{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:KXH723IEF5HB2QPB2HHSGLGDGF","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":"175216bf54f0aa15896fb2b5fef0f9756e44b8d6d2b2a740b94656ca5b4af74a","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"hep-th","submitted_at":"2003-09-24T19:39:20Z","title_canon_sha256":"19aa22f4440274820681e5e648dba95a6d528761deac1e990c50cca43f51cf3c"},"schema_version":"1.0","source":{"id":"hep-th/0309226","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/0309226","created_at":"2026-05-18T04:34:10Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0309226v2","created_at":"2026-05-18T04:34:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0309226","created_at":"2026-05-18T04:34:10Z"},{"alias_kind":"pith_short_12","alias_value":"KXH723IEF5HB","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"KXH723IEF5HB2QPB","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"KXH723IE","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:f17cad8b8fc4a31b95dc7ca8862621fd9d94e3f10b4dce3652ab9257e1103fb7","target":"graph","created_at":"2026-05-18T04:34:10Z","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 construct dual descriptions of (0,2) gauged linear sigma models. In some cases, the dual is a (0,2) Landau-Ginzburg theory, while in other cases, it is a non-linear sigma model. The duality map defines an analogue of mirror symmetry for (0,2) theories. Using the dual description, we determine the instanton corrected chiral ring for some illustrative examples. This ring defines a (0,2) generalization of the quantum cohomology ring of (2,2) theories.","authors_text":"Allan Adams, Anirban Basu, Savdeep Sethi","cross_cats":["math.AG"],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"2003-09-24T19:39:20Z","title":"(0,2) Duality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0309226","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":"sha256:3294ef569fef3058e3639884460a5ac2871d33d3df74c15fb89116ba35f793ed","target":"record","created_at":"2026-05-18T04:34:10Z","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":"175216bf54f0aa15896fb2b5fef0f9756e44b8d6d2b2a740b94656ca5b4af74a","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"hep-th","submitted_at":"2003-09-24T19:39:20Z","title_canon_sha256":"19aa22f4440274820681e5e648dba95a6d528761deac1e990c50cca43f51cf3c"},"schema_version":"1.0","source":{"id":"hep-th/0309226","kind":"arxiv","version":2}},"canonical_sha256":"55cffd6d042f4e1d41e1d1cf232cc3316dc99b1b0182d1fd7cc85c5396138f1a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"55cffd6d042f4e1d41e1d1cf232cc3316dc99b1b0182d1fd7cc85c5396138f1a","first_computed_at":"2026-05-18T04:34:10.772986Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:34:10.772986Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SL5pM7lN0cyihmDG/t0rOksVO3FaIYn9Z3r5QCuHOPLuCxdyM8oiQo+6s/CYWbfXXNNLPK1xeM8Z4qXX+tAbDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:34:10.773426Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/0309226","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3294ef569fef3058e3639884460a5ac2871d33d3df74c15fb89116ba35f793ed","sha256:f17cad8b8fc4a31b95dc7ca8862621fd9d94e3f10b4dce3652ab9257e1103fb7"],"state_sha256":"157aad8186c89dee92ae9763aa3cc6e0c8d613d9fb96a8b3cbff5d844df53a25"}