{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:GV4XL7F2K4T3326NH6VC62SEVU","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":"34e1a7b31a0a0a7ab2334aa06b139d086ee618a98837a9e4890f61d8f76c190d","cross_cats_sorted":["cond-mat.stat-mech","hep-th","math-ph","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2006-05-12T17:22:54Z","title_canon_sha256":"ea22574ee2cfad8a47f14a50d095afaccc9240fafa68d2b37039e82517559b51"},"schema_version":"1.0","source":{"id":"cond-mat/0605316","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0605316","created_at":"2026-05-18T02:39:30Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0605316v3","created_at":"2026-05-18T02:39:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0605316","created_at":"2026-05-18T02:39:30Z"},{"alias_kind":"pith_short_12","alias_value":"GV4XL7F2K4T3","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"GV4XL7F2K4T3326N","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"GV4XL7F2","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:6605e75059620830da544bb8db8a0f170b26834997b585fce2574592e2cd941f","target":"graph","created_at":"2026-05-18T02:39:30Z","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 prove sufficient conditions for Topological Quantum Order at both zero and finite temperatures. The crux of the proof hinges on the existence of low-dimensional Gauge-Like Symmetries (that notably extend and differ from standard local gauge symmetries) and their associated defects, thus providing a unifying framework based on a symmetry principle. These symmetries may be actual invariances of the system, or may emerge in the low-energy sector. Prominent examples of Topological Quantum Order display Gauge-Like Symmetries. New systems exhibiting such symmetries include Hamiltonians depicting ","authors_text":"Gerardo Ortiz, Zohar Nussinov","cross_cats":["cond-mat.stat-mech","hep-th","math-ph","math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2006-05-12T17:22:54Z","title":"Symmetry and Topological Order"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0605316","kind":"arxiv","version":3},"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":"sha256:8636800e33795e2c0b6771c91e43b95a906571decad012d5e0c5f1240f331b60","target":"record","created_at":"2026-05-18T02:39:30Z","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":"34e1a7b31a0a0a7ab2334aa06b139d086ee618a98837a9e4890f61d8f76c190d","cross_cats_sorted":["cond-mat.stat-mech","hep-th","math-ph","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2006-05-12T17:22:54Z","title_canon_sha256":"ea22574ee2cfad8a47f14a50d095afaccc9240fafa68d2b37039e82517559b51"},"schema_version":"1.0","source":{"id":"cond-mat/0605316","kind":"arxiv","version":3}},"canonical_sha256":"357975fcba5727bdebcd3faa2f6a44ad27fb770570c3fda1be7aa13c52f049fa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"357975fcba5727bdebcd3faa2f6a44ad27fb770570c3fda1be7aa13c52f049fa","first_computed_at":"2026-05-18T02:39:30.794031Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:39:30.794031Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O1c4fnaFysdVaDcYaCylrZ1iTZTCIFAZ6LBobUJoMr+5+RlqrW5V8YuC8iMxAHpUoNOXQAB+A1dUBMeOKeQgBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:39:30.794525Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/0605316","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8636800e33795e2c0b6771c91e43b95a906571decad012d5e0c5f1240f331b60","sha256:6605e75059620830da544bb8db8a0f170b26834997b585fce2574592e2cd941f"],"state_sha256":"4ae3a6884b3eab714579b3fc46e3d88896b87999660ab1de6436e45ba69273ee"}