{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2000:CEB7ROFGSXAQ5LWDCDU6M4JOSE","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":"1d24150348e1bf33e993418a40d4b177a807978e492f01560437af50e1055bf7","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"2000-02-25T23:10:34Z","title_canon_sha256":"c8289a42382138ebba7b7c9e8b36925428727c582009d8f5f892674b64bea8d3"},"schema_version":"1.0","source":{"id":"hep-th/0002222","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/0002222","created_at":"2026-07-04T14:31:19Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0002222v3","created_at":"2026-07-04T14:31:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0002222","created_at":"2026-07-04T14:31:19Z"},{"alias_kind":"pith_short_12","alias_value":"CEB7ROFGSXAQ","created_at":"2026-07-04T14:31:19Z"},{"alias_kind":"pith_short_16","alias_value":"CEB7ROFGSXAQ5LWD","created_at":"2026-07-04T14:31:19Z"},{"alias_kind":"pith_short_8","alias_value":"CEB7ROFG","created_at":"2026-07-04T14:31:19Z"}],"graph_snapshots":[{"event_id":"sha256:1143d1d45f1ea2da9e7a9fadb395956dfb5740c747cdf98edca4dba039ca4d7c","target":"graph","created_at":"2026-07-04T14:31:19Z","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/hep-th/0002222/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove mirror symmetry for supersymmetric sigma models on Kahler manifolds in 1+1 dimensions. The proof involves establishing the equivalence of the gauged linear sigma model, embedded in a theory with an enlarged gauge symmetry, with a Landau-Ginzburg theory of Toda type. Standard R -> 1/R duality and dynamical generation of superpotential by vortices are crucial in the derivation. This provides not only a proof of mirror symmetry in the case of (local and global) Calabi-Yau manifolds, but also for sigma models on manifolds with positive first Chern class, including deformations of the acti","authors_text":"Cumrun Vafa, Kentaro Hori","cross_cats":[],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"2000-02-25T23:10:34Z","title":"Mirror Symmetry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0002222","kind":"arxiv","version":3},"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":"sha256:51b2f4e7728a404645edefbcac501db0aaa0ab76888c13d8b122365bce57fcaa","target":"record","created_at":"2026-07-04T14:31:19Z","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":"1d24150348e1bf33e993418a40d4b177a807978e492f01560437af50e1055bf7","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"2000-02-25T23:10:34Z","title_canon_sha256":"c8289a42382138ebba7b7c9e8b36925428727c582009d8f5f892674b64bea8d3"},"schema_version":"1.0","source":{"id":"hep-th/0002222","kind":"arxiv","version":3}},"canonical_sha256":"1103f8b8a695c10eaec310e9e6712e91314d701821c1a377421e30e7e08a0e80","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1103f8b8a695c10eaec310e9e6712e91314d701821c1a377421e30e7e08a0e80","first_computed_at":"2026-07-04T14:31:19.266966Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:31:19.266966Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hvNd41xLOq5K93799MhIWE1U/0RzpzmxcViduHQ/ND6gon/u3gGoKN1An9M3jiMgyZvgumy2o5aadoqOXkmUDQ==","signature_status":"signed_v1","signed_at":"2026-07-04T14:31:19.267400Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/0002222","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:51b2f4e7728a404645edefbcac501db0aaa0ab76888c13d8b122365bce57fcaa","sha256:1143d1d45f1ea2da9e7a9fadb395956dfb5740c747cdf98edca4dba039ca4d7c"],"state_sha256":"57c9dddffa3517fc17ad03ad1b937395f7061394fa7cd52165bb69762aa3fb2d"}