{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:4KYRFCXXT7KI46ZIM3J4U2VNQV","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":"a04132b74564e0e08a74774fb50c3a6fa9ca51890c251ee91cea0fd66909df8d","cross_cats_sorted":["math.FA","math.LO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OA","submitted_at":"2024-12-15T13:53:32Z","title_canon_sha256":"df6e7e247fe743279405a0a32adaef724832c163c46ff49ace6dfe6f8ec0aed2"},"schema_version":"1.0","source":{"id":"2412.11191","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.11191","created_at":"2026-07-05T09:49:28Z"},{"alias_kind":"arxiv_version","alias_value":"2412.11191v1","created_at":"2026-07-05T09:49:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.11191","created_at":"2026-07-05T09:49:28Z"},{"alias_kind":"pith_short_12","alias_value":"4KYRFCXXT7KI","created_at":"2026-07-05T09:49:28Z"},{"alias_kind":"pith_short_16","alias_value":"4KYRFCXXT7KI46ZI","created_at":"2026-07-05T09:49:28Z"},{"alias_kind":"pith_short_8","alias_value":"4KYRFCXX","created_at":"2026-07-05T09:49:28Z"}],"graph_snapshots":[{"event_id":"sha256:d98d4a138d0fcc30e563f31d8d43262816526c9c62c44bb72f9b8a4f8c33e129","target":"graph","created_at":"2026-07-05T09:49:28Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2412.11191/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Damian G{\\l}odkowski, Piotr Koszmider","cross_cats":["math.FA","math.LO"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OA","submitted_at":"2024-12-15T13:53:32Z","title":"Products of C*-algebras that do not embed into the Calkin algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.11191","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":"sha256:20304e874233ffbb3c4ae09626f3ae2f563b324d9af6d780c679e3d0d67e2b4e","target":"record","created_at":"2026-07-05T09:49:28Z","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":"a04132b74564e0e08a74774fb50c3a6fa9ca51890c251ee91cea0fd66909df8d","cross_cats_sorted":["math.FA","math.LO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OA","submitted_at":"2024-12-15T13:53:32Z","title_canon_sha256":"df6e7e247fe743279405a0a32adaef724832c163c46ff49ace6dfe6f8ec0aed2"},"schema_version":"1.0","source":{"id":"2412.11191","kind":"arxiv","version":1}},"canonical_sha256":"e2b1128af79fd48e7b2866d3ca6aad8565965576dad5309667439124a776398f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e2b1128af79fd48e7b2866d3ca6aad8565965576dad5309667439124a776398f","first_computed_at":"2026-07-05T09:49:28.696534Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:49:28.696534Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s+g6U1uLCphMphIiU9cTbh9G0Jo3AdoDmAnhvfqntghF2AaEGWEbjnwmVEQYDtUtdtQ1lxxMTioyBDhytbXwDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:49:28.696930Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.11191","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:20304e874233ffbb3c4ae09626f3ae2f563b324d9af6d780c679e3d0d67e2b4e","sha256:d98d4a138d0fcc30e563f31d8d43262816526c9c62c44bb72f9b8a4f8c33e129"],"state_sha256":"16475ccc4d7acfbf9313ef472417734258abb68cb44ae4761d8c0ec78a7a6fe3"}