{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:PQJL564NNKZMPMJIGU2GDOTXSN","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":"0590d5fad3069bc4fe9f4ea2ce2d476b3b7b2ea8a45c719bb0d78423645505b8","cross_cats_sorted":["math-ph","math.CO","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-08-21T19:00:09Z","title_canon_sha256":"e6ff7b80238d9f0f9a5ab19fb653f7183505dae7a012c632dd999f9617dc54a3"},"schema_version":"1.0","source":{"id":"1208.4342","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.4342","created_at":"2026-05-18T02:29:53Z"},{"alias_kind":"arxiv_version","alias_value":"1208.4342v4","created_at":"2026-05-18T02:29:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.4342","created_at":"2026-05-18T02:29:53Z"},{"alias_kind":"pith_short_12","alias_value":"PQJL564NNKZM","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"PQJL564NNKZMPMJI","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"PQJL564N","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:e90c332d5e3d8c5b5e42609fd8f53aadf83044a4e0af477ef7286eb8638dc255","target":"graph","created_at":"2026-05-18T02:29:53Z","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":"We prove a formula for certain cubic $\\Z_n$-Hodge integrals in terms of loop Schur functions. We use this identity to prove the Gromov-Witten/Donaldson-Thomas correspondence for local $\\Z_n$-gerbes over $\\proj^1$.","authors_text":"Dustin Ross, Zhengyu Zong","cross_cats":["math-ph","math.CO","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-08-21T19:00:09Z","title":"The Gerby Gopakumar-Mari\\~no-Vafa Formula"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.4342","kind":"arxiv","version":4},"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":"sha256:33794653eab8fc863dc5d304cb825ab75f611643918e844546ca286258c4fd01","target":"record","created_at":"2026-05-18T02:29:53Z","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":"0590d5fad3069bc4fe9f4ea2ce2d476b3b7b2ea8a45c719bb0d78423645505b8","cross_cats_sorted":["math-ph","math.CO","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-08-21T19:00:09Z","title_canon_sha256":"e6ff7b80238d9f0f9a5ab19fb653f7183505dae7a012c632dd999f9617dc54a3"},"schema_version":"1.0","source":{"id":"1208.4342","kind":"arxiv","version":4}},"canonical_sha256":"7c12befb8d6ab2c7b128353461ba7793656adb6d084c59f0c3b736d6a915fcd1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7c12befb8d6ab2c7b128353461ba7793656adb6d084c59f0c3b736d6a915fcd1","first_computed_at":"2026-05-18T02:29:53.377511Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:53.377511Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OiFNzAlrsRiDLIKJrmCJFvgG5Ajwt7urNnUZ96H9SDVpUXqJr0wptmx1T5FlxVwEXA4dB1Xuqizw6ZR2InW1AA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:53.378180Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.4342","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:33794653eab8fc863dc5d304cb825ab75f611643918e844546ca286258c4fd01","sha256:e90c332d5e3d8c5b5e42609fd8f53aadf83044a4e0af477ef7286eb8638dc255"],"state_sha256":"5b82c8b3142c47169b53f2920a126f6bbce2832e31d25c2ecc5cb4b31717537b"}