{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:LVY3XAQCDDDQH7JMDW4W2RGSSN","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":"b5cce0c138ecbac7533a2bff7101c856f08810c818e89f7f915215cc25eeec02","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-03-31T07:51:07Z","title_canon_sha256":"c7c010eb75de144ad1c898b47ca17b107c23e3b2a6b70df18d88df3ed011e97a"},"schema_version":"1.0","source":{"id":"1703.10781","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.10781","created_at":"2026-05-18T00:38:35Z"},{"alias_kind":"arxiv_version","alias_value":"1703.10781v2","created_at":"2026-05-18T00:38:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.10781","created_at":"2026-05-18T00:38:35Z"},{"alias_kind":"pith_short_12","alias_value":"LVY3XAQCDDDQ","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LVY3XAQCDDDQH7JM","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LVY3XAQC","created_at":"2026-05-18T12:31:28Z"}],"graph_snapshots":[{"event_id":"sha256:7c9087bc035cb39e348373cf1e6f5dc2d0fa1acf86773e1ab5f94116be7a68ee","target":"graph","created_at":"2026-05-18T00:38:35Z","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":"Let $A$, $B$ be separable C*-algebras, $B$ stable. Elements of the E-theory group $E(A,B)$ are represented by asymptotic homomorphisms from the second suspension of $A$ to $B$. Our aim is to represent these elements by (families of) maps from $A$ itself to $B$. We have to pay for that by allowing these maps to be even further from $*$-homomorphisms. We prove that $E(A,B)$ can be represented by pairs $(\\varphi^+,\\varphi^-)$ of maps from $A$ to $B$ that are not necessarily asymptotic homomorphisms, but have the same deficiency from being ones. Not surprisingly, such pairs of maps can be viewed a","authors_text":"Vladimir Manuilov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-03-31T07:51:07Z","title":"A KK-like picture for E-theory of C*-algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.10781","kind":"arxiv","version":2},"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:f6bdb6fb137adf0e95e28125049af7a865da9e32cbfc75c9610c0e44c3e3ca8b","target":"record","created_at":"2026-05-18T00:38:35Z","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":"b5cce0c138ecbac7533a2bff7101c856f08810c818e89f7f915215cc25eeec02","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-03-31T07:51:07Z","title_canon_sha256":"c7c010eb75de144ad1c898b47ca17b107c23e3b2a6b70df18d88df3ed011e97a"},"schema_version":"1.0","source":{"id":"1703.10781","kind":"arxiv","version":2}},"canonical_sha256":"5d71bb820218c703fd2c1db96d44d293454f601d2048b7b8d0fbcd8be641937b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5d71bb820218c703fd2c1db96d44d293454f601d2048b7b8d0fbcd8be641937b","first_computed_at":"2026-05-18T00:38:35.810912Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:38:35.810912Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t9Hgg+hDjgaOdss1Q4mAcqmI5QtLsqVQjf7sXSISt9LWXmMQVa0mjHemKbJQSu1lrMnsdxUKHKTpcj26rpWQBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:38:35.811371Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.10781","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f6bdb6fb137adf0e95e28125049af7a865da9e32cbfc75c9610c0e44c3e3ca8b","sha256:7c9087bc035cb39e348373cf1e6f5dc2d0fa1acf86773e1ab5f94116be7a68ee"],"state_sha256":"98c7e738f7dbe2d4f4038f72ef94e01aa78d3aff00f67818e48e86ed2083cd7c"}