{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:IWD4LMBRQ2XI25C3PEF4PIYV4R","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":"6b4ed34e874e7ba02f75c0d6e16bceec2a825f8c3301351d123abb11984ef825","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2009-06-29T16:12:28Z","title_canon_sha256":"2d2283eab27ee2e97f56f8cec80e33968c8e4fe7e89db0684a8f08db35cc1981"},"schema_version":"1.0","source":{"id":"0906.5308","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0906.5308","created_at":"2026-05-18T02:13:11Z"},{"alias_kind":"arxiv_version","alias_value":"0906.5308v2","created_at":"2026-05-18T02:13:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.5308","created_at":"2026-05-18T02:13:11Z"},{"alias_kind":"pith_short_12","alias_value":"IWD4LMBRQ2XI","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"IWD4LMBRQ2XI25C3","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"IWD4LMBR","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:5d330e0a6b837dce15fa869798820a261803c7fdb6367c4b7a21b11500ecf3ee","target":"graph","created_at":"2026-05-18T02:13:11Z","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":"Following Grothendieck's characterization of Hilbert spaces we consider operator spaces $F$ such that both $F$ and $F^*$ completely embed into the dual of a C*-algebra. Due to Haagerup/Musat's improved version of Pisier/Shlyakhtenko's Grothendieck inequality for operator spaces, these spaces are quotients of subspaces of the direct sum $C\\oplus R$ of the column and row spaces (the corresponding class being denoted by $QS(C\\oplus R)$). We first prove a representation theorem for homogeneous $F\\in QS(C\\oplus R)$ starting from the fundamental sequences defined by column and row norms of unit vect","authors_text":"Marius Junge, Quanhua Xu","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2009-06-29T16:12:28Z","title":"Representation of certain homogeneous Hilbertian operator spaces and applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.5308","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":"sha256:1b5df45f35154234becd0c9ef9cfce1ec2639203275c5b7a21a233b774710db6","target":"record","created_at":"2026-05-18T02:13:11Z","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":"6b4ed34e874e7ba02f75c0d6e16bceec2a825f8c3301351d123abb11984ef825","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2009-06-29T16:12:28Z","title_canon_sha256":"2d2283eab27ee2e97f56f8cec80e33968c8e4fe7e89db0684a8f08db35cc1981"},"schema_version":"1.0","source":{"id":"0906.5308","kind":"arxiv","version":2}},"canonical_sha256":"4587c5b03186ae8d745b790bc7a315e4637e9bf6eb6583f7a398219bbf18c1de","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4587c5b03186ae8d745b790bc7a315e4637e9bf6eb6583f7a398219bbf18c1de","first_computed_at":"2026-05-18T02:13:11.984929Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:13:11.984929Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UMMBhI05qRGBfaFmtVzBAsvV1DtDa4z4nsx0E6wUyGbWOuXyxPhzqIalGy5FJIanf3/t4LVrMEDF9Em6IkuACA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:13:11.985491Z","signed_message":"canonical_sha256_bytes"},"source_id":"0906.5308","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1b5df45f35154234becd0c9ef9cfce1ec2639203275c5b7a21a233b774710db6","sha256:5d330e0a6b837dce15fa869798820a261803c7fdb6367c4b7a21b11500ecf3ee"],"state_sha256":"26abffde29f41f3b048afe74ee123f06e7aed286a87f16c2094b47411923ae8d"}