{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:SPELK3JMLSAAJ2YSP6MGKG5QOT","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":"c39ff1a057afc28bc916d3d6d87c8ddb3028bb0df1b518e71b8887a98b5ed96e","cross_cats_sorted":["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":"2012-01-12T19:06:34Z","title_canon_sha256":"fbe9850d42accf035304cdd9a9e8655a3092eabea9f8a78411a7126ed931717d"},"schema_version":"1.0","source":{"id":"1201.2648","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.2648","created_at":"2026-05-18T02:42:06Z"},{"alias_kind":"arxiv_version","alias_value":"1201.2648v4","created_at":"2026-05-18T02:42:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.2648","created_at":"2026-05-18T02:42:06Z"},{"alias_kind":"pith_short_12","alias_value":"SPELK3JMLSAA","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"SPELK3JMLSAAJ2YS","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"SPELK3JM","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:4e60b733e8548f31fb063915fa78cdf015f120e2bac688422cddb9e63ec4057d","target":"graph","created_at":"2026-05-18T02:42:06Z","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":"Symmetry-protected topological (SPT) phases are gapped short-range-entangled quantum phases with a symmetry $G$, which can all be smoothly connected to the trivial product states if we break the symmetry. It has been shown that a large class of interacting bosonic SPT phases can be systematically described by group cohomology theory. In this paper, we introduce a (special) group supercohomology theory which is a generalization of the standard group cohomology theory. We show that a large class of short-range interacting fermionic SPT phases can be described by the group supercohomology theory.","authors_text":"Xiao-Gang Wen, Zheng-Cheng Gu","cross_cats":["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":"2012-01-12T19:06:34Z","title":"Symmetry-protected topological orders for interacting fermions -- Fermionic topological nonlinear $\\sigma$ models and a special group supercohomology theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.2648","kind":"arxiv","version":4},"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":"sha256:20fbb6e9b4f0128e11faec51a75f42565ee12f48705ca2b7f4c8d133980b00b5","target":"record","created_at":"2026-05-18T02:42:06Z","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":"c39ff1a057afc28bc916d3d6d87c8ddb3028bb0df1b518e71b8887a98b5ed96e","cross_cats_sorted":["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":"2012-01-12T19:06:34Z","title_canon_sha256":"fbe9850d42accf035304cdd9a9e8655a3092eabea9f8a78411a7126ed931717d"},"schema_version":"1.0","source":{"id":"1201.2648","kind":"arxiv","version":4}},"canonical_sha256":"93c8b56d2c5c8004eb127f98651bb074d1f915cf230dbecbc32b7df4cce9ae41","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"93c8b56d2c5c8004eb127f98651bb074d1f915cf230dbecbc32b7df4cce9ae41","first_computed_at":"2026-05-18T02:42:06.361411Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:42:06.361411Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z4jwzKIaZkOgQUoTuo6OljY3r3o9XmfDWfdeONIcVjQDFw2Ro1BLDz/Ihf9QLmJ87JZQdSpnefW5QSnF+0n3CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:42:06.361926Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.2648","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:20fbb6e9b4f0128e11faec51a75f42565ee12f48705ca2b7f4c8d133980b00b5","sha256:4e60b733e8548f31fb063915fa78cdf015f120e2bac688422cddb9e63ec4057d"],"state_sha256":"0f129bc2664b0b290d8960e4a0719d6bd6f10c73ab752f4ec44134149295276e"}