{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:2ZHGQJW7WIR6FR6PBIEGTMKVPC","short_pith_number":"pith:2ZHGQJW7","schema_version":"1.0","canonical_sha256":"d64e6826dfb223e2c7cf0a0869b155789bd476f0d85298b6000f131ccaf1ca25","source":{"kind":"arxiv","id":"1803.03699","version":1},"attestation_state":"computed","paper":{"title":"Ideal convergent subseries in Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Artur Wachowicz, Marek Balcerzak, Micha{\\l} Pop{\\l}awski","submitted_at":"2018-03-09T21:34:00Z","abstract_excerpt":"Assume that $\\mathcal{I}$ is an ideal on $\\mathbb{N}$, and $\\sum_n x_n$ is a divergent series in a Banach space $X$. We study the Baire category, and the measure of the set $A(\\mathcal{I}):=\\left\\{t \\in \\{0,1\\}^{\\mathbb{N}} \\colon \\sum_n t(n)x_n \\textrm{ is } \\mathcal{I}\\textrm{-convergent}\\right\\}$. In the category case, we assume that $\\mathcal{I}$ has the Baire property and $\\sum_n x_n$ is not unconditionally convergent, and we deduce that $A(\\mathcal{I})$ is meager. We also study the smallness of $A(\\mathcal{I})$ in the measure case when the Haar probability measure $\\lambda$ on $\\{0,1\\}^{"},"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":"1803.03699","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-03-09T21:34:00Z","cross_cats_sorted":[],"title_canon_sha256":"402f66fa32e7b0a231ea112c8e36b4654280a82eb7342a624e5847850de00554","abstract_canon_sha256":"9e81a248db08611f90b575db6423afb6014da77e86fbc7ca3b2d6ecb2401f5dd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:21:38.433102Z","signature_b64":"fsW/XnaL8kaFaYthiTkqvxCHuifPw8H1UaqPtrtpEX8bkgLMx5BWAmTdFYJJ6DiRtzxPw4yUllF1g1TxJ7KNDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d64e6826dfb223e2c7cf0a0869b155789bd476f0d85298b6000f131ccaf1ca25","last_reissued_at":"2026-05-18T00:21:38.432295Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:21:38.432295Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ideal convergent subseries in Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Artur Wachowicz, Marek Balcerzak, Micha{\\l} Pop{\\l}awski","submitted_at":"2018-03-09T21:34:00Z","abstract_excerpt":"Assume that $\\mathcal{I}$ is an ideal on $\\mathbb{N}$, and $\\sum_n x_n$ is a divergent series in a Banach space $X$. We study the Baire category, and the measure of the set $A(\\mathcal{I}):=\\left\\{t \\in \\{0,1\\}^{\\mathbb{N}} \\colon \\sum_n t(n)x_n \\textrm{ is } \\mathcal{I}\\textrm{-convergent}\\right\\}$. In the category case, we assume that $\\mathcal{I}$ has the Baire property and $\\sum_n x_n$ is not unconditionally convergent, and we deduce that $A(\\mathcal{I})$ is meager. We also study the smallness of $A(\\mathcal{I})$ in the measure case when the Haar probability measure $\\lambda$ on $\\{0,1\\}^{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.03699","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":"1803.03699","created_at":"2026-05-18T00:21:38.432447+00:00"},{"alias_kind":"arxiv_version","alias_value":"1803.03699v1","created_at":"2026-05-18T00:21:38.432447+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.03699","created_at":"2026-05-18T00:21:38.432447+00:00"},{"alias_kind":"pith_short_12","alias_value":"2ZHGQJW7WIR6","created_at":"2026-05-18T12:32:02.567920+00:00"},{"alias_kind":"pith_short_16","alias_value":"2ZHGQJW7WIR6FR6P","created_at":"2026-05-18T12:32:02.567920+00:00"},{"alias_kind":"pith_short_8","alias_value":"2ZHGQJW7","created_at":"2026-05-18T12:32:02.567920+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/2ZHGQJW7WIR6FR6PBIEGTMKVPC","json":"https://pith.science/pith/2ZHGQJW7WIR6FR6PBIEGTMKVPC.json","graph_json":"https://pith.science/api/pith-number/2ZHGQJW7WIR6FR6PBIEGTMKVPC/graph.json","events_json":"https://pith.science/api/pith-number/2ZHGQJW7WIR6FR6PBIEGTMKVPC/events.json","paper":"https://pith.science/paper/2ZHGQJW7"},"agent_actions":{"view_html":"https://pith.science/pith/2ZHGQJW7WIR6FR6PBIEGTMKVPC","download_json":"https://pith.science/pith/2ZHGQJW7WIR6FR6PBIEGTMKVPC.json","view_paper":"https://pith.science/paper/2ZHGQJW7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1803.03699&json=true","fetch_graph":"https://pith.science/api/pith-number/2ZHGQJW7WIR6FR6PBIEGTMKVPC/graph.json","fetch_events":"https://pith.science/api/pith-number/2ZHGQJW7WIR6FR6PBIEGTMKVPC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2ZHGQJW7WIR6FR6PBIEGTMKVPC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2ZHGQJW7WIR6FR6PBIEGTMKVPC/action/storage_attestation","attest_author":"https://pith.science/pith/2ZHGQJW7WIR6FR6PBIEGTMKVPC/action/author_attestation","sign_citation":"https://pith.science/pith/2ZHGQJW7WIR6FR6PBIEGTMKVPC/action/citation_signature","submit_replication":"https://pith.science/pith/2ZHGQJW7WIR6FR6PBIEGTMKVPC/action/replication_record"}},"created_at":"2026-05-18T00:21:38.432447+00:00","updated_at":"2026-05-18T00:21:38.432447+00:00"}