{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:4KYRFCXXT7KI46ZIM3J4U2VNQV","short_pith_number":"pith:4KYRFCXX","schema_version":"1.0","canonical_sha256":"e2b1128af79fd48e7b2866d3ca6aad8565965576dad5309667439124a776398f","source":{"kind":"arxiv","id":"2412.11191","version":1},"attestation_state":"computed","paper":{"title":"Products of C*-algebras that do not embed into the Calkin algebra","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.FA","math.LO"],"primary_cat":"math.OA","authors_text":"Damian G{\\l}odkowski, Piotr Koszmider","submitted_at":"2024-12-15T13:53:32Z","abstract_excerpt":"We consider the Calkin algebra $\\mathcal{Q}(\\ell_2)$, i.e., the quotient of the algebra $\\mathcal B(\\ell_2)$ of all bounded linear operators on the separable Hilbert space $\\ell_2$ divided by the ideal $\\mathcal K(\\ell_2)$ of all compact operators on $\\ell_2$. We show that in the Cohen model of set theory ZFC there is no embedding of the product $(c_0(2^\\omega))^{\\mathbb{N}}$ of infinitely many copies of the abelian C*-algebra $c_0(2^\\omega)$ into $\\mathcal{Q}(\\ell_2)$ (while $c_0(2^\\omega)$ always embeds into $\\mathcal{Q}(\\ell_2)$). This enlarges the collection of the known examples due to Va"},"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":"2412.11191","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OA","submitted_at":"2024-12-15T13:53:32Z","cross_cats_sorted":["math.FA","math.LO"],"title_canon_sha256":"df6e7e247fe743279405a0a32adaef724832c163c46ff49ace6dfe6f8ec0aed2","abstract_canon_sha256":"a04132b74564e0e08a74774fb50c3a6fa9ca51890c251ee91cea0fd66909df8d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:49:28.696930Z","signature_b64":"s+g6U1uLCphMphIiU9cTbh9G0Jo3AdoDmAnhvfqntghF2AaEGWEbjnwmVEQYDtUtdtQ1lxxMTioyBDhytbXwDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e2b1128af79fd48e7b2866d3ca6aad8565965576dad5309667439124a776398f","last_reissued_at":"2026-07-05T09:49:28.696534Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:49:28.696534Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Products of C*-algebras that do not embed into the Calkin algebra","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.FA","math.LO"],"primary_cat":"math.OA","authors_text":"Damian G{\\l}odkowski, Piotr Koszmider","submitted_at":"2024-12-15T13:53:32Z","abstract_excerpt":"We consider the Calkin algebra $\\mathcal{Q}(\\ell_2)$, i.e., the quotient of the algebra $\\mathcal B(\\ell_2)$ of all bounded linear operators on the separable Hilbert space $\\ell_2$ divided by the ideal $\\mathcal K(\\ell_2)$ of all compact operators on $\\ell_2$. We show that in the Cohen model of set theory ZFC there is no embedding of the product $(c_0(2^\\omega))^{\\mathbb{N}}$ of infinitely many copies of the abelian C*-algebra $c_0(2^\\omega)$ into $\\mathcal{Q}(\\ell_2)$ (while $c_0(2^\\omega)$ always embeds into $\\mathcal{Q}(\\ell_2)$). This enlarges the collection of the known examples due to Va"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.11191","kind":"arxiv","version":1},"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/2412.11191/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":"2412.11191","created_at":"2026-07-05T09:49:28.696594+00:00"},{"alias_kind":"arxiv_version","alias_value":"2412.11191v1","created_at":"2026-07-05T09:49:28.696594+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.11191","created_at":"2026-07-05T09:49:28.696594+00:00"},{"alias_kind":"pith_short_12","alias_value":"4KYRFCXXT7KI","created_at":"2026-07-05T09:49:28.696594+00:00"},{"alias_kind":"pith_short_16","alias_value":"4KYRFCXXT7KI46ZI","created_at":"2026-07-05T09:49:28.696594+00:00"},{"alias_kind":"pith_short_8","alias_value":"4KYRFCXX","created_at":"2026-07-05T09:49:28.696594+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4KYRFCXXT7KI46ZIM3J4U2VNQV","json":"https://pith.science/pith/4KYRFCXXT7KI46ZIM3J4U2VNQV.json","graph_json":"https://pith.science/api/pith-number/4KYRFCXXT7KI46ZIM3J4U2VNQV/graph.json","events_json":"https://pith.science/api/pith-number/4KYRFCXXT7KI46ZIM3J4U2VNQV/events.json","paper":"https://pith.science/paper/4KYRFCXX"},"agent_actions":{"view_html":"https://pith.science/pith/4KYRFCXXT7KI46ZIM3J4U2VNQV","download_json":"https://pith.science/pith/4KYRFCXXT7KI46ZIM3J4U2VNQV.json","view_paper":"https://pith.science/paper/4KYRFCXX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2412.11191&json=true","fetch_graph":"https://pith.science/api/pith-number/4KYRFCXXT7KI46ZIM3J4U2VNQV/graph.json","fetch_events":"https://pith.science/api/pith-number/4KYRFCXXT7KI46ZIM3J4U2VNQV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4KYRFCXXT7KI46ZIM3J4U2VNQV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4KYRFCXXT7KI46ZIM3J4U2VNQV/action/storage_attestation","attest_author":"https://pith.science/pith/4KYRFCXXT7KI46ZIM3J4U2VNQV/action/author_attestation","sign_citation":"https://pith.science/pith/4KYRFCXXT7KI46ZIM3J4U2VNQV/action/citation_signature","submit_replication":"https://pith.science/pith/4KYRFCXXT7KI46ZIM3J4U2VNQV/action/replication_record"}},"created_at":"2026-07-05T09:49:28.696594+00:00","updated_at":"2026-07-05T09:49:28.696594+00:00"}