{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:LJB6K3MER6HLC7FYYQDG7VYDDR","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":"2575df39384bfa668b8a97079f02730142adc44d3788514b1bed87994d57592c","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2014-06-19T15:54:28Z","title_canon_sha256":"76e4d00bb407f51eefea53e7f8db928558a1d2d5c64e0fbbed7a02d1d89aa238"},"schema_version":"1.0","source":{"id":"1406.5090","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.5090","created_at":"2026-05-18T01:42:52Z"},{"alias_kind":"arxiv_version","alias_value":"1406.5090v2","created_at":"2026-05-18T01:42:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.5090","created_at":"2026-05-18T01:42:52Z"},{"alias_kind":"pith_short_12","alias_value":"LJB6K3MER6HL","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"LJB6K3MER6HLC7FY","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"LJB6K3ME","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:ab1e83d926001ab5799e314f5388b450136c12b856d61716760d27c5241b4dab","target":"graph","created_at":"2026-05-18T01:42:52Z","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":"In this work we present some new understanding of topological order, including three main aspects: (1) It was believed that classifying topological orders corresponds to classifying gapped quantum states. We show that such a statement is not precise. We introduce the concept of \\emph{gapped quantum liquid} as a special kind of gapped quantum states that can \"dissolve\" any product states on additional sites. Topologically ordered states actually correspond to gapped quantum liquids with stable ground-state degeneracy. Symmetry-breaking states for on-site symmetry are also gapped quantum liquids","authors_text":"Bei Zeng, Xiao-Gang Wen","cross_cats":["quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2014-06-19T15:54:28Z","title":"Gapped quantum liquids and topological order, stochastic local transformations and emergence of unitarity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.5090","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:c1977db44022f297396e33a71fa880dfd9ac3fe4ff1879c3dba10de6e7b23636","target":"record","created_at":"2026-05-18T01:42:52Z","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":"2575df39384bfa668b8a97079f02730142adc44d3788514b1bed87994d57592c","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2014-06-19T15:54:28Z","title_canon_sha256":"76e4d00bb407f51eefea53e7f8db928558a1d2d5c64e0fbbed7a02d1d89aa238"},"schema_version":"1.0","source":{"id":"1406.5090","kind":"arxiv","version":2}},"canonical_sha256":"5a43e56d848f8eb17cb8c4066fd7031c5ae61a78b022a28b1b88e302c7ec4a5e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5a43e56d848f8eb17cb8c4066fd7031c5ae61a78b022a28b1b88e302c7ec4a5e","first_computed_at":"2026-05-18T01:42:52.985531Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:42:52.985531Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Y3+rXATFbFt7WmHq+1MlASpN7QnGyQX6NEXsU1Ig19MdtqrHzSA3DsPA7p11/J1KBNL/wSnItEkBXBeg7lB/CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:42:52.986190Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.5090","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c1977db44022f297396e33a71fa880dfd9ac3fe4ff1879c3dba10de6e7b23636","sha256:ab1e83d926001ab5799e314f5388b450136c12b856d61716760d27c5241b4dab"],"state_sha256":"6b4dca1a5e1dc611b6025ed432872cccffbf596e989bb9d6d7289447d97d69f3"}