{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:3ZJ6DJ3E4C7SGEHP7KMM4MJYAY","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":"8432253245c8fecc66762fc85e77ca57763010eab7ea742c0b60e060e7a491fe","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-06-30T10:09:42Z","title_canon_sha256":"28f873cf153d9dfc49755aa8b458eab6aa036fcd8c934a009b0cc6a2dcbc351b"},"schema_version":"1.0","source":{"id":"1706.10100","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.10100","created_at":"2026-05-18T00:09:31Z"},{"alias_kind":"arxiv_version","alias_value":"1706.10100v2","created_at":"2026-05-18T00:09:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.10100","created_at":"2026-05-18T00:09:31Z"},{"alias_kind":"pith_short_12","alias_value":"3ZJ6DJ3E4C7S","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3ZJ6DJ3E4C7SGEHP","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3ZJ6DJ3E","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:fb1f818df1959b8f5c9d7c25a96a5bb97cf9aea58bf1943b71e2bf30a4a5215f","target":"graph","created_at":"2026-05-18T00:09:31Z","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":"Let $S$ be a K3 surface and let $E$ be an elliptic curve. We solve the reduced Gromov-Witten theory of the Calabi-Yau threefold $S \\times E$ for all curve classes which are primitive in the K3 factor. In particular, we deduce the Igusa cusp form conjecture.\n  The proof relies on new results in the Gromov-Witten theory of elliptic curves and K3 surfaces. We show the generating series of Gromov-Witten classes of an elliptic curve are cycle-valued quasimodular forms and satisfy a holomorphic anomaly equation. The quasimodularity generalizes a result by Okounkov and Pandharipande, and the holomorp","authors_text":"Aaron Pixton, Georg Oberdieck","cross_cats":["hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-06-30T10:09:42Z","title":"Holomorphic anomaly equations and the Igusa cusp form conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.10100","kind":"arxiv","version":2},"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":"sha256:4d13491738c3b4ed4b3e4e1a8eb444628ee521d56024533cd4ef5a31e3d2166a","target":"record","created_at":"2026-05-18T00:09:31Z","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":"8432253245c8fecc66762fc85e77ca57763010eab7ea742c0b60e060e7a491fe","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-06-30T10:09:42Z","title_canon_sha256":"28f873cf153d9dfc49755aa8b458eab6aa036fcd8c934a009b0cc6a2dcbc351b"},"schema_version":"1.0","source":{"id":"1706.10100","kind":"arxiv","version":2}},"canonical_sha256":"de53e1a764e0bf2310effa98ce3138060e27b5da937398f0d9bb619c4f5881af","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"de53e1a764e0bf2310effa98ce3138060e27b5da937398f0d9bb619c4f5881af","first_computed_at":"2026-05-18T00:09:31.104583Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:09:31.104583Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MeJXIIHDJOIiiypp++l1FagvfausALz6TsaPGLG0VeLRP+VW4TkakAQmEz1KsH3uycrIYpBeU/cOCMIjesCoDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:09:31.105256Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.10100","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4d13491738c3b4ed4b3e4e1a8eb444628ee521d56024533cd4ef5a31e3d2166a","sha256:fb1f818df1959b8f5c9d7c25a96a5bb97cf9aea58bf1943b71e2bf30a4a5215f"],"state_sha256":"f6886d8db90b81445e018eaa2605950b4a8a8ce0623dfe3927c5a3876b2635c7"}