{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:PJKJHBNKKBHHAKCRIA5TOS3D7J","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":"bebadce6a4820e8c7ddd0df536407eb11368e04fe229dde99470bf7365f6e112","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"2003-07-03T19:15:48Z","title_canon_sha256":"23d05096f3edf4ec0456da9d21be6dca7951683aedc7199a927dff338781c6ca"},"schema_version":"1.0","source":{"id":"hep-th/0307041","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/0307041","created_at":"2026-07-04T14:31:58Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0307041v3","created_at":"2026-07-04T14:31:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0307041","created_at":"2026-07-04T14:31:58Z"},{"alias_kind":"pith_short_12","alias_value":"PJKJHBNKKBHH","created_at":"2026-07-04T14:31:58Z"},{"alias_kind":"pith_short_16","alias_value":"PJKJHBNKKBHHAKCR","created_at":"2026-07-04T14:31:58Z"},{"alias_kind":"pith_short_8","alias_value":"PJKJHBNK","created_at":"2026-07-04T14:31:58Z"}],"graph_snapshots":[{"event_id":"sha256:ba128a5e7161d3b528de6c22fc9bb757822f77ae3a90866cf96f46997994aa3d","target":"graph","created_at":"2026-07-04T14:31:58Z","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/0307041/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"On the space of three-dimensional conformal field theories with U(1) symmetry and a chosen coupling to a background gauge field, there is a natural action of the group $SL(2,{\\bf Z})$. The generator $S$ of $SL(2,{\\bf Z})$ acts by letting the background gauge field become dynamical, an operation considered recently by Kapustin and Strassler in explaining three-dimensional mirror symmetry. The other generator $T$ acts by shifting the Chern-Simons coupling of the background field. This $SL(2,{\\bf Z})$ action in three dimensions is related by the AdS/CFT correspondence to $SL(2,{\\bf Z})$ duality o","authors_text":"Edward Witten","cross_cats":[],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"2003-07-03T19:15:48Z","title":"SL(2,Z) Action On Three-Dimensional Conformal Field Theories With Abelian Symmetry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0307041","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:be213544a4e603145d46c29cfe69f4fc2e46ad9836ff61015fbbbfd5364e0a37","target":"record","created_at":"2026-07-04T14:31:58Z","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":"bebadce6a4820e8c7ddd0df536407eb11368e04fe229dde99470bf7365f6e112","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"2003-07-03T19:15:48Z","title_canon_sha256":"23d05096f3edf4ec0456da9d21be6dca7951683aedc7199a927dff338781c6ca"},"schema_version":"1.0","source":{"id":"hep-th/0307041","kind":"arxiv","version":3}},"canonical_sha256":"7a549385aa504e702851403b374b63fa7e5905b2519f79fdbb4da01eb971841b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7a549385aa504e702851403b374b63fa7e5905b2519f79fdbb4da01eb971841b","first_computed_at":"2026-07-04T14:31:58.980378Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:31:58.980378Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mJISnWmQNyNpSqJMqVz92qP/gsPSWoC2RK5GX3KebDIxoo+l09yI74jtCPmjtWLp9/wuPKoZvzCld4gzHV9RDQ==","signature_status":"signed_v1","signed_at":"2026-07-04T14:31:58.980755Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/0307041","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:be213544a4e603145d46c29cfe69f4fc2e46ad9836ff61015fbbbfd5364e0a37","sha256:ba128a5e7161d3b528de6c22fc9bb757822f77ae3a90866cf96f46997994aa3d"],"state_sha256":"c6386d4d878c4c6ec09af1909fbe414bed1a3148e02068692b0d52a59141cac1"}