{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:P35LKHDXXEL7MB3ASLT4FCUOIW","short_pith_number":"pith:P35LKHDX","schema_version":"1.0","canonical_sha256":"7efab51c77b917f6076092e7c28a8e45bdf2bca3b373bd23e66595fe1918d7f6","source":{"kind":"arxiv","id":"1605.05238","version":2},"attestation_state":"computed","paper":{"title":"Gromov-Witten theory of $\\mathrm{K3} \\times \\mathbb{P}^1$ and quasi-Jacobi forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Georg Oberdieck","submitted_at":"2016-05-17T17:02:03Z","abstract_excerpt":"Let $S$ be a K3 surface with primitive curve class $\\beta$. We solve the relative Gromov-Witten theory of $S \\times \\mathbb{P}^1$ in classes $(\\beta,1)$ and $(\\beta,2)$. The generating series are quasi-Jacobi forms and equal to a corresponding series of genus $0$ Gromov-Witten invariants on the Hilbert scheme of points of $S$. This proves a special case of a conjecture of Pandharipande and the author. The new geometric input of the paper is a genus bound for hyperelliptic curves on K3 surfaces proven by Ciliberto and Knutsen. By exploiting various formal properties we find that a key generatin"},"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":"1605.05238","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-05-17T17:02:03Z","cross_cats_sorted":[],"title_canon_sha256":"9742d4f964c66f0023ff6f745840c21f8665f02b6953938fa2f687583dd9c0d0","abstract_canon_sha256":"095a68be43373b3caf966a9b36e94a4db1ad88994fe629bf5558541eaad85e20"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:02.492958Z","signature_b64":"RtSskqSpVuAn21GxZCpm5aVFbXZYuO5tStxbw5y2yX8/0AVzSm0VqOk5HgccQ16chLhmqF0ewN7eUnFfga2PBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7efab51c77b917f6076092e7c28a8e45bdf2bca3b373bd23e66595fe1918d7f6","last_reissued_at":"2026-05-18T00:33:02.492472Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:02.492472Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Gromov-Witten theory of $\\mathrm{K3} \\times \\mathbb{P}^1$ and quasi-Jacobi forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Georg Oberdieck","submitted_at":"2016-05-17T17:02:03Z","abstract_excerpt":"Let $S$ be a K3 surface with primitive curve class $\\beta$. We solve the relative Gromov-Witten theory of $S \\times \\mathbb{P}^1$ in classes $(\\beta,1)$ and $(\\beta,2)$. The generating series are quasi-Jacobi forms and equal to a corresponding series of genus $0$ Gromov-Witten invariants on the Hilbert scheme of points of $S$. This proves a special case of a conjecture of Pandharipande and the author. The new geometric input of the paper is a genus bound for hyperelliptic curves on K3 surfaces proven by Ciliberto and Knutsen. By exploiting various formal properties we find that a key generatin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.05238","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":"1605.05238","created_at":"2026-05-18T00:33:02.492545+00:00"},{"alias_kind":"arxiv_version","alias_value":"1605.05238v2","created_at":"2026-05-18T00:33:02.492545+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.05238","created_at":"2026-05-18T00:33:02.492545+00:00"},{"alias_kind":"pith_short_12","alias_value":"P35LKHDXXEL7","created_at":"2026-05-18T12:30:36.002864+00:00"},{"alias_kind":"pith_short_16","alias_value":"P35LKHDXXEL7MB3A","created_at":"2026-05-18T12:30:36.002864+00:00"},{"alias_kind":"pith_short_8","alias_value":"P35LKHDX","created_at":"2026-05-18T12:30:36.002864+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/P35LKHDXXEL7MB3ASLT4FCUOIW","json":"https://pith.science/pith/P35LKHDXXEL7MB3ASLT4FCUOIW.json","graph_json":"https://pith.science/api/pith-number/P35LKHDXXEL7MB3ASLT4FCUOIW/graph.json","events_json":"https://pith.science/api/pith-number/P35LKHDXXEL7MB3ASLT4FCUOIW/events.json","paper":"https://pith.science/paper/P35LKHDX"},"agent_actions":{"view_html":"https://pith.science/pith/P35LKHDXXEL7MB3ASLT4FCUOIW","download_json":"https://pith.science/pith/P35LKHDXXEL7MB3ASLT4FCUOIW.json","view_paper":"https://pith.science/paper/P35LKHDX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1605.05238&json=true","fetch_graph":"https://pith.science/api/pith-number/P35LKHDXXEL7MB3ASLT4FCUOIW/graph.json","fetch_events":"https://pith.science/api/pith-number/P35LKHDXXEL7MB3ASLT4FCUOIW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/P35LKHDXXEL7MB3ASLT4FCUOIW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/P35LKHDXXEL7MB3ASLT4FCUOIW/action/storage_attestation","attest_author":"https://pith.science/pith/P35LKHDXXEL7MB3ASLT4FCUOIW/action/author_attestation","sign_citation":"https://pith.science/pith/P35LKHDXXEL7MB3ASLT4FCUOIW/action/citation_signature","submit_replication":"https://pith.science/pith/P35LKHDXXEL7MB3ASLT4FCUOIW/action/replication_record"}},"created_at":"2026-05-18T00:33:02.492545+00:00","updated_at":"2026-05-18T00:33:02.492545+00:00"}