{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:WJFSLD4UHOCQ3IDTS32ACX326M","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":"7c1a19adf2eea6ee2683496c9ac19a5748a43764ad70c79171653d66639fb05c","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-lat","submitted_at":"2014-12-04T18:47:59Z","title_canon_sha256":"0d7f34d8643278139357c3db225984669caa90180b90b04d9e993f97e36706ac"},"schema_version":"1.0","source":{"id":"1412.1762","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.1762","created_at":"2026-05-18T01:41:23Z"},{"alias_kind":"arxiv_version","alias_value":"1412.1762v2","created_at":"2026-05-18T01:41:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.1762","created_at":"2026-05-18T01:41:23Z"},{"alias_kind":"pith_short_12","alias_value":"WJFSLD4UHOCQ","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"WJFSLD4UHOCQ3IDT","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"WJFSLD4U","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:4b557cbf83d72b3aff86b5c7928c8d1f1d8104bf2ff9f42253d1b7ea2372ccbb","target":"graph","created_at":"2026-05-18T01:41:23Z","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"},"paper":{"abstract_excerpt":"We study, for $SU(2)$ Yang-Mills theories discretized on a lattice, a non-local topological order parameter, the center flux ${{z}}$. We show that: i) well defined topological sectors classified by $\\pi_1(SO(3))=\\mathbb{Z}_2$ can only exist in the ordered phase of ${{z}}$; ii) depending on the dimension $2 \\leq d\\leq 4$ and action chosen, the center flux exhibits a critical behaviour sharing striking features with the Kosterlitz-Thouless type of transitions, although belonging to a novel universality class; iii) such critical behaviour does not depend on the temperature $T$. Yang-Mills theorie","authors_text":"Giuseppe Burgio, Hugo Reinhardt","cross_cats":["hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-lat","submitted_at":"2014-12-04T18:47:59Z","title":"Topological order and the vacuum of Yang-Mills theories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.1762","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":"sha256:502356a13469bf48618371ca7aa068cc6c1a057d190bf49013938f25588bb949","target":"record","created_at":"2026-05-18T01:41:23Z","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":"7c1a19adf2eea6ee2683496c9ac19a5748a43764ad70c79171653d66639fb05c","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-lat","submitted_at":"2014-12-04T18:47:59Z","title_canon_sha256":"0d7f34d8643278139357c3db225984669caa90180b90b04d9e993f97e36706ac"},"schema_version":"1.0","source":{"id":"1412.1762","kind":"arxiv","version":2}},"canonical_sha256":"b24b258f943b850da07396f4015f7af330634eacc24b3513922985a0aada89ec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b24b258f943b850da07396f4015f7af330634eacc24b3513922985a0aada89ec","first_computed_at":"2026-05-18T01:41:23.212018Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:41:23.212018Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LFYMwUbXLn8qwEEqK0dOnfZNdzQCuaT/4MntL6n/56MeABDZZXf8JnQhXs65W3H8xPAw1nVSZ6sDD9FcyNcMDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:41:23.212721Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.1762","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:502356a13469bf48618371ca7aa068cc6c1a057d190bf49013938f25588bb949","sha256:4b557cbf83d72b3aff86b5c7928c8d1f1d8104bf2ff9f42253d1b7ea2372ccbb"],"state_sha256":"5887a0d7ef499bebae9dde70863367b79b34039e25ee970ef32ec0da477aa4f8"}