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There exists a sequence of unitaries $\\{u_n\\}\\subset B$ such that $$ \\lim_{n\\to\\infty} u_n^*\\phi(a) u_n=\\psi(a)\\tforal a\\in A, $$ if and only if $$ [\\phi]=[\\psi]\\,\\,\\,\\text{in}\\,\\,\\, KL(A,B), \\phi_{\\sharp}=\\psi_{\\sharp}\\andeqn\\phi^{\\ddag}=\\psi^{\\ddag}, $$ where $\\phi_{\\sharp}, \\psi_{\\sharp}: \\aff(T(A))"},"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":"1003.1760","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-03-09T00:12:28Z","cross_cats_sorted":[],"title_canon_sha256":"bf103f8d3f05c86ec87837ad3749e829acd5f862455c3ad06afbaf9c5373d97b","abstract_canon_sha256":"0c19819db8d51f7fc32156cfcc6c4ecb793a48fb78fe7c9625e30997dc2b1655"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:50:59.412447Z","signature_b64":"q9SQ1nN5I+A2TTB3MAWKUzR76MDsjh1/722hJ6ilXC0E7QQ/OaQWa8VeoaB5Jtwgwpn1k58wda0544Ky3LmCDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"04fff63fe71f1326a7948d1652561e6e86bec5919c4953655ccf977b9d0d2d9b","last_reissued_at":"2026-05-18T03:50:59.411595Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:50:59.411595Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Homomorphisms into a simple Z-stable C*-Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Huaxin Lin, Zhuang Niu","submitted_at":"2010-03-09T00:12:28Z","abstract_excerpt":"Let $A$ and $B$ be unital separable simple amenable \\CA s which satisfy the Universal Coefficient Theorem. Suppose {that} $A$ and $B$ are $\\mathcal Z$-stable and are of rationally tracial rank no more than one. We prove the following: Suppose that $\\phi, \\psi: A\\to B$ are unital {monomorphisms}. There exists a sequence of unitaries $\\{u_n\\}\\subset B$ such that $$ \\lim_{n\\to\\infty} u_n^*\\phi(a) u_n=\\psi(a)\\tforal a\\in A, $$ if and only if $$ [\\phi]=[\\psi]\\,\\,\\,\\text{in}\\,\\,\\, KL(A,B), \\phi_{\\sharp}=\\psi_{\\sharp}\\andeqn\\phi^{\\ddag}=\\psi^{\\ddag}, $$ where $\\phi_{\\sharp}, \\psi_{\\sharp}: \\aff(T(A))"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.1760","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":"1003.1760","created_at":"2026-05-18T03:50:59.411736+00:00"},{"alias_kind":"arxiv_version","alias_value":"1003.1760v3","created_at":"2026-05-18T03:50:59.411736+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.1760","created_at":"2026-05-18T03:50:59.411736+00:00"},{"alias_kind":"pith_short_12","alias_value":"AT77MP7HD4JS","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_16","alias_value":"AT77MP7HD4JSNJ4U","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_8","alias_value":"AT77MP7H","created_at":"2026-05-18T12:26:05.355336+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/AT77MP7HD4JSNJ4URULFEVQ6N2","json":"https://pith.science/pith/AT77MP7HD4JSNJ4URULFEVQ6N2.json","graph_json":"https://pith.science/api/pith-number/AT77MP7HD4JSNJ4URULFEVQ6N2/graph.json","events_json":"https://pith.science/api/pith-number/AT77MP7HD4JSNJ4URULFEVQ6N2/events.json","paper":"https://pith.science/paper/AT77MP7H"},"agent_actions":{"view_html":"https://pith.science/pith/AT77MP7HD4JSNJ4URULFEVQ6N2","download_json":"https://pith.science/pith/AT77MP7HD4JSNJ4URULFEVQ6N2.json","view_paper":"https://pith.science/paper/AT77MP7H","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1003.1760&json=true","fetch_graph":"https://pith.science/api/pith-number/AT77MP7HD4JSNJ4URULFEVQ6N2/graph.json","fetch_events":"https://pith.science/api/pith-number/AT77MP7HD4JSNJ4URULFEVQ6N2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AT77MP7HD4JSNJ4URULFEVQ6N2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AT77MP7HD4JSNJ4URULFEVQ6N2/action/storage_attestation","attest_author":"https://pith.science/pith/AT77MP7HD4JSNJ4URULFEVQ6N2/action/author_attestation","sign_citation":"https://pith.science/pith/AT77MP7HD4JSNJ4URULFEVQ6N2/action/citation_signature","submit_replication":"https://pith.science/pith/AT77MP7HD4JSNJ4URULFEVQ6N2/action/replication_record"}},"created_at":"2026-05-18T03:50:59.411736+00:00","updated_at":"2026-05-18T03:50:59.411736+00:00"}