{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:JDS7CI6FIZ66OIPSWTHAAWAINJ","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":"72b3fdd70bc0a1db7826f176227e941946b59ab69a0c4f00ea87cafde58b59a8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-11-23T18:56:30Z","title_canon_sha256":"f0d65c481f469a10d6e77c5d55809b1eaa41e07a55c0277b67d3323f3fe3a440"},"schema_version":"1.0","source":{"id":"1711.08802","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.08802","created_at":"2026-05-18T00:29:44Z"},{"alias_kind":"arxiv_version","alias_value":"1711.08802v1","created_at":"2026-05-18T00:29:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.08802","created_at":"2026-05-18T00:29:44Z"},{"alias_kind":"pith_short_12","alias_value":"JDS7CI6FIZ66","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"JDS7CI6FIZ66OIPS","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"JDS7CI6F","created_at":"2026-05-18T12:31:24Z"}],"graph_snapshots":[{"event_id":"sha256:60c80c47ea2bcb7123848abacc750376212656146ab7ccb283a8da8e222affec","target":"graph","created_at":"2026-05-18T00:29:44Z","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 $A$ be a C$*^$-algebra. Given a representation $A\\subset B(L)$ in a Hilbert space $L$, the set $G^+\\subset A$ of positive invertible elements can be thought as the set of inner products in $L$, related to $A$, which are equivalent to the original inner product. The set $G^+$ has a rich geometry, it is a homogeneous space of the invertible group $G$ of $A$, with an invariant Finsler metric. In the present paper we study the tangent bundle $TG^+$ of $G^+$, as a homogenous Finsler space of a natural group of invertible matrices in $M_2(A)$, identifying $TG^+$ with the {\\it Poincar\\'e halfspac","authors_text":"Esteban Andruchow, Gustavo Corach, L\\'azaro Recht","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-11-23T18:56:30Z","title":"Poncar\\'e half-space of a C*-algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.08802","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":"sha256:605481bd50417190bedf536dd93532201f9fb74bb64ab9184ef7a78ea3050228","target":"record","created_at":"2026-05-18T00:29:44Z","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":"72b3fdd70bc0a1db7826f176227e941946b59ab69a0c4f00ea87cafde58b59a8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-11-23T18:56:30Z","title_canon_sha256":"f0d65c481f469a10d6e77c5d55809b1eaa41e07a55c0277b67d3323f3fe3a440"},"schema_version":"1.0","source":{"id":"1711.08802","kind":"arxiv","version":1}},"canonical_sha256":"48e5f123c5467de721f2b4ce0058086a7c54fc09b49154b781494a127b053f4c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"48e5f123c5467de721f2b4ce0058086a7c54fc09b49154b781494a127b053f4c","first_computed_at":"2026-05-18T00:29:44.045566Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:44.045566Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6sP2OdU+qasWDyLPmkccuLpMdirDoSsKAojBg5GBREIth4JAZYbex2B4w41UZZtwC/Dylecv5PRkilerKgmBCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:44.046159Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.08802","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:605481bd50417190bedf536dd93532201f9fb74bb64ab9184ef7a78ea3050228","sha256:60c80c47ea2bcb7123848abacc750376212656146ab7ccb283a8da8e222affec"],"state_sha256":"636fd6cde3529e4c92c7293fa4e424b7aacbd72114d412a5b6eaa852ec762893"}