{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:QPNRJRFWJYN7TZZHE2GCXKX2TK","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":"9dccad193f33af4a5ab0264852f825108d4d9a0b901b22879132219def39a13a","cross_cats_sorted":["math.AG","math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2019-10-20T14:30:33Z","title_canon_sha256":"e485a35a58ef196c846e45ce3027c970ee801310cee9937bac0596858b3a9c31"},"schema_version":"1.0","source":{"id":"1910.08990","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1910.08990","created_at":"2026-07-05T07:14:48Z"},{"alias_kind":"arxiv_version","alias_value":"1910.08990v2","created_at":"2026-07-05T07:14:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1910.08990","created_at":"2026-07-05T07:14:48Z"},{"alias_kind":"pith_short_12","alias_value":"QPNRJRFWJYN7","created_at":"2026-07-05T07:14:48Z"},{"alias_kind":"pith_short_16","alias_value":"QPNRJRFWJYN7TZZH","created_at":"2026-07-05T07:14:48Z"},{"alias_kind":"pith_short_8","alias_value":"QPNRJRFW","created_at":"2026-07-05T07:14:48Z"}],"graph_snapshots":[{"event_id":"sha256:0bdbf959b41495384e7f33b087b0653b3bd03b91f4ad48badb26b945b7025db6","target":"graph","created_at":"2026-07-05T07:14:48Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1910.08990/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We use chain level genus zero Gromov-Witten theory to associate to any closed monotone symplectic manifold a formal group (loosely interpreted), whose Lie algebra is the odd degree cohomology of the manifold (with vanishing bracket). When taken with coefficients mod p, the p-th power map of the formal group is related to quantum Steenrod operations. The motivation for this construction comes from derived Picard groups of Fukaya categories, and from arithmetic aspects of mirror symmetry.","authors_text":"Paul Seidel","cross_cats":["math.AG","math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2019-10-20T14:30:33Z","title":"Formal groups and quantum cohomology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1910.08990","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":"sha256:60adcc8f2ac20f3d7bbc03fc0c0271617bdb6b29af8740757ca764a27987923d","target":"record","created_at":"2026-07-05T07:14:48Z","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":"9dccad193f33af4a5ab0264852f825108d4d9a0b901b22879132219def39a13a","cross_cats_sorted":["math.AG","math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2019-10-20T14:30:33Z","title_canon_sha256":"e485a35a58ef196c846e45ce3027c970ee801310cee9937bac0596858b3a9c31"},"schema_version":"1.0","source":{"id":"1910.08990","kind":"arxiv","version":2}},"canonical_sha256":"83db14c4b64e1bf9e727268c2baafa9a997392487712cf2af27078e9d6e7a64d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"83db14c4b64e1bf9e727268c2baafa9a997392487712cf2af27078e9d6e7a64d","first_computed_at":"2026-07-05T07:14:48.109983Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:14:48.109983Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UDeWFZY0qP7YgfR+v9rQ9QJWdR2owFG+IHNhGZa3i7u3DvcRN70Xi39zyXPJCXoTCuhM3blrY69miDr48FK8Cw==","signature_status":"signed_v1","signed_at":"2026-07-05T07:14:48.110494Z","signed_message":"canonical_sha256_bytes"},"source_id":"1910.08990","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:60adcc8f2ac20f3d7bbc03fc0c0271617bdb6b29af8740757ca764a27987923d","sha256:0bdbf959b41495384e7f33b087b0653b3bd03b91f4ad48badb26b945b7025db6"],"state_sha256":"d517f09c7e18cb69d6036b72fe54f73b65267dc279d158483084f524ed3d36e0"}