{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:MUJOLYWUWKOBWYRXH3WHFGFKZ6","short_pith_number":"pith:MUJOLYWU","schema_version":"1.0","canonical_sha256":"6512e5e2d4b29c1b62373eec7298aacfaea08bc49271e558038df210c3d3e27a","source":{"kind":"arxiv","id":"1810.09383","version":1},"attestation_state":"computed","paper":{"title":"A letter concerning Leonetti's paper `Continuous Projections onto Ideal Convergent Sequences'","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Tomasz Kania","submitted_at":"2018-10-22T16:07:17Z","abstract_excerpt":"Leonetti proved that whenever $\\mathcal I$ is an ideal on $\\mathbb N$ such that there exists an~uncountable family of sets that are not in $\\mathcal I$ with the property that the intersection of any two distinct members of that family is in $\\mathcal I$, then the space $c_{0,\\mathcal I}$ of sequences in $\\ell_\\infty$ that converge to 0 along $\\mathcal I$ is not complemented. We provide a shorter proof of a more general fact that the quotient space $\\ell_\\infty / c_{0,\\mathcal I}$ does not even embed into $\\ell_\\infty$."},"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":"1810.09383","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-10-22T16:07:17Z","cross_cats_sorted":[],"title_canon_sha256":"f1a53efa5cc84e8007bb0bb818c637f896e63290e20b2fcf9d65746f1842456d","abstract_canon_sha256":"1b58a3c60f0d1a9186e647246c4a43df3344dbc0abfe3e16a5f09bfe808dc60e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:40.260102Z","signature_b64":"zBQfDNHnZjHz/HrGSKGsehqok55HBjoinJ+PrUMwYprfw5fB5ikyPVRm5l+OaCvauT+kKM4oBS4Qkc/MyXNjBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6512e5e2d4b29c1b62373eec7298aacfaea08bc49271e558038df210c3d3e27a","last_reissued_at":"2026-05-18T00:02:40.259499Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:40.259499Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A letter concerning Leonetti's paper `Continuous Projections onto Ideal Convergent Sequences'","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Tomasz Kania","submitted_at":"2018-10-22T16:07:17Z","abstract_excerpt":"Leonetti proved that whenever $\\mathcal I$ is an ideal on $\\mathbb N$ such that there exists an~uncountable family of sets that are not in $\\mathcal I$ with the property that the intersection of any two distinct members of that family is in $\\mathcal I$, then the space $c_{0,\\mathcal I}$ of sequences in $\\ell_\\infty$ that converge to 0 along $\\mathcal I$ is not complemented. We provide a shorter proof of a more general fact that the quotient space $\\ell_\\infty / c_{0,\\mathcal I}$ does not even embed into $\\ell_\\infty$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.09383","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":""},"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":"1810.09383","created_at":"2026-05-18T00:02:40.259583+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.09383v1","created_at":"2026-05-18T00:02:40.259583+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.09383","created_at":"2026-05-18T00:02:40.259583+00:00"},{"alias_kind":"pith_short_12","alias_value":"MUJOLYWUWKOB","created_at":"2026-05-18T12:32:40.477152+00:00"},{"alias_kind":"pith_short_16","alias_value":"MUJOLYWUWKOBWYRX","created_at":"2026-05-18T12:32:40.477152+00:00"},{"alias_kind":"pith_short_8","alias_value":"MUJOLYWU","created_at":"2026-05-18T12:32:40.477152+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/MUJOLYWUWKOBWYRXH3WHFGFKZ6","json":"https://pith.science/pith/MUJOLYWUWKOBWYRXH3WHFGFKZ6.json","graph_json":"https://pith.science/api/pith-number/MUJOLYWUWKOBWYRXH3WHFGFKZ6/graph.json","events_json":"https://pith.science/api/pith-number/MUJOLYWUWKOBWYRXH3WHFGFKZ6/events.json","paper":"https://pith.science/paper/MUJOLYWU"},"agent_actions":{"view_html":"https://pith.science/pith/MUJOLYWUWKOBWYRXH3WHFGFKZ6","download_json":"https://pith.science/pith/MUJOLYWUWKOBWYRXH3WHFGFKZ6.json","view_paper":"https://pith.science/paper/MUJOLYWU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.09383&json=true","fetch_graph":"https://pith.science/api/pith-number/MUJOLYWUWKOBWYRXH3WHFGFKZ6/graph.json","fetch_events":"https://pith.science/api/pith-number/MUJOLYWUWKOBWYRXH3WHFGFKZ6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MUJOLYWUWKOBWYRXH3WHFGFKZ6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MUJOLYWUWKOBWYRXH3WHFGFKZ6/action/storage_attestation","attest_author":"https://pith.science/pith/MUJOLYWUWKOBWYRXH3WHFGFKZ6/action/author_attestation","sign_citation":"https://pith.science/pith/MUJOLYWUWKOBWYRXH3WHFGFKZ6/action/citation_signature","submit_replication":"https://pith.science/pith/MUJOLYWUWKOBWYRXH3WHFGFKZ6/action/replication_record"}},"created_at":"2026-05-18T00:02:40.259583+00:00","updated_at":"2026-05-18T00:02:40.259583+00:00"}