{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:SGZE3YYWZTKHOBRZ4UYSA4IP72","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":"4bb5c5b5043090ec4b4086660c4fcb3a8abdf8cff7489c9699ef64fc75291ac7","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2009-07-17T15:53:34Z","title_canon_sha256":"0443f06b12421e04d86815798f906ce970a5fa633d0b439ee3d1d8c1690cb0f5"},"schema_version":"1.0","source":{"id":"0907.3103","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0907.3103","created_at":"2026-05-18T04:34:01Z"},{"alias_kind":"arxiv_version","alias_value":"0907.3103v5","created_at":"2026-05-18T04:34:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.3103","created_at":"2026-05-18T04:34:01Z"},{"alias_kind":"pith_short_12","alias_value":"SGZE3YYWZTKH","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"SGZE3YYWZTKHOBRZ","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"SGZE3YYW","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:fdfaf69c9be0dfede0312b8087c81b92b5708ba4a545d66ce2d7f8679d30b4c6","target":"graph","created_at":"2026-05-18T04:34:01Z","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 continue the study of r-ideals, l-ideals, and HSA's in operator algebras. Some applications are made to the structure of operator algebras, including Wedderburn type theorems for a class of operator algebras. We also consider the one-sided $M$-ideal structure of certain tensor products of operator algebras.","authors_text":"David P. Blecher, Melahat Almus, Sonia Sharma","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2009-07-17T15:53:34Z","title":"Ideals and structure of operator algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.3103","kind":"arxiv","version":5},"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":"sha256:1a0ab4c0dd76d76f9f8a95477e164d7aa965850be078ea5d30dd131065f4f94a","target":"record","created_at":"2026-05-18T04:34:01Z","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":"4bb5c5b5043090ec4b4086660c4fcb3a8abdf8cff7489c9699ef64fc75291ac7","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2009-07-17T15:53:34Z","title_canon_sha256":"0443f06b12421e04d86815798f906ce970a5fa633d0b439ee3d1d8c1690cb0f5"},"schema_version":"1.0","source":{"id":"0907.3103","kind":"arxiv","version":5}},"canonical_sha256":"91b24de316ccd4770639e53120710ffea0a2d4c15ddd18c3d9ab9f5849cb4adf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"91b24de316ccd4770639e53120710ffea0a2d4c15ddd18c3d9ab9f5849cb4adf","first_computed_at":"2026-05-18T04:34:01.480092Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:34:01.480092Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Jhaa/748JYdQundaZ04XqMWOR+yiBPTT4ZyH4tN40OELACqQYmdbDsOc4/GcH0vF5kDHVch+UJtnQ0wPE+aiDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:34:01.480528Z","signed_message":"canonical_sha256_bytes"},"source_id":"0907.3103","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1a0ab4c0dd76d76f9f8a95477e164d7aa965850be078ea5d30dd131065f4f94a","sha256:fdfaf69c9be0dfede0312b8087c81b92b5708ba4a545d66ce2d7f8679d30b4c6"],"state_sha256":"43c47e4572644e23d346c4b6f68aaf4c8534a6c49bc0f1b94c41deb120e514bc"}