{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:P2YAOZINIVKE2YYWWBL2QGB46R","short_pith_number":"pith:P2YAOZIN","schema_version":"1.0","canonical_sha256":"7eb007650d45544d6316b057a8183cf447ff604550bb4bc83c6a05bb09598d0a","source":{"kind":"arxiv","id":"2409.00502","version":2},"attestation_state":"computed","paper":{"title":"Generalized BKT Transitions and Persistent Order on the Lattice","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"hep-lat","authors_text":"Aleksey Cherman, Evan Berkowitz, Seth Buesing, Shi Chen, Srimoyee Sen","submitted_at":"2024-08-31T16:49:58Z","abstract_excerpt":"The BKT transition in low-dimensional systems with a $U(1)$ global symmetry separates a gapless conformal phase from a trivially gapped, disordered phase, and is driven by vortex proliferation. Recent developments in modified Villain discretizations provide a class of lattice models which have a $\\mathbb{Z}_W$ global symmetry that counts vortices mod W, mixed 't Hooft anomalies, and persistent order even at finite lattice spacing. While there is no fully-disordered phase (except in the original BKT limit $W=1$) there is still a phase boundary which separates gapped ordered phases from gapless "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2409.00502","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"hep-lat","submitted_at":"2024-08-31T16:49:58Z","cross_cats_sorted":[],"title_canon_sha256":"38cd130651fda1d95c4c960e7e6ddb991fb60b4a4bbbd509b98cae4c8e8a35fa","abstract_canon_sha256":"03b0d743676d9a0e838e7cb8171e2acebeaeb9c61818e0fe445ef4417b97251a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:08:28.780398Z","signature_b64":"48stgTubdCRerLI6s1TpO+wB4cmlRCQEdrljm9KRdEeXU/ItS9DcZB9gEjxxux8DiR3A0vSFiKZFRdMVY6VPCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7eb007650d45544d6316b057a8183cf447ff604550bb4bc83c6a05bb09598d0a","last_reissued_at":"2026-07-05T09:08:28.779832Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:08:28.779832Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generalized BKT Transitions and Persistent Order on the Lattice","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"hep-lat","authors_text":"Aleksey Cherman, Evan Berkowitz, Seth Buesing, Shi Chen, Srimoyee Sen","submitted_at":"2024-08-31T16:49:58Z","abstract_excerpt":"The BKT transition in low-dimensional systems with a $U(1)$ global symmetry separates a gapless conformal phase from a trivially gapped, disordered phase, and is driven by vortex proliferation. Recent developments in modified Villain discretizations provide a class of lattice models which have a $\\mathbb{Z}_W$ global symmetry that counts vortices mod W, mixed 't Hooft anomalies, and persistent order even at finite lattice spacing. While there is no fully-disordered phase (except in the original BKT limit $W=1$) there is still a phase boundary which separates gapped ordered phases from gapless "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.00502","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/2409.00502/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2409.00502","created_at":"2026-07-05T09:08:28.779896+00:00"},{"alias_kind":"arxiv_version","alias_value":"2409.00502v2","created_at":"2026-07-05T09:08:28.779896+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.00502","created_at":"2026-07-05T09:08:28.779896+00:00"},{"alias_kind":"pith_short_12","alias_value":"P2YAOZINIVKE","created_at":"2026-07-05T09:08:28.779896+00:00"},{"alias_kind":"pith_short_16","alias_value":"P2YAOZINIVKE2YYW","created_at":"2026-07-05T09:08:28.779896+00:00"},{"alias_kind":"pith_short_8","alias_value":"P2YAOZIN","created_at":"2026-07-05T09:08:28.779896+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2608.02728","citing_title":"Fermionic Villain model with exact lattice chiral symmetries","ref_index":84,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/P2YAOZINIVKE2YYWWBL2QGB46R","json":"https://pith.science/pith/P2YAOZINIVKE2YYWWBL2QGB46R.json","graph_json":"https://pith.science/api/pith-number/P2YAOZINIVKE2YYWWBL2QGB46R/graph.json","events_json":"https://pith.science/api/pith-number/P2YAOZINIVKE2YYWWBL2QGB46R/events.json","paper":"https://pith.science/paper/P2YAOZIN"},"agent_actions":{"view_html":"https://pith.science/pith/P2YAOZINIVKE2YYWWBL2QGB46R","download_json":"https://pith.science/pith/P2YAOZINIVKE2YYWWBL2QGB46R.json","view_paper":"https://pith.science/paper/P2YAOZIN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2409.00502&json=true","fetch_graph":"https://pith.science/api/pith-number/P2YAOZINIVKE2YYWWBL2QGB46R/graph.json","fetch_events":"https://pith.science/api/pith-number/P2YAOZINIVKE2YYWWBL2QGB46R/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/P2YAOZINIVKE2YYWWBL2QGB46R/action/timestamp_anchor","attest_storage":"https://pith.science/pith/P2YAOZINIVKE2YYWWBL2QGB46R/action/storage_attestation","attest_author":"https://pith.science/pith/P2YAOZINIVKE2YYWWBL2QGB46R/action/author_attestation","sign_citation":"https://pith.science/pith/P2YAOZINIVKE2YYWWBL2QGB46R/action/citation_signature","submit_replication":"https://pith.science/pith/P2YAOZINIVKE2YYWWBL2QGB46R/action/replication_record"}},"created_at":"2026-07-05T09:08:28.779896+00:00","updated_at":"2026-07-05T09:08:28.779896+00:00"}