{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2002:G5QL6TQHN634V5EWY3KHHYFHQG","short_pith_number":"pith:G5QL6TQH","canonical_record":{"source":{"id":"hep-th/0205144","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"2002-05-15T16:25:16Z","cross_cats_sorted":[],"title_canon_sha256":"00c00dfabbd3d7c88d4f09205a2c3763df23b2f13f02e31c4bf67b921f449a87","abstract_canon_sha256":"29a7a9b79bb13c9f6cbc1168ee8a323706a28a736a40c407917849ec120b8bb7"},"schema_version":"1.0"},"canonical_sha256":"3760bf4e076fb7caf496c6d473e0a78180c09a07ee6de26d4bd00135940808c4","source":{"kind":"arxiv","id":"hep-th/0205144","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/0205144","created_at":"2026-07-04T16:34:45Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0205144v3","created_at":"2026-07-04T16:34:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0205144","created_at":"2026-07-04T16:34:45Z"},{"alias_kind":"pith_short_12","alias_value":"G5QL6TQHN634","created_at":"2026-07-04T16:34:45Z"},{"alias_kind":"pith_short_16","alias_value":"G5QL6TQHN634V5EW","created_at":"2026-07-04T16:34:45Z"},{"alias_kind":"pith_short_8","alias_value":"G5QL6TQH","created_at":"2026-07-04T16:34:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2002:G5QL6TQHN634V5EWY3KHHYFHQG","target":"record","payload":{"canonical_record":{"source":{"id":"hep-th/0205144","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"2002-05-15T16:25:16Z","cross_cats_sorted":[],"title_canon_sha256":"00c00dfabbd3d7c88d4f09205a2c3763df23b2f13f02e31c4bf67b921f449a87","abstract_canon_sha256":"29a7a9b79bb13c9f6cbc1168ee8a323706a28a736a40c407917849ec120b8bb7"},"schema_version":"1.0"},"canonical_sha256":"3760bf4e076fb7caf496c6d473e0a78180c09a07ee6de26d4bd00135940808c4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:34:45.784282Z","signature_b64":"Luha3SL5I4hVQQpkYC8fVcvSWWFfMFfyS7oOvFQrLF8pej1eIjx44u42wKjuNHnBnxKd6M5kyDCCgIVXhxAeCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3760bf4e076fb7caf496c6d473e0a78180c09a07ee6de26d4bd00135940808c4","last_reissued_at":"2026-07-04T16:34:45.783921Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:34:45.783921Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"hep-th/0205144","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":"2026-07-04T16:34:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AgKtnkbQWKH938T5EldF9r3drnuE7KfKj57PUx3QYzUatYeFBrLvqaCenmAvZ6xb9z3ge1Fn0Lk5mHW2EKI0DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T16:38:32.852196Z"},"content_sha256":"0e0b16f5324649100337c348bbc693903cf1900615ce71cee14fae5258aa87c3","schema_version":"1.0","event_id":"sha256:0e0b16f5324649100337c348bbc693903cf1900615ce71cee14fae5258aa87c3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2002:G5QL6TQHN634V5EWY3KHHYFHQG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Symmetries of Toric Duality","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Amihay Hanany, Bo Feng, Sebastian Franco, Yang-Hui He","submitted_at":"2002-05-15T16:25:16Z","abstract_excerpt":"This paper serves to elucidate the nature of toric duality dubbed in hep-th/0003085 in the construction for world volume theories of D-branes probing arbitrary toric singularities. This duality will be seen to be due to certain permutation symmetries of multiplicities in the gauged linear sigma model fields. To this symmetry we shall refer as ``multiplicity symmetry.'' We present beautiful combinatorial properties of these multiplicities and rederive all known cases of torically dual theories under this new light. We also initiate an understanding of why such multiplicity symmetry naturally le"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0205144","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/0205144/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":"2026-07-04T16:34:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r9niMNxp/5+QNpW95/cPSFnVCrGhvD4WTrH5YhfTFwp58P/Xes2Zm7ya14bUQj4IOnrHJA66tO4AKjG/MQxnAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T16:38:32.852696Z"},"content_sha256":"eb11fd373b6ef3b7e1e4dfc9bc52d6586c1c86007ad193735af69a3618603ea1","schema_version":"1.0","event_id":"sha256:eb11fd373b6ef3b7e1e4dfc9bc52d6586c1c86007ad193735af69a3618603ea1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G5QL6TQHN634V5EWY3KHHYFHQG/bundle.json","state_url":"https://pith.science