{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:DYA3DGQ3GOBP5A5USWJ5WSOZ66","short_pith_number":"pith:DYA3DGQ3","canonical_record":{"source":{"id":"1911.05080","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-11-12T19:00:01Z","cross_cats_sorted":[],"title_canon_sha256":"b9a8b3641b368a62fd17ae80807d45192adf36c28c13a80be4ffc03778ecbd40","abstract_canon_sha256":"892d841a8a28bdba8de1ffe01b13257855fb79607a08c1935a878453c1794ccb"},"schema_version":"1.0"},"canonical_sha256":"1e01b19a1b3382fe83b49593db49d9f793ad2965de9a97e0fbdf18080050ff63","source":{"kind":"arxiv","id":"1911.05080","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1911.05080","created_at":"2026-07-05T00:37:18Z"},{"alias_kind":"arxiv_version","alias_value":"1911.05080v2","created_at":"2026-07-05T00:37:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1911.05080","created_at":"2026-07-05T00:37:18Z"},{"alias_kind":"pith_short_12","alias_value":"DYA3DGQ3GOBP","created_at":"2026-07-05T00:37:18Z"},{"alias_kind":"pith_short_16","alias_value":"DYA3DGQ3GOBP5A5U","created_at":"2026-07-05T00:37:18Z"},{"alias_kind":"pith_short_8","alias_value":"DYA3DGQ3","created_at":"2026-07-05T00:37:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:DYA3DGQ3GOBP5A5USWJ5WSOZ66","target":"record","payload":{"canonical_record":{"source":{"id":"1911.05080","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-11-12T19:00:01Z","cross_cats_sorted":[],"title_canon_sha256":"b9a8b3641b368a62fd17ae80807d45192adf36c28c13a80be4ffc03778ecbd40","abstract_canon_sha256":"892d841a8a28bdba8de1ffe01b13257855fb79607a08c1935a878453c1794ccb"},"schema_version":"1.0"},"canonical_sha256":"1e01b19a1b3382fe83b49593db49d9f793ad2965de9a97e0fbdf18080050ff63","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:37:18.674407Z","signature_b64":"fv6ghYjE6cL+aKHWiywK4RtDvuptx5DiuY4Jzz9p9uOXGHIOqcKasjFPOOYqt4gBfi//Jd0KxQCycy5DuYkJBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1e01b19a1b3382fe83b49593db49d9f793ad2965de9a97e0fbdf18080050ff63","last_reissued_at":"2026-07-05T00:37:18.674041Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:37:18.674041Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1911.05080","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T00:37:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Si9vmrqWqGC6NVsBK2UqljkY1hvfI56CtCTKkng3c2Vs2gezPRdFgsWRq90xYsd+S0PPbB78y5oyQpnjt/DfBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T20:20:50.167606Z"},"content_sha256":"a4b5b2d9c2f24263e47d52a86cce12c812f5f14ab3cd25459e1a1301b7c81c34","schema_version":"1.0","event_id":"sha256:a4b5b2d9c2f24263e47d52a86cce12c812f5f14ab3cd25459e1a1301b7c81c34"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:DYA3DGQ3GOBP5A5USWJ5WSOZ66","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Undoing decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"E. Sharpe","submitted_at":"2019-11-12T19:00:01Z","abstract_excerpt":"In this paper we discuss gauging one-form symmetries in two-dimensional theories. The existence of a global one-form symmetry in two dimensions typically signals a violation of cluster decomposition -- an issue resolved by the observation that such theories decompose into disjoint unions, a result that has been applied to, for example, Gromov-Witten theory and gauged linear sigma model phases. In this paper we describe how gauging one-form symmetries in two-dimensional theories can be used to select particular elements of that disjoint union, effectively undoing decomposition. We examine such "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1911.05080","kind":"arxiv","version":2},"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/1911.05080/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":"2026-07-05T00:37:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yXSx4ecOPp9Ptnf2B3zZ98cUchFcTHPdew3pLOvwUy5/9FadKJnETBCUMe571lwq9uLZKkzZVDNsxqcX5JlGAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T20:20:50.168136Z"},"content_sha256":"51ddce962dda9772aabe3b586fc6e68582aa6757d6d7bdaaf6c761982f080ac5","schema_version":"1.0","event_id":"sha256:51ddce962dda9772aabe3b586fc6e68582aa6757d6d7bdaaf6c761982f080ac5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DYA3DGQ3GOBP5A5USWJ5WSOZ66/bundle.json","state_url":"https://pith.science/