{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:N636HWO5XL7RQVHSDO6PA7WQVH","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":"37f715f39053d09d4ea909dce0a5fb7cf67e5da6ad2f6135b2a11bfe6e60b578","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-11-26T17:23:10Z","title_canon_sha256":"4663eab0238d42485e0f3a06a3328c1a0bf27659b9886e223a316cf9d2e7259f"},"schema_version":"1.0","source":{"id":"1311.6744","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.6744","created_at":"2026-05-18T03:02:58Z"},{"alias_kind":"arxiv_version","alias_value":"1311.6744v2","created_at":"2026-05-18T03:02:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.6744","created_at":"2026-05-18T03:02:58Z"},{"alias_kind":"pith_short_12","alias_value":"N636HWO5XL7R","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"N636HWO5XL7RQVHS","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"N636HWO5","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:9392fbf85ad244a5b9bc9bfc863f44819606a95c5f7fd7f4a74542d96ed478b6","target":"graph","created_at":"2026-05-18T03:02:58Z","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 consider amalgamated unital full free products of the form $A_1*_DA_2$, where $A_1, A_2$ and $D$ are finite dimensional C*-algebras and there are faithful traces on $A_1$ and $A_2$ whose restrictions to $D$ agree. We provide several conditions on the matrices of partial multiplicities of the inclusions $D\\hookrightarrow A_1$ and $D\\hookrightarrow A_2$ that guarantee that the C*-algebra $A_1*_DA_2$ is primitive. If the ranks of the matrices of partial multiplicities are one, we prove that the algebra $A_1*_DA_2$ is primitive if and only if it has a trivial center.","authors_text":"Francisco Torres-Ayala","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-11-26T17:23:10Z","title":"Conditions for Primitivity of unital amalgamated full free products of finite dimensional C*-algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.6744","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:a95b0b22c5226a6afa4b035d2e8c4138aee90c3bb5f037b8b116179858ef948b","target":"record","created_at":"2026-05-18T03:02:58Z","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":"37f715f39053d09d4ea909dce0a5fb7cf67e5da6ad2f6135b2a11bfe6e60b578","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-11-26T17:23:10Z","title_canon_sha256":"4663eab0238d42485e0f3a06a3328c1a0bf27659b9886e223a316cf9d2e7259f"},"schema_version":"1.0","source":{"id":"1311.6744","kind":"arxiv","version":2}},"canonical_sha256":"6fb7e3d9ddbaff1854f21bbcf07ed0a9d0c61343a48c537b5d218f95c4efa2ff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6fb7e3d9ddbaff1854f21bbcf07ed0a9d0c61343a48c537b5d218f95c4efa2ff","first_computed_at":"2026-05-18T03:02:58.921759Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:02:58.921759Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6F16VdRu5hqWnCkylMjpu7Xh+dndSD8kyiw6+NIPUpSTy9jLp6C0yuTfCqzDz5Be4TBCw2GDS+h5zK/qyURGCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:02:58.922530Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.6744","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a95b0b22c5226a6afa4b035d2e8c4138aee90c3bb5f037b8b116179858ef948b","sha256:9392fbf85ad244a5b9bc9bfc863f44819606a95c5f7fd7f4a74542d96ed478b6"],"state_sha256":"a8a615393dddf1839db2c06447e3949514dc076fb7979cbab38229cc8440945a"}