/pith/G5QL6TQHN634V5EWY3KHHYFHQG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G5QL6TQHN634V5EWY3KHHYFHQG/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":"2026-08-17T16:38:32Z","links":{"resolver":"https://pith.science/pith/G5QL6TQHN634V5EWY3KHHYFHQG","bundle":"https://pith.science/pith/G5QL6TQHN634V5EWY3KHHYFHQG/bundle.json","state":"https://pith.science/pith/G5QL6TQHN634V5EWY3KHHYFHQG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G5QL6TQHN634V5EWY3KHHYFHQG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:G5QL6TQHN634V5EWY3KHHYFHQG","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":"29a7a9b79bb13c9f6cbc1168ee8a323706a28a736a40c407917849ec120b8bb7","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"2002-05-15T16:25:16Z","title_canon_sha256":"00c00dfabbd3d7c88d4f09205a2c3763df23b2f13f02e31c4bf67b921f449a87"},"schema_version":"1.0","source":{"id":"hep-th/0205144","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/0205144","created_at":"2026-07-04T16:34:45Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0205144v3","created_at":"2026-07-04T16:34:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0205144","created_at":"2026-07-04T16:34:45Z"},{"alias_kind":"pith_short_12","alias_value":"G5QL6TQHN634","created_at":"2026-07-04T16:34:45Z"},{"alias_kind":"pith_short_16","alias_value":"G5QL6TQHN634V5EW","created_at":"2026-07-04T16:34:45Z"},{"alias_kind":"pith_short_8","alias_value":"G5QL6TQH","created_at":"2026-07-04T16:34:45Z"}],"graph_snapshots":[{"event_id":"sha256:eb11fd373b6ef3b7e1e4dfc9bc52d6586c1c86007ad193735af69a3618603ea1","target":"graph","created_at":"2026-07-04T16:34:45Z","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/0205144/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper serves to elucidate the nature of toric duality dubbed in hep-th/0003085 in the construction for world volume theories of D-branes probing arbitrary toric singularities. This duality will be seen to be due to certain permutation symmetries of multiplicities in the gauged linear sigma model fields. To this symmetry we shall refer as ``multiplicity symmetry.'' We present beautiful combinatorial properties of these multiplicities and rederive all known cases of torically dual theories under this new light. We also initiate an understanding of why such multiplicity symmetry naturally le","authors_text":"Amihay Hanany, Bo Feng, Sebastian Franco, Yang-Hui He","cross_cats":[],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"2002-05-15T16:25:16Z","title":"Symmetries of Toric Duality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0205144","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":"sha256:0e0b16f5324649100337c348bbc693903cf1900615ce71cee14fae5258aa87c3","target":"record","created_at":"2026-07-04T16:34:45Z","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":"29a7a9b79bb13c9f6cbc1168ee8a323706a28a736a40c407917849ec120b8bb7","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"2002-05-15T16:25:16Z","title_canon_sha256":"00c00dfabbd3d7c88d4f09205a2c3763df23b2f13f02e31c4bf67b921f449a87"},"schema_version":"1.0","source":{"id":"hep-th/0205144","kind":"arxiv","version":3}},"canonical_sha256":"3760bf4e076fb7caf496c6d473e0a78180c09a07ee6de26d4bd00135940808c4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3760bf4e076fb7caf496c6d473e0a78180c09a07ee6de26d4bd00135940808c4","first_computed_at":"2026-07-04T16:34:45.783921Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:34:45.783921Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Luha3SL5I4hVQQpkYC8fVcvSWWFfMFfyS7oOvFQrLF8pej1eIjx44u42wKjuNHnBnxKd6M5kyDCCgIVXhxAeCw==","signature_status":"signed_v1","signed_at":"2026-07-04T16:34:45.784282Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/0205144","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0e0b16f5324649100337c348bbc693903cf1900615ce71cee14fae5258aa87c3","sha256:eb11fd373b6ef3b7e1e4dfc9bc52d6586c1c86007ad193735af69a3618603ea1"],"state_sha256":"82e5038ed16286a4fc0dc629dbd1298a6b37a1e171f1645df76e26b303d856ae"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a0pq2ivTnOvOckfTTCFQqIYPYtNsyzjktHuN1kFv66+D989ou58F98cNFuLV3pNBP5GSgpCKH0U4ImJ47aLwAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T16:38:32.857171Z","bundle_sha256":"e0305df20caf5cbe024355b88a536662896047aa46f1921817e6721a0fae0b2d"}}