{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:MIFRVONPV2UEQLLJITXEUU37QR","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":"1845406dfeff97874d45fa0aa730abbf8047127203bcb67db32ab8c87abc8ed6","cross_cats_sorted":["hep-lat","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2026-01-31T01:16:53Z","title_canon_sha256":"ebbc5ef119ce9b3f5e5ca10e1599cbf53a77fa93660ccd94ff5e65e32f508b70"},"schema_version":"1.0","source":{"id":"2602.00436","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2602.00436","created_at":"2026-06-10T01:08:32Z"},{"alias_kind":"arxiv_version","alias_value":"2602.00436v2","created_at":"2026-06-10T01:08:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.00436","created_at":"2026-06-10T01:08:32Z"},{"alias_kind":"pith_short_12","alias_value":"MIFRVONPV2UE","created_at":"2026-06-10T01:08:32Z"},{"alias_kind":"pith_short_16","alias_value":"MIFRVONPV2UEQLLJ","created_at":"2026-06-10T01:08:32Z"},{"alias_kind":"pith_short_8","alias_value":"MIFRVONP","created_at":"2026-06-10T01:08:32Z"}],"graph_snapshots":[{"event_id":"sha256:b8960eb515e572387e084adcbeb877ca685f33f02fbfee44d8b049655fc34218","target":"graph","created_at":"2026-06-10T01:08:32Z","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/2602.00436/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Pure lattice gauge theories in three dimensions are widely expected to confine. A rigorous proof of confinement for three-dimensional $\\mathrm{U}(1)$ lattice gauge theory with Villain action was given by G\\\"opfert and Mack. Beyond the abelian case, rigorous confinement results are comparatively scarce; one general mechanism applies when the gauge group has a central copy of $\\mathrm{U}(1)$. Indeed, combining a comparison inequality of Fr{\\\"o}hlich with earlier work of Glimm and Jaffe yields confinement with a logarithmically growing quark-antiquark potential for this class of theories. The pur","authors_text":"Sourav Chatterjee","cross_cats":["hep-lat","math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2026-01-31T01:16:53Z","title":"A short proof of confinement in three-dimensional lattice gauge theories with a central $\\mathrm{U}(1)$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.00436","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":"sha256:196c98ff2f6b042f268e7b4f2f9d134cb594ce422bb04f7df6966a31db5a5994","target":"record","created_at":"2026-06-10T01:08:32Z","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":"1845406dfeff97874d45fa0aa730abbf8047127203bcb67db32ab8c87abc8ed6","cross_cats_sorted":["hep-lat","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2026-01-31T01:16:53Z","title_canon_sha256":"ebbc5ef119ce9b3f5e5ca10e1599cbf53a77fa93660ccd94ff5e65e32f508b70"},"schema_version":"1.0","source":{"id":"2602.00436","kind":"arxiv","version":2}},"canonical_sha256":"620b1ab9afaea8482d6944ee4a537f8465e1a3b8067dd0cec588e74cc6647cf2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"620b1ab9afaea8482d6944ee4a537f8465e1a3b8067dd0cec588e74cc6647cf2","first_computed_at":"2026-06-10T01:08:32.913034Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-10T01:08:32.913034Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yd8p1H1ESHog1LQ+KRL4oWVtDXHX3FNmtngLCdqVdO9Gyd+B7nFTMK4uCG96WAKtO9cMQOzbNCp5ZdZfnPJaCw==","signature_status":"signed_v1","signed_at":"2026-06-10T01:08:32.914138Z","signed_message":"canonical_sha256_bytes"},"source_id":"2602.00436","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:196c98ff2f6b042f268e7b4f2f9d134cb594ce422bb04f7df6966a31db5a5994","sha256:b8960eb515e572387e084adcbeb877ca685f33f02fbfee44d8b049655fc34218"],"state_sha256":"a04b2d35f997ad4e52d7425a2c1dd7f12082cd084ba71fe557162e949a8653dd"}