{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:2ZHGQJW7WIR6FR6PBIEGTMKVPC","short_pith_number":"pith:2ZHGQJW7","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"},"canonical_sha256":"d64e6826dfb223e2c7cf0a0869b155789bd476f0d85298b6000f131ccaf1ca25","source":{"kind":"arxiv","id":"1803.03699","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.03699","created_at":"2026-05-18T00:21:38Z"},{"alias_kind":"arxiv_version","alias_value":"1803.03699v1","created_at":"2026-05-18T00:21:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.03699","created_at":"2026-05-18T00:21:38Z"},{"alias_kind":"pith_short_12","alias_value":"2ZHGQJW7WIR6","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"2ZHGQJW7WIR6FR6P","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"2ZHGQJW7","created_at":"2026-05-18T12:32:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:2ZHGQJW7WIR6FR6PBIEGTMKVPC","target":"record","payload":{"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"},"canonical_sha256":"d64e6826dfb223e2c7cf0a0869b155789bd476f0d85298b6000f131ccaf1ca25","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"},"source_kind":"arxiv","source_id":"1803.03699","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:21:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F6DD+n+cLjDZORg9/AcrAioXPi70bie5xGl3RaJpxwqDmGn3iuyVyghN1qNas+bk/sNnvOqG5uruCvZhxYwSCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T16:26:50.018892Z"},"content_sha256":"0618f3b75c95a31b802b3c099ad60779227939dfeb806b210dade6b820e47d66","schema_version":"1.0","event_id":"sha256:0618f3b75c95a31b802b3c099ad60779227939dfeb806b210dade6b820e47d66"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:2ZHGQJW7WIR6FR6PBIEGTMKVPC","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:21:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8h5H2ZVhJaQr1i3GLgBDietMsIHed0HphkfNwe6ZfP1WIiG8N4rHdRAejlXtazwQDyOGn4G8kX92X7ewoxD/Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T16:26:50.019595Z"},"content_sha256":"33f95d95f0134271714d2c44eeeb7f8013a7697de0ecc78dddb23ab0ab26e8cd","schema_version":"1.0","event_id":"sha256:33f95d95f0134271714d2c44eeeb7f8013a7697de0ecc78dddb23ab0ab26e8cd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2ZHGQJW7WIR6FR6PBIEGTMKVPC/bundle.json","state_url":"https://pith.science/pith/2ZHGQJW7WIR6FR6PBIEGTMKVPC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2ZHGQJW7WIR6FR6PBIEGTMKVPC/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-31T16:26:50Z","links":{"resolver":"https://pith.science/pith/2ZHGQJW7WIR6FR6PBIEGTMKVPC","bundle":"https://pith.science/pith/2ZHGQJW7WIR6FR6PBIEGTMKVPC/bundle.json","state":"https://pith.science/pith/2ZHGQJW7WIR6FR6PBIEGTMKVPC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2ZHGQJW7WIR6FR6PBIEGTMKVPC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:2ZHGQJW7WIR6FR6PBIEGTMKVPC","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":"9e81a248db08611f90b575db6423afb6014da77e86fbc7ca3b2d6ecb2401f5dd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-03-09T21:34:00Z","title_canon_sha256":"402f66fa32e7b0a231ea112c8e36b4654280a82eb7342a624e5847850de00554"},"schema_version":"1.0","source":{"id":"1803.03699","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.03699","created_at":"2026-05-18T00:21:38Z"},{"alias_kind":"arxiv_version","alias_value":"1803.03699v1","created_at":"2026-05-18T00:21:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.03699","created_at":"2026-05-18T00:21:38Z"},{"alias_kind":"pith_short_12","alias_value":"2ZHGQJW7WIR6","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"2ZHGQJW7WIR6FR6P","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"2ZHGQJW7","created_at":"2026-05-18T12:32:02Z"}],"graph_snapshots":[{"event_id":"sha256:33f95d95f0134271714d2c44eeeb7f8013a7697de0ecc78dddb23ab0ab26e8cd","target":"graph","created_at":"2026-05-18T00:21:38Z","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":"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\\}^{","authors_text":"Artur Wachowicz, Marek Balcerzak, Micha{\\l} Pop{\\l}awski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-03-09T21:34:00Z","title":"Ideal convergent subseries in Banach spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.03699","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":"sha256:0618f3b75c95a31b802b3c099ad60779227939dfeb806b210dade6b820e47d66","target":"record","created_at":"2026-05-18T00:21:38Z","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":"9e81a248db08611f90b575db6423afb6014da77e86fbc7ca3b2d6ecb2401f5dd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-03-09T21:34:00Z","title_canon_sha256":"402f66fa32e7b0a231ea112c8e36b4654280a82eb7342a624e5847850de00554"},"schema_version":"1.0","source":{"id":"1803.03699","kind":"arxiv","version":1}},"canonical_sha256":"d64e6826dfb223e2c7cf0a0869b155789bd476f0d85298b6000f131ccaf1ca25","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d64e6826dfb223e2c7cf0a0869b155789bd476f0d85298b6000f131ccaf1ca25","first_computed_at":"2026-05-18T00:21:38.432295Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:21:38.432295Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fsW/XnaL8kaFaYthiTkqvxCHuifPw8H1UaqPtrtpEX8bkgLMx5BWAmTdFYJJ6DiRtzxPw4yUllF1g1TxJ7KNDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:21:38.433102Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.03699","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0618f3b75c95a31b802b3c099ad60779227939dfeb806b210dade6b820e47d66","sha256:33f95d95f0134271714d2c44eeeb7f8013a7697de0ecc78dddb23ab0ab26e8cd"],"state_sha256":"9bcf980edd79da7ca84f93d4f7a2cbac373734a286db2a77b6bfbd202504565a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HhpCH0EfqLS/n0i0qcLogKHnn+HbMAaP6JhgCpu3KB/OJHbr7q8a151Ma23pjdi7el+2uFAH1ZmkJJcDFHoPAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T16:26:50.023675Z","bundle_sha256":"f50457c5580a33a30bfb21390d915f35395cfa00c4bf18390e93eb10bb23133d"}}