{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:SMB4U4AXDKZRDIB33FQYDCTQ7E","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":"23bc346ab78c69888bb80d94bebcc26a12774f59c0c22b7ec79b5caded9e693f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-03-20T17:22:56Z","title_canon_sha256":"93b91af363fbb277cb06fe7b4e31fc88af4a1ba17e5fb31d1c4c4914eefc2828"},"schema_version":"1.0","source":{"id":"1503.06170","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.06170","created_at":"2026-05-18T02:20:48Z"},{"alias_kind":"arxiv_version","alias_value":"1503.06170v1","created_at":"2026-05-18T02:20:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.06170","created_at":"2026-05-18T02:20:48Z"},{"alias_kind":"pith_short_12","alias_value":"SMB4U4AXDKZR","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SMB4U4AXDKZRDIB3","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SMB4U4AX","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:ebd49f53d28506eb3619af7290bd734f7747995fbf272a487f661574579b7b26","target":"graph","created_at":"2026-05-18T02:20:48Z","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 give a rigorous account and prove continuity properties for the correspondence between almost flat bundles on a triangularizable compact connected space and the quasi-representations of its fundamental group. For a discrete countable group $\\Gamma$ with finite classifying space $B\\Gamma$, we study a correspondence between between almost flat K-theory classes on $B\\Gamma$ and group homomorphism $K_0(C^*(\\Gamma))\\to \\mathbb{Z}$ that are implemented by pairs of discrete asymptotic homomorphisms from $C^*(\\Gamma)$ to matrix algebras.","authors_text":"Jos\\'e R. Carri\\'on, Marius Dadarlat","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-03-20T17:22:56Z","title":"Almost flat K-theory of classifying spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.06170","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":"sha256:3ad0c931b698ec9e990987dc3e7bf4feb32103ec1cbef05c9648b22c57fd6f87","target":"record","created_at":"2026-05-18T02:20:48Z","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":"23bc346ab78c69888bb80d94bebcc26a12774f59c0c22b7ec79b5caded9e693f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-03-20T17:22:56Z","title_canon_sha256":"93b91af363fbb277cb06fe7b4e31fc88af4a1ba17e5fb31d1c4c4914eefc2828"},"schema_version":"1.0","source":{"id":"1503.06170","kind":"arxiv","version":1}},"canonical_sha256":"9303ca70171ab311a03bd961818a70f9380af27a677aa34b869d8fa946b0c18b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9303ca70171ab311a03bd961818a70f9380af27a677aa34b869d8fa946b0c18b","first_computed_at":"2026-05-18T02:20:48.427653Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:20:48.427653Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FXQD+tk35IrSAmMPaYmJzlHZgqyAqqCcWHUjlFBilI+LRcQGvjgLC0jiHFLMz3VN4Wj7JmV+Kmlt2Ub0Exs5Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:20:48.428458Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.06170","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3ad0c931b698ec9e990987dc3e7bf4feb32103ec1cbef05c9648b22c57fd6f87","sha256:ebd49f53d28506eb3619af7290bd734f7747995fbf272a487f661574579b7b26"],"state_sha256":"bd4de362d0c20dc108f5e6bf426325d4deb2a83609d75400ad70b24f0379ad03"}