{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:TOWAWDICBYDVQUG4N64DIP26II","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":"07c485432cd6ac8794c8501af60152bcdf0b9d581379d06841105be2d53314e6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-06-10T01:41:49Z","title_canon_sha256":"dd09f4da50790ebeaf2a1fc47088189108160ea9aca79081d0a3ac73644c7f53"},"schema_version":"1.0","source":{"id":"1606.03156","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.03156","created_at":"2026-05-18T01:12:37Z"},{"alias_kind":"arxiv_version","alias_value":"1606.03156v1","created_at":"2026-05-18T01:12:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.03156","created_at":"2026-05-18T01:12:37Z"},{"alias_kind":"pith_short_12","alias_value":"TOWAWDICBYDV","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"TOWAWDICBYDVQUG4","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"TOWAWDIC","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:a4cc997ed9fe6b26097446a843df6ecf47745656ef5d6d24411a9f3afb0701ee","target":"graph","created_at":"2026-05-18T01:12:37Z","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 give a new proof of a theorem due to Alain Connes, that an injective factor $N$ of type III$_1$ with separable predual and with trivial bicentralizer is isomorphic to the Araki--Woods type III$_1$ factor $R_{\\infty}$. This, combined with the author's solution to the bicentralizer problem for injective III$_1$ factors provides a new proof of the theorem that up to $*$-isomorphism, there exists a unique injective factor of type III$_1$ on a separable Hilbert space.","authors_text":"Uffe Haagerup","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-06-10T01:41:49Z","title":"On the uniqueness of injective III$_1$ factor"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.03156","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:b3400f84ecdbd457a7fa23fcdf15b667f54fe7f379cc15fd8381cffb66813015","target":"record","created_at":"2026-05-18T01:12:37Z","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":"07c485432cd6ac8794c8501af60152bcdf0b9d581379d06841105be2d53314e6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-06-10T01:41:49Z","title_canon_sha256":"dd09f4da50790ebeaf2a1fc47088189108160ea9aca79081d0a3ac73644c7f53"},"schema_version":"1.0","source":{"id":"1606.03156","kind":"arxiv","version":1}},"canonical_sha256":"9bac0b0d020e075850dc6fb8343f5e4208c5ecc4512e6b70323669b306ad0bca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9bac0b0d020e075850dc6fb8343f5e4208c5ecc4512e6b70323669b306ad0bca","first_computed_at":"2026-05-18T01:12:37.457945Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:37.457945Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kaB/FCNU6CxPx8idkq5n0RlgoiFAYDeoYF/SUoz96r2uuWVQ1lnAtzvsayTm4WvbomE/IdF+pwLNHxsRvUOZAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:37.458483Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.03156","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b3400f84ecdbd457a7fa23fcdf15b667f54fe7f379cc15fd8381cffb66813015","sha256:a4cc997ed9fe6b26097446a843df6ecf47745656ef5d6d24411a9f3afb0701ee"],"state_sha256":"7934d4fde177faa6a4a275ec4ca171f620440ce995694cbe40e6abdbfbe31048"}