{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:VLMRVZGU6VY3FQ4EXUARQFUNLK","short_pith_number":"pith:VLMRVZGU","schema_version":"1.0","canonical_sha256":"aad91ae4d4f571b2c384bd0118168d5a89f2c7f60aade9d208b5ee718c84f61b","source":{"kind":"arxiv","id":"1606.04544","version":3},"attestation_state":"computed","paper":{"title":"Classification of symmetry fractionalization in gapped $\\mathbb Z_2$ spin liquids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.str-el","authors_text":"Meng Cheng, Yang Qi","submitted_at":"2016-06-14T20:00:22Z","abstract_excerpt":"In quantum spin liquids, fractional spinon excitations carry half-integer spins and other fractional quantum numbers of lattice and time-reversal symmetries. Different patterns of symmetry fractionalization distinguish different spin liquid phases. In this work, we derive a general constraint on the symmetry fractionalization of spinons in a gapped spin liquid, realized in a system with an odd number of spin-$1/2$ per unit cell. In particular, when applied to kagome/triangular lattices, we obtain a complete classification of symmetric gapped $\\mathbb{Z_2}$ spin liquids."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1606.04544","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2016-06-14T20:00:22Z","cross_cats_sorted":[],"title_canon_sha256":"5ce185c63dc3a68ea9462a7d229a39dc80c725217b45bd16181d4bb69920c89e","abstract_canon_sha256":"b99ada9c6caa31f57dce1d260e8fcee071e38a8c84d16471b8ff49b329987329"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:40.180238Z","signature_b64":"xrT+4mAJxwFIxIjZ/gpppAOnzCQ44GmwBwAG/RtG38YW2IkFuSzgMVDOMlK2Q6JAMJqzvzmCNIQZ83+xCaZWDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aad91ae4d4f571b2c384bd0118168d5a89f2c7f60aade9d208b5ee718c84f61b","last_reissued_at":"2026-05-18T00:20:40.179572Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:40.179572Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Classification of symmetry fractionalization in gapped $\\mathbb Z_2$ spin liquids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.str-el","authors_text":"Meng Cheng, Yang Qi","submitted_at":"2016-06-14T20:00:22Z","abstract_excerpt":"In quantum spin liquids, fractional spinon excitations carry half-integer spins and other fractional quantum numbers of lattice and time-reversal symmetries. Different patterns of symmetry fractionalization distinguish different spin liquid phases. In this work, we derive a general constraint on the symmetry fractionalization of spinons in a gapped spin liquid, realized in a system with an odd number of spin-$1/2$ per unit cell. In particular, when applied to kagome/triangular lattices, we obtain a complete classification of symmetric gapped $\\mathbb{Z_2}$ spin liquids."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.04544","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1606.04544","created_at":"2026-05-18T00:20:40.179674+00:00"},{"alias_kind":"arxiv_version","alias_value":"1606.04544v3","created_at":"2026-05-18T00:20:40.179674+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.04544","created_at":"2026-05-18T00:20:40.179674+00:00"},{"alias_kind":"pith_short_12","alias_value":"VLMRVZGU6VY3","created_at":"2026-05-18T12:30:48.956258+00:00"},{"alias_kind":"pith_short_16","alias_value":"VLMRVZGU6VY3FQ4E","created_at":"2026-05-18T12:30:48.956258+00:00"},{"alias_kind":"pith_short_8","alias_value":"VLMRVZGU","created_at":"2026-05-18T12:30:48.956258+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/VLMRVZGU6VY3FQ4EXUARQFUNLK","json":"https://pith.science/pith/VLMRVZGU6VY3FQ4EXUARQFUNLK.json","graph_json":"https://pith.science/api/pith-number/VLMRVZGU6VY3FQ4EXUARQFUNLK/graph.json","events_json":"https://pith.science/api/pith-number/VLMRVZGU6VY3FQ4EXUARQFUNLK/events.json","paper":"https://pith.science/paper/VLMRVZGU"},"agent_actions":{"view_html":"https://pith.science/pith/VLMRVZGU6VY3FQ4EXUARQFUNLK","download_json":"https://pith.science/pith/VLMRVZGU6VY3FQ4EXUARQFUNLK.json","view_paper":"https://pith.science/paper/VLMRVZGU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1606.04544&json=true","fetch_graph":"https://pith.science/api/pith-number/VLMRVZGU6VY3FQ4EXUARQFUNLK/graph.json","fetch_events":"https://pith.science/api/pith-number/VLMRVZGU6VY3FQ4EXUARQFUNLK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VLMRVZGU6VY3FQ4EXUARQFUNLK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VLMRVZGU6VY3FQ4EXUARQFUNLK/action/storage_attestation","attest_author":"https://pith.science/pith/VLMRVZGU6VY3FQ4EXUARQFUNLK/action/author_attestation","sign_citation":"https://pith.science/pith/VLMRVZGU6VY3FQ4EXUARQFUNLK/action/citation_signature","submit_replication":"https://pith.science/pith/VLMRVZGU6VY3FQ4EXUARQFUNLK/action/replication_record"}},"created_at":"2026-05-18T00:20:40.179674+00:00","updated_at":"2026-05-18T00:20:40.179674+00:00"}