{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:O4RUBMDLGNB6MG7EF73EXTON6J","short_pith_number":"pith:O4RUBMDL","schema_version":"1.0","canonical_sha256":"772340b06b3343e61be42ff64bcdcdf25e60f8eb7b09655faad3d6c034d409ee","source":{"kind":"arxiv","id":"2203.15123","version":1},"attestation_state":"computed","paper":{"title":"Continuity of coordinate functionals of filter bases in Banach spaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Jaros{\\l}aw Swaczyna, No\\'e de Rancourt, Tomasz Kania","submitted_at":"2022-03-28T22:01:40Z","abstract_excerpt":"We prove that the coordinate functionals associated with filter bases in Banach spaces are continuous as long as the underlying filter is analytic. This removes the large-cardinal hypothesis from the result established by the two last-named authors ([Bull. Lond. Math. Soc. 53 (2021)]) at the expense of reducing the generality from projective to analytic. In particular, we obtain a ZFC solution to Kadets' problem of continuity of coordinate functionals associated with bases with respect to the filter of statistical convergence. Even though the automatic continuity of coordinate functionals beyo"},"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":"2203.15123","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2022-03-28T22:01:40Z","cross_cats_sorted":[],"title_canon_sha256":"0cab46f4fd70ae83afe69544588c6b2561735129b3173a0ea02a0f9ce65e4975","abstract_canon_sha256":"ca014bb5ac89e06f1e4bb15a570295a5c86ebe48107b3b09b5398cb4eb1a1437"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:09:21.851573Z","signature_b64":"Bvb+fq+PYWOaE0Ngo/FtB7fLf1yxvcBfyU+wYqhz4UxBozPzzislqVsF7hEV2ChueQ93jVAXa8VRyEcRdrrMDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"772340b06b3343e61be42ff64bcdcdf25e60f8eb7b09655faad3d6c034d409ee","last_reissued_at":"2026-07-05T04:09:21.851217Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:09:21.851217Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Continuity of coordinate functionals of filter bases in Banach spaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Jaros{\\l}aw Swaczyna, No\\'e de Rancourt, Tomasz Kania","submitted_at":"2022-03-28T22:01:40Z","abstract_excerpt":"We prove that the coordinate functionals associated with filter bases in Banach spaces are continuous as long as the underlying filter is analytic. This removes the large-cardinal hypothesis from the result established by the two last-named authors ([Bull. Lond. Math. Soc. 53 (2021)]) at the expense of reducing the generality from projective to analytic. In particular, we obtain a ZFC solution to Kadets' problem of continuity of coordinate functionals associated with bases with respect to the filter of statistical convergence. Even though the automatic continuity of coordinate functionals beyo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.15123","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/2203.15123/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":"2203.15123","created_at":"2026-07-05T04:09:21.851272+00:00"},{"alias_kind":"arxiv_version","alias_value":"2203.15123v1","created_at":"2026-07-05T04:09:21.851272+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.15123","created_at":"2026-07-05T04:09:21.851272+00:00"},{"alias_kind":"pith_short_12","alias_value":"O4RUBMDLGNB6","created_at":"2026-07-05T04:09:21.851272+00:00"},{"alias_kind":"pith_short_16","alias_value":"O4RUBMDLGNB6MG7E","created_at":"2026-07-05T04:09:21.851272+00:00"},{"alias_kind":"pith_short_8","alias_value":"O4RUBMDL","created_at":"2026-07-05T04:09:21.851272+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/O4RUBMDLGNB6MG7EF73EXTON6J","json":"https://pith.science/pith/O4RUBMDLGNB6MG7EF73EXTON6J.json","graph_json":"https://pith.science/api/pith-number/O4RUBMDLGNB6MG7EF73EXTON6J/graph.json","events_json":"https://pith.science/api/pith-number/O4RUBMDLGNB6MG7EF73EXTON6J/events.json","paper":"https://pith.science/paper/O4RUBMDL"},"agent_actions":{"view_html":"https://pith.science/pith/O4RUBMDLGNB6MG7EF73EXTON6J","download_json":"https://pith.science/pith/O4RUBMDLGNB6MG7EF73EXTON6J.json","view_paper":"https://pith.science/paper/O4RUBMDL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2203.15123&json=true","fetch_graph":"https://pith.science/api/pith-number/O4RUBMDLGNB6MG7EF73EXTON6J/graph.json","fetch_events":"https://pith.science/api/pith-number/O4RUBMDLGNB6MG7EF73EXTON6J/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/O4RUBMDLGNB6MG7EF73EXTON6J/action/timestamp_anchor","attest_storage":"https://pith.science/pith/O4RUBMDLGNB6MG7EF73EXTON6J/action/storage_attestation","attest_author":"https://pith.science/pith/O4RUBMDLGNB6MG7EF73EXTON6J/action/author_attestation","sign_citation":"https://pith.science/pith/O4RUBMDLGNB6MG7EF73EXTON6J/action/citation_signature","submit_replication":"https://pith.science/pith/O4RUBMDLGNB6MG7EF73EXTON6J/action/replication_record"}},"created_at":"2026-07-05T04:09:21.851272+00:00","updated_at":"2026-07-05T04:09:21.851272+00:00"}