{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:4SMZYFBNAU222FH7DX6Z3N7NBP","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":"a66cc36665e4b7196f54371129758720f3df714a3d3481dab0cd88e4e89d6d26","cross_cats_sorted":["hep-th","math.CV"],"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.AG","submitted_at":"2012-06-18T10:31:24Z","title_canon_sha256":"f601e3ba6ac5e637bfb5f9ceac711733a31438c6921f98e322f7a8f466ecb9d8"},"schema_version":"1.0","source":{"id":"1206.3879","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.3879","created_at":"2026-05-18T03:53:18Z"},{"alias_kind":"arxiv_version","alias_value":"1206.3879v1","created_at":"2026-05-18T03:53:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.3879","created_at":"2026-05-18T03:53:18Z"},{"alias_kind":"pith_short_12","alias_value":"4SMZYFBNAU22","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"4SMZYFBNAU222FH7","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"4SMZYFBN","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:0b7b23f32f3e067f01d8e980f7357766ffd1730efd4d3dab080e78f62fe8b6e6","target":"graph","created_at":"2026-05-18T03:53:18Z","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":"In this paper, we proved generating functions of Gromov-Witten cycles of the elliptic orbifold lines with weights (3,3,3), (4,4,2), and (6,3,2) are cycle-valued quasi-modular forms. This is a generalization of Milanov and Ruan's work on cycle-valued level. First we construct a global cohomology field theory (CohFT) for simple elliptic singularities (modulo an extension problem) and prove its modularity. Then, we apply Teleman's reconstruction theorem to prove mirror theorems on cycled-valued level and match it with a CohFT from Gromov-Witten theory of a corresponding orbifold.This solves the e","authors_text":"Todor MIlanov, Yefeng Shen, Yongbin Ruan","cross_cats":["hep-th","math.CV"],"headline":"","license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.AG","submitted_at":"2012-06-18T10:31:24Z","title":"Gromov-Witten theory and cycle-valued modular forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.3879","kind":"arxiv","version":1},"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:b9d78930f3ffaf11f217277cd23a52f449f6398f141d03340d9e42bcdb3e875c","target":"record","created_at":"2026-05-18T03:53:18Z","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":"a66cc36665e4b7196f54371129758720f3df714a3d3481dab0cd88e4e89d6d26","cross_cats_sorted":["hep-th","math.CV"],"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.AG","submitted_at":"2012-06-18T10:31:24Z","title_canon_sha256":"f601e3ba6ac5e637bfb5f9ceac711733a31438c6921f98e322f7a8f466ecb9d8"},"schema_version":"1.0","source":{"id":"1206.3879","kind":"arxiv","version":1}},"canonical_sha256":"e4999c142d0535ad14ff1dfd9db7ed0bd32d1fc5f79401a495bed2bdbdbc9a47","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e4999c142d0535ad14ff1dfd9db7ed0bd32d1fc5f79401a495bed2bdbdbc9a47","first_computed_at":"2026-05-18T03:53:18.549040Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:53:18.549040Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hvBvQr2zoCM9UO8OYhcx2fJmE2Fp4TYm57gk1QnoHNUWFHTBU08EoAFkdIhn6bn4im5RejXChNwbZbNCenuEAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:53:18.549941Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.3879","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b9d78930f3ffaf11f217277cd23a52f449f6398f141d03340d9e42bcdb3e875c","sha256:0b7b23f32f3e067f01d8e980f7357766ffd1730efd4d3dab080e78f62fe8b6e6"],"state_sha256":"b15738f6e2890baba3d39c4d4e685ea4bebb20d12c7ca6cf6c68f87c05c22f8a"}