{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2000:CEB7ROFGSXAQ5LWDCDU6M4JOSE","short_pith_number":"pith:CEB7ROFG","canonical_record":{"source":{"id":"hep-th/0002222","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"2000-02-25T23:10:34Z","cross_cats_sorted":[],"title_canon_sha256":"c8289a42382138ebba7b7c9e8b36925428727c582009d8f5f892674b64bea8d3","abstract_canon_sha256":"1d24150348e1bf33e993418a40d4b177a807978e492f01560437af50e1055bf7"},"schema_version":"1.0"},"canonical_sha256":"1103f8b8a695c10eaec310e9e6712e91314d701821c1a377421e30e7e08a0e80","source":{"kind":"arxiv","id":"hep-th/0002222","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2000:CEB7ROFGSXAQ5LWDCDU6M4JOSE","target":"record","payload":{"canonical_record":{"source":{"id":"hep-th/0002222","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"2000-02-25T23:10:34Z","cross_cats_sorted":[],"title_canon_sha256":"c8289a42382138ebba7b7c9e8b36925428727c582009d8f5f892674b64bea8d3","abstract_canon_sha256":"1d24150348e1bf33e993418a40d4b177a807978e492f01560437af50e1055bf7"},"schema_version":"1.0"},"canonical_sha256":"1103f8b8a695c10eaec310e9e6712e91314d701821c1a377421e30e7e08a0e80","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:31:19.267400Z","signature_b64":"hvNd41xLOq5K93799MhIWE1U/0RzpzmxcViduHQ/ND6gon/u3gGoKN1An9M3jiMgyZvgumy2o5aadoqOXkmUDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1103f8b8a695c10eaec310e9e6712e91314d701821c1a377421e30e7e08a0e80","last_reissued_at":"2026-07-04T14:31:19.266966Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:31:19.266966Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"hep-th/0002222","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T14:31:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4hBMu0IuArKkh3bixNpmHfdpIaheQBY9mPCfriiFktVtjfG2Rku8CgBzoTBYtC28rfdjYhTaiGYuO8V7JxSkDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T05:41:06.957087Z"},"content_sha256":"51b2f4e7728a404645edefbcac501db0aaa0ab76888c13d8b122365bce57fcaa","schema_version":"1.0","event_id":"sha256:51b2f4e7728a404645edefbcac501db0aaa0ab76888c13d8b122365bce57fcaa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2000:CEB7ROFGSXAQ5LWDCDU6M4JOSE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mirror Symmetry","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Cumrun Vafa, Kentaro Hori","submitted_at":"2000-02-25T23:10:34Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0002222","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/hep-th/0002222/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T14:31:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PFpyRK6MZRvwZpixfZNfMQAWsSlfNCjjB/thawCBjFSzvYdQH+hdj1R18VliJjJgxybf9sYAfKR9DVUtR43kBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T05:41:06.957611Z"},"content_sha256":"1143d1d45f1ea2da9e7a9fadb395956dfb5740c747cdf98edca4dba039ca4d7c","schema_version":"1.0","event_id":"sha256:1143d1d45f1ea2da9e7a9fadb395956dfb5740c747cdf98edca4dba039ca4d7c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CEB7ROFGSXAQ5LWDCDU6M4JOSE/bundle.json","state_url":"https://pith.science/pith/CEB7ROFGSXAQ5LWDCDU6M4JOSE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CEB7ROFGSXAQ5LWDCDU6M4JOSE/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-15T05:41:06Z","links":{"resolver":"https://pith.science/pith/CEB7ROFGSXAQ5LWDCDU6M4JOSE","bundle":"https://pith.science/pith/CEB7ROFGSXAQ5LWDCDU6M4JOSE/bundle.json","state":"https://pith.science/pith/CEB7ROFGSXAQ5LWDCDU6M4JOSE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CEB7ROFGSXAQ5LWDCDU6M4JOSE/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4+IqN80a5vqbTvGzD5PhZx63xaesc28p2EaNKSCIglQHYz3O5w8lpILy+SinQBgzeQ14JJQbD6IK+Y4+9qPSDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T05:41:06.961190Z","bundle_sha256":"67f96ac36965517e06701b807f91d33244cee226bbb621de488173698939ab25"}}