{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:P7THVMCJB5XNU3EG6WMEGNKMDK","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":"760a3fde01fa132325a00c82b72bdafbe081929a11c3c535f7f9203eafd9d593","cross_cats_sorted":["gr-qc","math-ph","math.GT","math.MP"],"license":"","primary_cat":"hep-th","submitted_at":"2002-05-27T10:10:25Z","title_canon_sha256":"c2882944fa03b3e3fbb787e830a23e8a4568c68013c9768a0a1cee3305afed9c"},"schema_version":"1.0","source":{"id":"hep-th/0205276","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/0205276","created_at":"2026-07-04T16:34:46Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0205276v3","created_at":"2026-07-04T16:34:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0205276","created_at":"2026-07-04T16:34:46Z"},{"alias_kind":"pith_short_12","alias_value":"P7THVMCJB5XN","created_at":"2026-07-04T16:34:46Z"},{"alias_kind":"pith_short_16","alias_value":"P7THVMCJB5XNU3EG","created_at":"2026-07-04T16:34:46Z"},{"alias_kind":"pith_short_8","alias_value":"P7THVMCJ","created_at":"2026-07-04T16:34:46Z"}],"graph_snapshots":[{"event_id":"sha256:ef1fc3958a004c9a7b22dda1147fe3494d4e3ffdba2dd984a2bc3cc8404fbcda","target":"graph","created_at":"2026-07-04T16:34:46Z","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/0205276/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In three dimensions, a `master theory' for all Thurston geometries requires imaginary flux. However, these geometries can be obtained from physical three-dimensional theories with various additional scalar fields, which can be interpreted as moduli in various compactifications of a higher-dimensional `master theory'. Three Thurston geometries are of the form N_2 x S^1, where N_2 denotes a two-dimensional Riemannian space of constant curvature. This enables us to twist these spaces, via T-duality, into other Thurston geometries as a U(1) bundle over N_2. In this way, Hopf T-duality relates all ","authors_text":"J.F. Vazquez-Poritz, J. Gegenberg, S. Vaidya","cross_cats":["gr-qc","math-ph","math.GT","math.MP"],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"2002-05-27T10:10:25Z","title":"Thurston Geometries from Eleven Dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0205276","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":"sha256:02a0c888d9be26e2f004e108a312a0ca361351ab714d396a74c6c88f86714cb6","target":"record","created_at":"2026-07-04T16:34:46Z","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":"760a3fde01fa132325a00c82b72bdafbe081929a11c3c535f7f9203eafd9d593","cross_cats_sorted":["gr-qc","math-ph","math.GT","math.MP"],"license":"","primary_cat":"hep-th","submitted_at":"2002-05-27T10:10:25Z","title_canon_sha256":"c2882944fa03b3e3fbb787e830a23e8a4568c68013c9768a0a1cee3305afed9c"},"schema_version":"1.0","source":{"id":"hep-th/0205276","kind":"arxiv","version":3}},"canonical_sha256":"7fe67ab0490f6eda6c86f59843354c1a9dbb3ad187df8bfec901c02655e86909","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7fe67ab0490f6eda6c86f59843354c1a9dbb3ad187df8bfec901c02655e86909","first_computed_at":"2026-07-04T16:34:46.651615Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:34:46.651615Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Y6aBqUKNtoDgtF+G/66ooaOaxLqFed0RbFqC0UWjr5Ffy72GUrKwxp1lAn5L4qqbPzTs8zR+Sjb6k4F/ki2FBg==","signature_status":"signed_v1","signed_at":"2026-07-04T16:34:46.651973Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/0205276","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:02a0c888d9be26e2f004e108a312a0ca361351ab714d396a74c6c88f86714cb6","sha256:ef1fc3958a004c9a7b22dda1147fe3494d4e3ffdba2dd984a2bc3cc8404fbcda"],"state_sha256":"9599ad116518394304aa428006d02ad07742265fef0ca51e9b84731a37adf8f8"}