{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:OEB3DEDB7SPQFSZBP3XZOR6WCF","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":"86b013ebb4ffc121660f841e7bf4d8b27898129604596e7f24beaf98b51333a1","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-06-26T03:14:06Z","title_canon_sha256":"ad73de5dd0d32af01884546f831b9082004840ff2c9e14059995a14c7a0619a9"},"schema_version":"1.0","source":{"id":"1906.10824","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.10824","created_at":"2026-05-17T23:42:13Z"},{"alias_kind":"arxiv_version","alias_value":"1906.10824v1","created_at":"2026-05-17T23:42:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.10824","created_at":"2026-05-17T23:42:13Z"},{"alias_kind":"pith_short_12","alias_value":"OEB3DEDB7SPQ","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"OEB3DEDB7SPQFSZB","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"OEB3DEDB","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:54b48505de753ad25b8b6c9cf438dc2acb75a8146be5da7618b7b4829394490a","target":"graph","created_at":"2026-05-17T23:42:13Z","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 describe an attempt to make quantum K-theory (of stable maps) more amenable to the self-duality/rigidity arguments of arXiv:1512.07363 in quasimap theory, by twisting the virtual structure sheaf. For $\\mathbb{P}^n$ this twist produces invariants which are self-dual rational functions, but asymptotic analysis shows this is no longer the case for general GKM manifolds such as flag varieties. Such analysis is done via an explicit combinatorial description of localization for quantum K-theory on GKM manifolds, and Givental's adelic characterization.","authors_text":"Henry Liu","cross_cats":["hep-th","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-06-26T03:14:06Z","title":"Self-duality in quantum K-theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.10824","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":"sha256:37038b852712b022709e803c71f35e7c573a15610572af00a13439acd73cce79","target":"record","created_at":"2026-05-17T23:42:13Z","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":"86b013ebb4ffc121660f841e7bf4d8b27898129604596e7f24beaf98b51333a1","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-06-26T03:14:06Z","title_canon_sha256":"ad73de5dd0d32af01884546f831b9082004840ff2c9e14059995a14c7a0619a9"},"schema_version":"1.0","source":{"id":"1906.10824","kind":"arxiv","version":1}},"canonical_sha256":"7103b19061fc9f02cb217eef9747d611682551d25eb0c7a3ae3a3761933cbaa9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7103b19061fc9f02cb217eef9747d611682551d25eb0c7a3ae3a3761933cbaa9","first_computed_at":"2026-05-17T23:42:13.140031Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:13.140031Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+j1dzZ6VJ49rSsV+IjCH7uUunAHhE5CME4kIrT+oQrqe1Iik2j0YyZW1zSiH/0B5VblMui43VdyMed2EdE9eAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:13.140700Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.10824","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:37038b852712b022709e803c71f35e7c573a15610572af00a13439acd73cce79","sha256:54b48505de753ad25b8b6c9cf438dc2acb75a8146be5da7618b7b4829394490a"],"state_sha256":"873108f9b779f7e08e3bb12a906cf5375b4956789daffab9b496789d30055215"}