{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:XJGMAUL3BSYVYO5XRFRDZ3RQZB","short_pith_number":"pith:XJGMAUL3","schema_version":"1.0","canonical_sha256":"ba4cc0517b0cb15c3bb789623cee30c878eaa8f11cbe1cb392d009867440118b","source":{"kind":"arxiv","id":"2411.02274","version":2},"attestation_state":"computed","paper":{"title":"Coronas and strongly self-absorbing C*-algebras","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"G\\'abor Szab\\'o, Ilijas Farah","submitted_at":"2024-11-04T17:05:32Z","abstract_excerpt":"Let $\\mathcal D$ be a strongly self-absorbing $\\mathrm{C}^*$-algebra. Given any separable $\\mathrm{C}^*$-algebra $A$, our two main results assert the following. If $A$ is $\\mathcal D$-stable, then the corona algebra of $A$ is $\\mathcal D$-saturated, i.e., $\\mathcal D$ embeds unitally into the relative commutant of every separable $\\mathrm{C}^*$-subalgebra. Conversely, assuming that the stable corona of $A$ is separably $\\mathcal D$-stable, we prove that $A$ is $\\mathcal D$-stable. This generalizes recent work by the first-named author on the structure of the Calkin algebra. As an immediate cor"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2411.02274","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OA","submitted_at":"2024-11-04T17:05:32Z","cross_cats_sorted":[],"title_canon_sha256":"792ccac4f257912ec4387b6635b3f4261aa31251ff695a22bd6aacfe4c85ed0e","abstract_canon_sha256":"9a4e6b1b73c3d71fba20fc5b79d8ab788fccc061a93bf02c6316dd3b1ca51bc2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:04:41.496170Z","signature_b64":"V6JySOQlfJD846kCvxh0d+1w2xdYtfn1F4T373dCBox6u9Uilsrm0zoouxy3fzPAn2LKr/EKd2rZy+jZSNWCDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ba4cc0517b0cb15c3bb789623cee30c878eaa8f11cbe1cb392d009867440118b","last_reissued_at":"2026-07-05T11:04:41.495664Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:04:41.495664Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Coronas and strongly self-absorbing C*-algebras","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"G\\'abor Szab\\'o, Ilijas Farah","submitted_at":"2024-11-04T17:05:32Z","abstract_excerpt":"Let $\\mathcal D$ be a strongly self-absorbing $\\mathrm{C}^*$-algebra. Given any separable $\\mathrm{C}^*$-algebra $A$, our two main results assert the following. If $A$ is $\\mathcal D$-stable, then the corona algebra of $A$ is $\\mathcal D$-saturated, i.e., $\\mathcal D$ embeds unitally into the relative commutant of every separable $\\mathrm{C}^*$-subalgebra. Conversely, assuming that the stable corona of $A$ is separably $\\mathcal D$-stable, we prove that $A$ is $\\mathcal D$-stable. This generalizes recent work by the first-named author on the structure of the Calkin algebra. As an immediate cor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.02274","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.02274/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2411.02274","created_at":"2026-07-05T11:04:41.495731+00:00"},{"alias_kind":"arxiv_version","alias_value":"2411.02274v2","created_at":"2026-07-05T11:04:41.495731+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.02274","created_at":"2026-07-05T11:04:41.495731+00:00"},{"alias_kind":"pith_short_12","alias_value":"XJGMAUL3BSYV","created_at":"2026-07-05T11:04:41.495731+00:00"},{"alias_kind":"pith_short_16","alias_value":"XJGMAUL3BSYVYO5X","created_at":"2026-07-05T11:04:41.495731+00:00"},{"alias_kind":"pith_short_8","alias_value":"XJGMAUL3","created_at":"2026-07-05T11:04:41.495731+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2506.10902","citing_title":"Nuclear C*-algebras: 99 problems","ref_index":157,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XJGMAUL3BSYVYO5XRFRDZ3RQZB","json":"https://pith.science/pith/XJGMAUL3BSYVYO5XRFRDZ3RQZB.json","graph_json":"https://pith.science/api/pith-number/XJGMAUL3BSYVYO5XRFRDZ3RQZB/graph.json","events_json":"https://pith.science/api/pith-number/XJGMAUL3BSYVYO5XRFRDZ3RQZB/events.json","paper":"https://pith.science/paper/XJGMAUL3"},"agent_actions":{"view_html":"https://pith.science/pith/XJGMAUL3BSYVYO5XRFRDZ3RQZB","download_json":"https://pith.science/pith/XJGMAUL3BSYVYO5XRFRDZ3RQZB.json","view_paper":"https://pith.science/paper/XJGMAUL3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2411.02274&json=true","fetch_graph":"https://pith.science/api/pith-number/XJGMAUL3BSYVYO5XRFRDZ3RQZB/graph.json","fetch_events":"https://pith.science/api/pith-number/XJGMAUL3BSYVYO5XRFRDZ3RQZB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XJGMAUL3BSYVYO5XRFRDZ3RQZB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XJGMAUL3BSYVYO5XRFRDZ3RQZB/action/storage_attestation","attest_author":"https://pith.science/pith/XJGMAUL3BSYVYO5XRFRDZ3RQZB/action/author_attestation","sign_citation":"https://pith.science/pith/XJGMAUL3BSYVYO5XRFRDZ3RQZB/action/citation_signature","submit_replication":"https://pith.science/pith/XJGMAUL3BSYVYO5XRFRDZ3RQZB/action/replication_record"}},"created_at":"2026-07-05T11:04:41.495731+00:00","updated_at":"2026-07-05T11:04:41.495731+00:00"}