{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:P6RRGAJWJBN5HQJVRPNTCUBFDU","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":"a1d1df6615ffc5763aa3502cd7ccf4ee6dcb75f4e583b8d3ec220303bb36436f","cross_cats_sorted":["cond-mat.str-el","hep-lat"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2024-01-09T19:49:52Z","title_canon_sha256":"52462f9f3f9da2c93411ded1bb065293b9fd07694031c24cfc7e491c54ea3ad3"},"schema_version":"1.0","source":{"id":"2401.04800","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2401.04800","created_at":"2026-07-05T07:58:26Z"},{"alias_kind":"arxiv_version","alias_value":"2401.04800v2","created_at":"2026-07-05T07:58:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.04800","created_at":"2026-07-05T07:58:26Z"},{"alias_kind":"pith_short_12","alias_value":"P6RRGAJWJBN5","created_at":"2026-07-05T07:58:26Z"},{"alias_kind":"pith_short_16","alias_value":"P6RRGAJWJBN5HQJV","created_at":"2026-07-05T07:58:26Z"},{"alias_kind":"pith_short_8","alias_value":"P6RRGAJW","created_at":"2026-07-05T07:58:26Z"}],"graph_snapshots":[{"event_id":"sha256:72d0bddac4c2030a9f617aa6e8831e1876f837007bca9ce77ecf21a121809560","target":"graph","created_at":"2026-07-05T07:58:26Z","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/2401.04800/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We analyze the phases of theories which only have a microscopic $\\mathbb{Z}_N$ 1-form symmetry, starting with a topological BF theory and deforming it in accordance with microscopic symmetry. These theories have a well-defined notion of confinement. Prototypical examples are pure $SU(N)$ gauge theories and $\\mathbb{Z}_N$ lattice gauge theories. Our analysis shows that the only generic phases are in $d=2$, only the confined phase; in $d=3$, both the confined phase and the topological BF phase; and in $d=4$, the confined phase, the topological BF phase, and a phase with a massless photon. We con","authors_text":"Mendel Nguyen, Mithat \\\"Unsal, Tin Sulejmanpasic","cross_cats":["cond-mat.str-el","hep-lat"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2024-01-09T19:49:52Z","title":"Phases of theories with $\\mathbb{Z}_N$ 1-form symmetry and the roles of center vortices and magnetic monopoles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.04800","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":"sha256:210495ff9426869b4ea63417488c43e614404f7dd2f2e4e749f1b09c81fa5cc2","target":"record","created_at":"2026-07-05T07:58:26Z","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":"a1d1df6615ffc5763aa3502cd7ccf4ee6dcb75f4e583b8d3ec220303bb36436f","cross_cats_sorted":["cond-mat.str-el","hep-lat"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2024-01-09T19:49:52Z","title_canon_sha256":"52462f9f3f9da2c93411ded1bb065293b9fd07694031c24cfc7e491c54ea3ad3"},"schema_version":"1.0","source":{"id":"2401.04800","kind":"arxiv","version":2}},"canonical_sha256":"7fa3130136485bd3c1358bdb3150251d1ffcb8817bb7188e032096f09a56611f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7fa3130136485bd3c1358bdb3150251d1ffcb8817bb7188e032096f09a56611f","first_computed_at":"2026-07-05T07:58:26.471961Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:58:26.471961Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"C35k5fvbLR0+31q6MEQGsyY2O5qUMax8vumm5GLjNeNriHhJpNTbJj37kWnw9/LieuNSto0Uvtb4YRfEWOXnBw==","signature_status":"signed_v1","signed_at":"2026-07-05T07:58:26.472481Z","signed_message":"canonical_sha256_bytes"},"source_id":"2401.04800","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:210495ff9426869b4ea63417488c43e614404f7dd2f2e4e749f1b09c81fa5cc2","sha256:72d0bddac4c2030a9f617aa6e8831e1876f837007bca9ce77ecf21a121809560"],"state_sha256":"1663277b458c612f1caef7d30278272c3f62c8fde9bf2194859265cf93296e99"}