{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:MUJOLYWUWKOBWYRXH3WHFGFKZ6","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":"1b58a3c60f0d1a9186e647246c4a43df3344dbc0abfe3e16a5f09bfe808dc60e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-10-22T16:07:17Z","title_canon_sha256":"f1a53efa5cc84e8007bb0bb818c637f896e63290e20b2fcf9d65746f1842456d"},"schema_version":"1.0","source":{"id":"1810.09383","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.09383","created_at":"2026-05-18T00:02:40Z"},{"alias_kind":"arxiv_version","alias_value":"1810.09383v1","created_at":"2026-05-18T00:02:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.09383","created_at":"2026-05-18T00:02:40Z"},{"alias_kind":"pith_short_12","alias_value":"MUJOLYWUWKOB","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"MUJOLYWUWKOBWYRX","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"MUJOLYWU","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:36fe5a3d250b6098340537aa24609c5692069be2d3dfae39061fb3cf5c91d075","target":"graph","created_at":"2026-05-18T00:02:40Z","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":"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 $\\ell_\\infty$.","authors_text":"Tomasz Kania","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-10-22T16:07:17Z","title":"A letter concerning Leonetti's paper `Continuous Projections onto Ideal Convergent Sequences'"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.09383","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":"sha256:771385a1220edb8de57c6ef87a31e1a81d3c80ab254290faf7cd6b1359bd9fb7","target":"record","created_at":"2026-05-18T00:02:40Z","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":"1b58a3c60f0d1a9186e647246c4a43df3344dbc0abfe3e16a5f09bfe808dc60e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-10-22T16:07:17Z","title_canon_sha256":"f1a53efa5cc84e8007bb0bb818c637f896e63290e20b2fcf9d65746f1842456d"},"schema_version":"1.0","source":{"id":"1810.09383","kind":"arxiv","version":1}},"canonical_sha256":"6512e5e2d4b29c1b62373eec7298aacfaea08bc49271e558038df210c3d3e27a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6512e5e2d4b29c1b62373eec7298aacfaea08bc49271e558038df210c3d3e27a","first_computed_at":"2026-05-18T00:02:40.259499Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:40.259499Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zBQfDNHnZjHz/HrGSKGsehqok55HBjoinJ+PrUMwYprfw5fB5ikyPVRm5l+OaCvauT+kKM4oBS4Qkc/MyXNjBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:40.260102Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.09383","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:771385a1220edb8de57c6ef87a31e1a81d3c80ab254290faf7cd6b1359bd9fb7","sha256:36fe5a3d250b6098340537aa24609c5692069be2d3dfae39061fb3cf5c91d075"],"state_sha256":"004e1f68708216085fbe05db2b06cb8135e9ec29393f1671dac902127c5529cb"}