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We show that $\\phi$ and $\\psi$ are approximately unitarily equivalent if and only if \\beq[\\phi]&=&[\\psi] {\\rm in} KL(C,A), \\phi_{\\sharp}&=&\\psi_{\\sharp}\\tand \\phi^{\\dag}&=&\\psi^{\\dag}, \\eneq where $\\phi_{\\sharp}$ and $\\psi_{\\sharp}$ are continuous affine maps from tracial state space $T(A)$ of $A$ to faithful tracial state space $T_{\\rm f}(C)$ of $C$ induced by $\\phi$ and $\\psi,$ respectively, and $\\phi^{\\ddag}$ and $"},"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":"1102.4631","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-02-22T21:40:21Z","cross_cats_sorted":[],"title_canon_sha256":"42b38784dead4eb37e277f56645a9739afca5bf18087dc8bdc60c96d8f6aab45","abstract_canon_sha256":"c0ed207345011fa26d74188d269b8324ff718ab60e423271294913251e4e54ee"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:35:52.625452Z","signature_b64":"z0yze2GvBDKQKE2vigM/aMVjQLnSy2xCsgBphDmmKh9xuTmRLFR5cT14cgEh27LnYCgtlfcD3U1SE3FYYGnRCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"410363dc46dfb76b0264dafa5ef50f9f3aa3f0c11d87e302a794d6c7a617a679","last_reissued_at":"2026-05-18T01:35:52.624612Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:35:52.624612Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Homomorphisms from AH-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Huaxin Lin","submitted_at":"2011-02-22T21:40:21Z","abstract_excerpt":"Let $C$ be a general unital AH-algebra and let $A$ be a unital simple $C^*$-algebra with tracial rank at most one. Suppose that $\\phi, \\psi: C\\to A$ are two unital monomorphisms. We show that $\\phi$ and $\\psi$ are approximately unitarily equivalent if and only if \\beq[\\phi]&=&[\\psi] {\\rm in} KL(C,A), \\phi_{\\sharp}&=&\\psi_{\\sharp}\\tand \\phi^{\\dag}&=&\\psi^{\\dag}, \\eneq where $\\phi_{\\sharp}$ and $\\psi_{\\sharp}$ are continuous affine maps from tracial state space $T(A)$ of $A$ to faithful tracial state space $T_{\\rm f}(C)$ of $C$ induced by $\\phi$ and $\\psi,$ respectively, and $\\phi^{\\ddag}$ and $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4631","kind":"arxiv","version":6},"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":"1102.4631","created_at":"2026-05-18T01:35:52.624754+00:00"},{"alias_kind":"arxiv_version","alias_value":"1102.4631v6","created_at":"2026-05-18T01:35:52.624754+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.4631","created_at":"2026-05-18T01:35:52.624754+00:00"},{"alias_kind":"pith_short_12","alias_value":"IEBWHXCG363W","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_16","alias_value":"IEBWHXCG363WWATE","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_8","alias_value":"IEBWHXCG","created_at":"2026-05-18T12:26:30.835961+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/IEBWHXCG363WWATE3L5F55IPT4","json":"https://pith.science/pith/IEBWHXCG363WWATE3L5F55IPT4.json","graph_json":"https://pith.science/api/pith-number/IEBWHXCG363WWATE3L5F55IPT4/graph.json","events_json":"https://pith.science/api/pith-number/IEBWHXCG363WWATE3L5F55IPT4/events.json","paper":"https://pith.science/paper/IEBWHXCG"},"agent_actions":{"view_html":"https://pith.science/pith/IEBWHXCG363WWATE3L5F55IPT4","download_json":"https://pith.science/pith/IEBWHXCG363WWATE3L5F55IPT4.json","view_paper":"https://pith.science/paper/IEBWHXCG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1102.4631&json=true","fetch_graph":"https://pith.science/api/pith-number/IEBWHXCG363WWATE3L5F55IPT4/graph.json","fetch_events":"https://pith.science/api/pith-number/IEBWHXCG363WWATE3L5F55IPT4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IEBWHXCG363WWATE3L5F55IPT4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IEBWHXCG363WWATE3L5F55IPT4/action/storage_attestation","attest_author":"https://pith.science/pith/IEBWHXCG363WWATE3L5F55IPT4/action/author_attestation","sign_citation":"https://pith.science/pith/IEBWHXCG363WWATE3L5F55IPT4/action/citation_signature","submit_replication":"https://pith.science/pith/IEBWHXCG363WWATE3L5F55IPT4/action/replication_record"}},"created_at":"2026-05-18T01:35:52.624754+00:00","updated_at":"2026-05-18T01:35:52.624754+00:00"}