{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:XCBY3FMJSFVN6SU3FCDHM7Q6DY","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":"ddb12378a2ae4792c7a2a9f2f680cf0d5ca15a77033f5833463eb5a5e883c11c","cross_cats_sorted":["cond-mat.quant-gas","cond-mat.stat-mech","hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2018-05-17T17:55:43Z","title_canon_sha256":"d0fe14378317dfcaa5d1afcefe8b27653e250547380d6a5614e4a1cba61823a8"},"schema_version":"1.0","source":{"id":"1805.06885","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.06885","created_at":"2026-07-05T00:16:57Z"},{"alias_kind":"arxiv_version","alias_value":"1805.06885v3","created_at":"2026-07-05T00:16:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.06885","created_at":"2026-07-05T00:16:57Z"},{"alias_kind":"pith_short_12","alias_value":"XCBY3FMJSFVN","created_at":"2026-07-05T00:16:57Z"},{"alias_kind":"pith_short_16","alias_value":"XCBY3FMJSFVN6SU3","created_at":"2026-07-05T00:16:57Z"},{"alias_kind":"pith_short_8","alias_value":"XCBY3FMJ","created_at":"2026-07-05T00:16:57Z"}],"graph_snapshots":[{"event_id":"sha256:741adf8a11e7399c6d22c21f8f8db7b7c737305695a4418e034cae148821cd95","target":"graph","created_at":"2026-07-05T00:16:57Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1805.06885/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study $(1+1)$-dimensional $SU(N)$ spin systems in the presence of the global $SU(N)$ rotation and lattice translation symmetries. By matching the mixed anomaly of the $PSU(N)\\times\\mathbb{Z}$ symmetry in the continuum limit, we identify a topological index for spin model evaluated as the total number of Young-tableaux boxes of spins per unit cell modulo $N$, which characterizes the \"ingappability\" of the system. A nontrivial index implies either a ground-state degeneracy in a gapped phase, which can be regarded as a field-theory version of the Lieb-Schultz-Mattis theorem, or a restriction o","authors_text":"Chang-Tse Hsieh, Masaki Oshikawa, Yuan Yao","cross_cats":["cond-mat.quant-gas","cond-mat.stat-mech","hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2018-05-17T17:55:43Z","title":"Anomaly matching and symmetry-protected critical phases in $SU(N)$ spin systems in 1+1 dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.06885","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":"sha256:9b52327567eb0bbde3cac3b34856b7837ff062a7727af0ee2a7c140ded6a527e","target":"record","created_at":"2026-07-05T00:16:57Z","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":"ddb12378a2ae4792c7a2a9f2f680cf0d5ca15a77033f5833463eb5a5e883c11c","cross_cats_sorted":["cond-mat.quant-gas","cond-mat.stat-mech","hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2018-05-17T17:55:43Z","title_canon_sha256":"d0fe14378317dfcaa5d1afcefe8b27653e250547380d6a5614e4a1cba61823a8"},"schema_version":"1.0","source":{"id":"1805.06885","kind":"arxiv","version":3}},"canonical_sha256":"b8838d9589916adf4a9b2886767e1e1e3a29c39a9d081252796e0bd837f21349","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b8838d9589916adf4a9b2886767e1e1e3a29c39a9d081252796e0bd837f21349","first_computed_at":"2026-07-05T00:16:57.836887Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:16:57.836887Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PQY4GOq3hAbXYpteFCmuWgORn4RsqPrrNxyQOz3duOn9mS3U+6d/Wr7ec43TVIJhGuY6l6K4PD7M+cZXsALMDw==","signature_status":"signed_v1","signed_at":"2026-07-05T00:16:57.837483Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.06885","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9b52327567eb0bbde3cac3b34856b7837ff062a7727af0ee2a7c140ded6a527e","sha256:741adf8a11e7399c6d22c21f8f8db7b7c737305695a4418e034cae148821cd95"],"state_sha256":"a22df25accf2f998ea6006a83088d8320a660e8b1e8bda6481bc812c4f7bef4f"}