pith/DYA3DGQ3GOBP5A5USWJ5WSOZ66/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DYA3DGQ3GOBP5A5USWJ5WSOZ66/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":"2026-08-12T20:20:50Z","links":{"resolver":"https://pith.science/pith/DYA3DGQ3GOBP5A5USWJ5WSOZ66","bundle":"https://pith.science/pith/DYA3DGQ3GOBP5A5USWJ5WSOZ66/bundle.json","state":"https://pith.science/pith/DYA3DGQ3GOBP5A5USWJ5WSOZ66/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DYA3DGQ3GOBP5A5USWJ5WSOZ66/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:DYA3DGQ3GOBP5A5USWJ5WSOZ66","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":"892d841a8a28bdba8de1ffe01b13257855fb79607a08c1935a878453c1794ccb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-11-12T19:00:01Z","title_canon_sha256":"b9a8b3641b368a62fd17ae80807d45192adf36c28c13a80be4ffc03778ecbd40"},"schema_version":"1.0","source":{"id":"1911.05080","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1911.05080","created_at":"2026-07-05T00:37:18Z"},{"alias_kind":"arxiv_version","alias_value":"1911.05080v2","created_at":"2026-07-05T00:37:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1911.05080","created_at":"2026-07-05T00:37:18Z"},{"alias_kind":"pith_short_12","alias_value":"DYA3DGQ3GOBP","created_at":"2026-07-05T00:37:18Z"},{"alias_kind":"pith_short_16","alias_value":"DYA3DGQ3GOBP5A5U","created_at":"2026-07-05T00:37:18Z"},{"alias_kind":"pith_short_8","alias_value":"DYA3DGQ3","created_at":"2026-07-05T00:37:18Z"}],"graph_snapshots":[{"event_id":"sha256:51ddce962dda9772aabe3b586fc6e68582aa6757d6d7bdaaf6c761982f080ac5","target":"graph","created_at":"2026-07-05T00:37:18Z","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/1911.05080/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we discuss gauging one-form symmetries in two-dimensional theories. The existence of a global one-form symmetry in two dimensions typically signals a violation of cluster decomposition -- an issue resolved by the observation that such theories decompose into disjoint unions, a result that has been applied to, for example, Gromov-Witten theory and gauged linear sigma model phases. In this paper we describe how gauging one-form symmetries in two-dimensional theories can be used to select particular elements of that disjoint union, effectively undoing decomposition. We examine such ","authors_text":"E. Sharpe","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-11-12T19:00:01Z","title":"Undoing decomposition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1911.05080","kind":"arxiv","version":2},"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:a4b5b2d9c2f24263e47d52a86cce12c812f5f14ab3cd25459e1a1301b7c81c34","target":"record","created_at":"2026-07-05T00:37:18Z","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":"892d841a8a28bdba8de1ffe01b13257855fb79607a08c1935a878453c1794ccb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-11-12T19:00:01Z","title_canon_sha256":"b9a8b3641b368a62fd17ae80807d45192adf36c28c13a80be4ffc03778ecbd40"},"schema_version":"1.0","source":{"id":"1911.05080","kind":"arxiv","version":2}},"canonical_sha256":"1e01b19a1b3382fe83b49593db49d9f793ad2965de9a97e0fbdf18080050ff63","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1e01b19a1b3382fe83b49593db49d9f793ad2965de9a97e0fbdf18080050ff63","first_computed_at":"2026-07-05T00:37:18.674041Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:37:18.674041Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fv6ghYjE6cL+aKHWiywK4RtDvuptx5DiuY4Jzz9p9uOXGHIOqcKasjFPOOYqt4gBfi//Jd0KxQCycy5DuYkJBg==","signature_status":"signed_v1","signed_at":"2026-07-05T00:37:18.674407Z","signed_message":"canonical_sha256_bytes"},"source_id":"1911.05080","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a4b5b2d9c2f24263e47d52a86cce12c812f5f14ab3cd25459e1a1301b7c81c34","sha256:51ddce962dda9772aabe3b586fc6e68582aa6757d6d7bdaaf6c761982f080ac5"],"state_sha256":"c5daae09c4c690f613bdc3af019baf6b40c6f5d34a2a1540444d1d44b5364438"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0jNEwtPfiGai4UKB0sO4kDa7GPHHU2OOly4hjFUD/EfpHAMGIuLEAXrS9JKflSde343bulFhPAPlVo2nzepACQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T20:20:50.172531Z","bundle_sha256":"c4fea5ac9fa08f39f61131fe188fdb928235d588cb580e6ee30582b94bc3ea97"}}