{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:J46E6NP4B3G3SRVFDQOL2KQRD3","short_pith_number":"pith:J46E6NP4","schema_version":"1.0","canonical_sha256":"4f3c4f35fc0ecdb946a51c1cbd2a111ec59ee0417c1278c6767ee18f2fb3b2ed","source":{"kind":"arxiv","id":"1101.1054","version":2},"attestation_state":"computed","paper":{"title":"Clifford modules and symmetries of topological insulators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.other","math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Gilles Abramovici (LPS), Pavel Kalugin (LPS)","submitted_at":"2011-01-05T19:41:38Z","abstract_excerpt":"We complete the classification of symmetry constraints on gapped quadratic fermion hamiltonians proposed by Kitaev. The symmetry group is supposed compact and can include arbitrary unitary or antiunitary operators in the Fock space that conserve the algebra of quadratic observables. We analyze the multiplicity spaces of {\\em real} irreducible representations of unitary symmetries in the Nambu space. The joint action of intertwining operators and antiunitary symmetries provides these spaces with the structure of Clifford module: we prove a one-to-one correspondence between the ten Altland-Zirnb"},"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":"1101.1054","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-01-05T19:41:38Z","cross_cats_sorted":["cond-mat.other","math.MP","quant-ph"],"title_canon_sha256":"0fea519a2240e856389aecb5b719c110e73ca9a7af1364f626cc0d7892e79da8","abstract_canon_sha256":"fde5707bf243c5fb23e830fddbc6f6a517ff442f3e2ebadf290c557e2bf5cf9a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:21:52.812531Z","signature_b64":"OEHY73qmt4SLU+I95TSFT2kkoCWhp3iiQSEPCnIxDF++StPN0JKR/CIGLFzVSHVe37rIbg/YkHLPA5nHPqBMBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4f3c4f35fc0ecdb946a51c1cbd2a111ec59ee0417c1278c6767ee18f2fb3b2ed","last_reissued_at":"2026-05-18T04:21:52.811917Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:21:52.811917Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Clifford modules and symmetries of topological insulators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.other","math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Gilles Abramovici (LPS), Pavel Kalugin (LPS)","submitted_at":"2011-01-05T19:41:38Z","abstract_excerpt":"We complete the classification of symmetry constraints on gapped quadratic fermion hamiltonians proposed by Kitaev. The symmetry group is supposed compact and can include arbitrary unitary or antiunitary operators in the Fock space that conserve the algebra of quadratic observables. We analyze the multiplicity spaces of {\\em real} irreducible representations of unitary symmetries in the Nambu space. The joint action of intertwining operators and antiunitary symmetries provides these spaces with the structure of Clifford module: we prove a one-to-one correspondence between the ten Altland-Zirnb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.1054","kind":"arxiv","version":2},"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":"1101.1054","created_at":"2026-05-18T04:21:52.812003+00:00"},{"alias_kind":"arxiv_version","alias_value":"1101.1054v2","created_at":"2026-05-18T04:21:52.812003+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.1054","created_at":"2026-05-18T04:21:52.812003+00:00"},{"alias_kind":"pith_short_12","alias_value":"J46E6NP4B3G3","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_16","alias_value":"J46E6NP4B3G3SRVF","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_8","alias_value":"J46E6NP4","created_at":"2026-05-18T12:26:32.869790+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/J46E6NP4B3G3SRVFDQOL2KQRD3","json":"https://pith.science/pith/J46E6NP4B3G3SRVFDQOL2KQRD3.json","graph_json":"https://pith.science/api/pith-number/J46E6NP4B3G3SRVFDQOL2KQRD3/graph.json","events_json":"https://pith.science/api/pith-number/J46E6NP4B3G3SRVFDQOL2KQRD3/events.json","paper":"https://pith.science/paper/J46E6NP4"},"agent_actions":{"view_html":"https://pith.science/pith/J46E6NP4B3G3SRVFDQOL2KQRD3","download_json":"https://pith.science/pith/J46E6NP4B3G3SRVFDQOL2KQRD3.json","view_paper":"https://pith.science/paper/J46E6NP4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1101.1054&json=true","fetch_graph":"https://pith.science/api/pith-number/J46E6NP4B3G3SRVFDQOL2KQRD3/graph.json","fetch_events":"https://pith.science/api/pith-number/J46E6NP4B3G3SRVFDQOL2KQRD3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/J46E6NP4B3G3SRVFDQOL2KQRD3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/J46E6NP4B3G3SRVFDQOL2KQRD3/action/storage_attestation","attest_author":"https://pith.science/pith/J46E6NP4B3G3SRVFDQOL2KQRD3/action/author_attestation","sign_citation":"https://pith.science/pith/J46E6NP4B3G3SRVFDQOL2KQRD3/action/citation_signature","submit_replication":"https://pith.science/pith/J46E6NP4B3G3SRVFDQOL2KQRD3/action/replication_record"}},"created_at":"2026-05-18T04:21:52.812003+00:00","updated_at":"2026-05-18T04:21:52.812003+00:00"}