430Z","signature_b64":"c+VE7dtUGHJ6adiTISuvrSWb/1PKbykdR7cL4MYk5uKTLsuvmbYhvH5TxK9oIyNX2vwDbnfV+/D9mHOM6CXFCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"55b3817485736ab76662c8cbfcba92a0e05105941d601412a3c748edb2e8923d","last_reissued_at":"2026-05-18T00:30:09.584867Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:30:09.584867Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Donaldson-Thomas theory of $K3\\times E$ via the topological vertex","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"math.AG","authors_text":"Jim Bryan","submitted_at":"2015-04-11T22:28:22Z","abstract_excerpt":"Oberdieck and Pandharipande conjectured that the curve counting invariants of $S\\times E$, the product of a $K3$ surface and an elliptic curve, is given by minus the reciprocal of the Igusa cusp form of weight 10. For a fixed primitive curve class in $S$ of square $2h-2$, their conjecture predicts that the corresponding partition functions are given by meromorphic Jacobi forms of weight $-10$ and index $h-1$. We calculate the partition functions for primitive classes of square -2 and of square 0.\n  Our computation uses reduced Donaldson-Thomas invariants which are defined as the Behrend functi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.02920","kind":"arxiv","version":2},"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":"1504.02920","created_at":"2026-05-18T00:30:09.584948+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.02920v2","created_at":"2026-05-18T00:30:09.584948+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.02920","created_at":"2026-05-18T00:30:09.584948+00:00"},{"alias_kind":"pith_short_12","alias_value":"KWZYC5EFONVL","created_at":"2026-05-18T12:29:29.992203+00:00"},{"alias_kind":"pith_short_16","alias_value":"KWZYC5EFONVLOZTC","created_at":"2026-05-18T12:29:29.992203+00:00"},{"alias_kind":"pith_short_8","alias_value":"KWZYC5EF","created_at":"2026-05-18T12:29:29.992203+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KWZYC5EFONVLOZTCZDF7ZOUSUD","json":"https://pith.science/pith/KWZYC5EFONVLOZTCZDF7ZOUSUD.json","graph_json":"https://pith.science/api/pith-number/KWZYC5EFONVLOZTCZDF7ZOUSUD/graph.json","events_json":"https://pith.science/api/pith-number/KWZYC5EFONVLOZTCZDF7ZOUSUD/events.json","paper":"https://pith.science/paper/KWZYC5EF"},"agent_actions":{"view_html":"https://pith.science/pith/KWZYC5EFONVLOZTCZDF7ZOUSUD","download_json":"https://pith.science/pith/KWZYC5EFONVLOZTCZDF7ZOUSUD.json","view_paper":"https://pith.science/paper/KWZYC5EF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.02920&json=true","fetch_graph":"https://pith.science/api/pith-number/KWZYC5EFONVLOZTCZDF7ZOUSUD/graph.json","fetch_events":"https://pith.science/api/pith-number/KWZYC5EFONVLOZTCZDF7ZOUSUD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KWZYC5EFONVLOZTCZDF7ZOUSUD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KWZYC5EFONVLOZTCZDF7ZOUSUD/action/storage_attestation","attest_author":"https://pith.science/pith/KWZYC5EFONVLOZTCZDF7ZOUSUD/action/author_attestation","sign_citation":"https://pith.science/pith/KWZYC5EFONVLOZTCZDF7ZOUSUD/action/citation_signature","submit_replication":"https://pith.science/pith/KWZYC5EFONVLOZTCZDF7ZOUSUD/action/replication_record"}},"created_at":"2026-05-18T00:30:09.584948+00:00","updated_at":"2026-05-18T00:30:09.584948+00:00"}