{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:A2T4QQZQVUOPCBTPFBJSRQGQBR","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":"7224863109cd41fd6d52d36188581d2f146ba9fdc25137617b3b3093f9cba090","cross_cats_sorted":["math.AG","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2022-02-11T17:29:05Z","title_canon_sha256":"8d7a9bb610ee5c46b077a447fadea8d1f6d40557e380110e878e398ff2d26e3c"},"schema_version":"1.0","source":{"id":"2202.05785","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2202.05785","created_at":"2026-07-05T04:18:51Z"},{"alias_kind":"arxiv_version","alias_value":"2202.05785v2","created_at":"2026-07-05T04:18:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2202.05785","created_at":"2026-07-05T04:18:51Z"},{"alias_kind":"pith_short_12","alias_value":"A2T4QQZQVUOP","created_at":"2026-07-05T04:18:51Z"},{"alias_kind":"pith_short_16","alias_value":"A2T4QQZQVUOPCBTP","created_at":"2026-07-05T04:18:51Z"},{"alias_kind":"pith_short_8","alias_value":"A2T4QQZQ","created_at":"2026-07-05T04:18:51Z"}],"graph_snapshots":[{"event_id":"sha256:099c2b1392e090e400d6fa92fcfca3037cee06ac8012e3c95b8a24737d3c3149","target":"graph","created_at":"2026-07-05T04:18:51Z","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/2202.05785/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $G$ be a compact, connected Lie group and $T \\subset G$ a maximal torus. Let $(M,\\omega)$ be a monotone closed symplectic manifold equipped with a Hamiltonian action of $G$. We construct a module action of the affine nil-Hecke algebra $\\hat{H}_*^{S^1 \\times T}(LG/T)$ on the $S^1 \\times T$-equivariant quantum cohomology of $M$, $QH^*_{S^1 \\times T}(M).$ Our construction generalizes the theory of shift operators for Hamiltonian torus actions [OP,LJ]. We show that, as in the abelian case, this action behaves well with respect to the quantum connection. As an application of our construction, w","authors_text":"Cheuk Yu Mak, Dan Pomerleano, Eduardo Gonz\\'alez","cross_cats":["math.AG","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2022-02-11T17:29:05Z","title":"Affine nil-Hecke algebras and Quantum cohomology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2202.05785","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:acc131660d60ad12137a9b045dc5cea3066d4305144470d01d1d32ad72117e8f","target":"record","created_at":"2026-07-05T04:18:51Z","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":"7224863109cd41fd6d52d36188581d2f146ba9fdc25137617b3b3093f9cba090","cross_cats_sorted":["math.AG","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2022-02-11T17:29:05Z","title_canon_sha256":"8d7a9bb610ee5c46b077a447fadea8d1f6d40557e380110e878e398ff2d26e3c"},"schema_version":"1.0","source":{"id":"2202.05785","kind":"arxiv","version":2}},"canonical_sha256":"06a7c84330ad1cf1066f285328c0d00c59b7d22f19b395b1ddb4d4755c262490","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"06a7c84330ad1cf1066f285328c0d00c59b7d22f19b395b1ddb4d4755c262490","first_computed_at":"2026-07-05T04:18:51.259265Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:18:51.259265Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qqHCuL5ZS50jjPxWATy1bnBJYP44u6MnuPXK/s2jlADhAZdslZ+TV0e4jYq4y2Uw+fFGDXtJfDjBhzd78KjZBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T04:18:51.259749Z","signed_message":"canonical_sha256_bytes"},"source_id":"2202.05785","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:acc131660d60ad12137a9b045dc5cea3066d4305144470d01d1d32ad72117e8f","sha256:099c2b1392e090e400d6fa92fcfca3037cee06ac8012e3c95b8a24737d3c3149"],"state_sha256":"1c524a0774727f26a96f8f30b34256403f9f63d2ac0dd7a7f3f6c5f15a7f7653"}