{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:QPHFPG3ZZUO2TJZ2JKJOIIMUUT","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":"40e25544d3655deed3ac4011f7386a51a1f0e4167e1ef2f7a915951f69736c17","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-07-10T20:32:12Z","title_canon_sha256":"7398170b96985d7f03457324de2607f1c502ec6730f1e7f36e724f6a696a9273"},"schema_version":"1.0","source":{"id":"1907.04912","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.04912","created_at":"2026-05-17T23:40:54Z"},{"alias_kind":"arxiv_version","alias_value":"1907.04912v1","created_at":"2026-05-17T23:40:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.04912","created_at":"2026-05-17T23:40:54Z"},{"alias_kind":"pith_short_12","alias_value":"QPHFPG3ZZUO2","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"QPHFPG3ZZUO2TJZ2","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"QPHFPG3Z","created_at":"2026-05-18T12:33:27Z"}],"graph_snapshots":[{"event_id":"sha256:ddc1ceb3e8266e57a8bc984bae95868ca99b118bba6c69890ef6cfdbc2a2c61c","target":"graph","created_at":"2026-05-17T23:40:54Z","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 study the Poincar\\'e disk $\\d=\\{z\\in\\a: \\|z\\|<1\\}$ of a C$^*$-algebra $\\a$ as a homogeneous space under the action of an appropriate Banach-Lie group $\\u(\\theta)$ of $2\\times 2$ matrices with entries in $\\a$. We define on $\\d$ a homogeneous K\\\"ahler structure in a non commutative sense. In particular, this K\\\"ahler structure defines on $\\d$ a homogeneous symplectic structure under the action of $\\u(\\theta)$. This action has a moment map that we explicitly compute. In the presence of a trace in $\\a$, we show that the moment map has a convex image when restricted to appropriate subgroups of $","authors_text":"Esteban Andruchow, Gustavo Corach, L\\'azaro Recht","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-07-10T20:32:12Z","title":"A non commutative K\\\"ahler structure on the Poincar\\'e disk of a C*-algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.04912","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":"sha256:18740b2fbbbcad91277ce0a46aba0af21542ec647adae5e7db8b9e34ad4271fa","target":"record","created_at":"2026-05-17T23:40:54Z","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":"40e25544d3655deed3ac4011f7386a51a1f0e4167e1ef2f7a915951f69736c17","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-07-10T20:32:12Z","title_canon_sha256":"7398170b96985d7f03457324de2607f1c502ec6730f1e7f36e724f6a696a9273"},"schema_version":"1.0","source":{"id":"1907.04912","kind":"arxiv","version":1}},"canonical_sha256":"83ce579b79cd1da9a73a4a92e42194a4fb13665410750d27faf675b8b7fa5a3e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"83ce579b79cd1da9a73a4a92e42194a4fb13665410750d27faf675b8b7fa5a3e","first_computed_at":"2026-05-17T23:40:54.522572Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:54.522572Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M8rhPrwM1nDeLXSzRBF7WIxndi/6m6Q5YZocQfiaJ8fd/qDxL3B+6EgWCXAaXxN0/JqQ1kvMU+HUuHKW5G3vAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:54.523222Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.04912","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:18740b2fbbbcad91277ce0a46aba0af21542ec647adae5e7db8b9e34ad4271fa","sha256:ddc1ceb3e8266e57a8bc984bae95868ca99b118bba6c69890ef6cfdbc2a2c61c"],"state_sha256":"6bcbf5ec7bb64c7760921dd521a451d53f17311673d4ca87df5cd57972660fc6"}