{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:W64SR4AYQILXKTNRJF2HXO6O7L","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":"3946980323814161d2398e25d81a4b197b81ade0431f3ab8d41e4eb90be366ae","cross_cats_sorted":["cond-mat.other","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-05-31T02:32:41Z","title_canon_sha256":"e4e59dd2dff8287ef3f1ccd472f417573ae928434001cf79721e6abdb059135d"},"schema_version":"1.0","source":{"id":"1605.09470","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.09470","created_at":"2026-05-18T01:13:17Z"},{"alias_kind":"arxiv_version","alias_value":"1605.09470v1","created_at":"2026-05-18T01:13:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.09470","created_at":"2026-05-18T01:13:17Z"},{"alias_kind":"pith_short_12","alias_value":"W64SR4AYQILX","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"W64SR4AYQILXKTNR","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"W64SR4AY","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:c3ab9aafd81040edc61ea9964dd09d2e40f2456fe5d4070386cb77b49ffdd3c4","target":"graph","created_at":"2026-05-18T01:13:17Z","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":"We generalize the $\\mathbb{Z}_2$ invariant of topological insulators using noncommutative differential geometry in two different ways. First, we model Majorana zero modes by KQ-cycles in the framework of analytic K-homology, and we define the noncommutative $\\mathbb{Z}_2$ invariant as a topological index in noncommutative topology. Second, we look at the geometric picture of the Pfaffian formalism of the $\\mathbb{Z}_2$ invariant, i.e., the Kane--Mele invariant, and we define the noncommutative Kane--Mele invariant over the fixed point algebra of the time reversal symmetry in the noncommutative","authors_text":"Birgit Wehefritz-Kaufmann, Dan Li, Ralph M. Kaufmann","cross_cats":["cond-mat.other","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-05-31T02:32:41Z","title":"Noncommutative topological $\\mathbb{Z}_2$ invariant"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.09470","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":"sha256:8007ed5d1a7010d1e94999e7d196ec1644da81d601fd892d91d5bafe07c6e910","target":"record","created_at":"2026-05-18T01:13:17Z","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":"3946980323814161d2398e25d81a4b197b81ade0431f3ab8d41e4eb90be366ae","cross_cats_sorted":["cond-mat.other","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-05-31T02:32:41Z","title_canon_sha256":"e4e59dd2dff8287ef3f1ccd472f417573ae928434001cf79721e6abdb059135d"},"schema_version":"1.0","source":{"id":"1605.09470","kind":"arxiv","version":1}},"canonical_sha256":"b7b928f0188217754db149747bbbcefafd33c51fc8d2a276a3ec09a4b1119591","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b7b928f0188217754db149747bbbcefafd33c51fc8d2a276a3ec09a4b1119591","first_computed_at":"2026-05-18T01:13:17.215789Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:13:17.215789Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1LuJ8uYbFv0CY5TrYLF1qdoTZJi+i0USP9r1Y58WMK9NCgJLhQ3BhwGxRptUvN8f3qAQhps6LjBLaTm7yr2wBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:13:17.216349Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.09470","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8007ed5d1a7010d1e94999e7d196ec1644da81d601fd892d91d5bafe07c6e910","sha256:c3ab9aafd81040edc61ea9964dd09d2e40f2456fe5d4070386cb77b49ffdd3c4"],"state_sha256":"6b92783876e8f17009272c8090b8f473fa76dddb77137d411734a6b23d5c2bff"}