{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:CAIOEP5U3OQ7RWKKLNOXS2LUND","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":"a9ff5eb92ac28e9c86836d0c037d9cdd282a5141577a089c5d96972259c75f09","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2018-08-28T16:30:24Z","title_canon_sha256":"dff81a80dbb6e381a89b1b758b09dbf010adfa50126fb3eb32bcc60bd7fc2fd2"},"schema_version":"1.0","source":{"id":"1808.09394","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.09394","created_at":"2026-05-17T23:40:34Z"},{"alias_kind":"arxiv_version","alias_value":"1808.09394v1","created_at":"2026-05-17T23:40:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.09394","created_at":"2026-05-17T23:40:34Z"},{"alias_kind":"pith_short_12","alias_value":"CAIOEP5U3OQ7","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"CAIOEP5U3OQ7RWKK","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"CAIOEP5U","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:442664a9fb12c3c4add02e6e24eac538525b791abf6db54801f50802673a45e4","target":"graph","created_at":"2026-05-17T23:40:34Z","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":"A discrete non-linear $\\sigma$-model is obtained by triangulate both the space-time $M^{d+1}$ and the target space $K$. If the path integral is given by the sum of all the complex homomorphisms $\\phi: M^{d+1} \\to K$, with an partition function that is independent of space-time triangulation, then the corresponding non-linear $\\sigma$-model will be called topological non-linear $\\sigma$-model which is exactly soluble. Those exactly soluble models suggest that phase transitions induced by fluctuations with no topological defects (i.e. fluctuations described by homomorphisms $\\phi$) usually produ","authors_text":"Chenchang Zhu, Tian Lan, Xiao-Gang Wen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2018-08-28T16:30:24Z","title":"Topological non-linear $\\sigma$-model, higher gauge theory, and a realization of all 3+1D topological orders for boson systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.09394","kind":"arxiv","version":1},"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":"sha256:3781230f95002e45e83fa91ecab44f5434e87ece1c36ce495f1170ed5ac1742c","target":"record","created_at":"2026-05-17T23:40:34Z","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":"a9ff5eb92ac28e9c86836d0c037d9cdd282a5141577a089c5d96972259c75f09","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2018-08-28T16:30:24Z","title_canon_sha256":"dff81a80dbb6e381a89b1b758b09dbf010adfa50126fb3eb32bcc60bd7fc2fd2"},"schema_version":"1.0","source":{"id":"1808.09394","kind":"arxiv","version":1}},"canonical_sha256":"1010e23fb4dba1f8d94a5b5d79697468cec06ba934dfae544b0adb79bd6d3d2a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1010e23fb4dba1f8d94a5b5d79697468cec06ba934dfae544b0adb79bd6d3d2a","first_computed_at":"2026-05-17T23:40:34.488888Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:34.488888Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/lJ6mkDOo71JhWaYZoTnWL43GHW3YB4QCXbw5jD39vWl0PZFMU8soMi+UAIGahGub3+NDk4UH9Mxihg2Z7aCDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:34.489357Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.09394","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3781230f95002e45e83fa91ecab44f5434e87ece1c36ce495f1170ed5ac1742c","sha256:442664a9fb12c3c4add02e6e24eac538525b791abf6db54801f50802673a45e4"],"state_sha256":"6ca27f2c1c7786012c264ad6932fa01502cad3ca6761966c1385294fcb97b5b9"}