{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:7ZL3KDAYVZEZK6NBZAICVFEQEB","short_pith_number":"pith:7ZL3KDAY","schema_version":"1.0","canonical_sha256":"fe57b50c18ae499579a1c8102a94902071d062f7ce4b151bf481bac9c2d87144","source":{"kind":"arxiv","id":"1406.5526","version":3},"attestation_state":"computed","paper":{"title":"Tukey classification of some ideals in $\\omega$ and the lattices of weakly compact sets in Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.FA","authors_text":"Antonio Avil\\'es, Grzegorz Plebanek, Jos\\'e Rodr\\'iguez","submitted_at":"2014-06-20T20:24:41Z","abstract_excerpt":"We study the lattice structure of the family of weakly compact subsets of the unit ball $B_X$ of a separable Banach space $X$, equipped with the inclusion relation (this structure is denoted by $\\mathcal{K}(B_X)$) and also with the parametrized family of almost inclusion relations $K \\subseteq L+\\epsilon B_X$, where $\\epsilon>0$ (this structure is denoted by $\\mathcal{AK}(B_X)$). Tukey equivalence between partially ordered sets and a suitable extension to deal with $\\mathcal{AK}(B_X)$ are used. Assuming the axiom of analytic determinacy, we prove that separable Banach spaces fall into four cat"},"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":"1406.5526","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-06-20T20:24:41Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"58630bfb97c3a2507ac5407670aa39c10523764219ac024c6eeefc2e31bfa9ad","abstract_canon_sha256":"0794a466d63ae2e4664167793b9bde9c15e5282b965f2bc37d704f32dd9e5ff9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:58.778602Z","signature_b64":"5GThmEVVkvqU3z9JnRGxxBDsVBYVio5kyC8gjIbAUCnbHPh3RGMLOHt6z7dCFUvK59UEFqKWbT4UYV8PnR6zDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fe57b50c18ae499579a1c8102a94902071d062f7ce4b151bf481bac9c2d87144","last_reissued_at":"2026-05-18T01:12:58.778241Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:58.778241Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tukey classification of some ideals in $\\omega$ and the lattices of weakly compact sets in Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.FA","authors_text":"Antonio Avil\\'es, Grzegorz Plebanek, Jos\\'e Rodr\\'iguez","submitted_at":"2014-06-20T20:24:41Z","abstract_excerpt":"We study the lattice structure of the family of weakly compact subsets of the unit ball $B_X$ of a separable Banach space $X$, equipped with the inclusion relation (this structure is denoted by $\\mathcal{K}(B_X)$) and also with the parametrized family of almost inclusion relations $K \\subseteq L+\\epsilon B_X$, where $\\epsilon>0$ (this structure is denoted by $\\mathcal{AK}(B_X)$). Tukey equivalence between partially ordered sets and a suitable extension to deal with $\\mathcal{AK}(B_X)$ are used. Assuming the axiom of analytic determinacy, we prove that separable Banach spaces fall into four cat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.5526","kind":"arxiv","version":3},"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":"1406.5526","created_at":"2026-05-18T01:12:58.778308+00:00"},{"alias_kind":"arxiv_version","alias_value":"1406.5526v3","created_at":"2026-05-18T01:12:58.778308+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.5526","created_at":"2026-05-18T01:12:58.778308+00:00"},{"alias_kind":"pith_short_12","alias_value":"7ZL3KDAYVZEZ","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_16","alias_value":"7ZL3KDAYVZEZK6NB","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_8","alias_value":"7ZL3KDAY","created_at":"2026-05-18T12:28:19.803747+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/7ZL3KDAYVZEZK6NBZAICVFEQEB","json":"https://pith.science/pith/7ZL3KDAYVZEZK6NBZAICVFEQEB.json","graph_json":"https://pith.science/api/pith-number/7ZL3KDAYVZEZK6NBZAICVFEQEB/graph.json","events_json":"https://pith.science/api/pith-number/7ZL3KDAYVZEZK6NBZAICVFEQEB/events.json","paper":"https://pith.science/paper/7ZL3KDAY"},"agent_actions":{"view_html":"https://pith.science/pith/7ZL3KDAYVZEZK6NBZAICVFEQEB","download_json":"https://pith.science/pith/7ZL3KDAYVZEZK6NBZAICVFEQEB.json","view_paper":"https://pith.science/paper/7ZL3KDAY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1406.5526&json=true","fetch_graph":"https://pith.science/api/pith-number/7ZL3KDAYVZEZK6NBZAICVFEQEB/graph.json","fetch_events":"https://pith.science/api/pith-number/7ZL3KDAYVZEZK6NBZAICVFEQEB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7ZL3KDAYVZEZK6NBZAICVFEQEB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7ZL3KDAYVZEZK6NBZAICVFEQEB/action/storage_attestation","attest_author":"https://pith.science/pith/7ZL3KDAYVZEZK6NBZAICVFEQEB/action/author_attestation","sign_citation":"https://pith.science/pith/7ZL3KDAYVZEZK6NBZAICVFEQEB/action/citation_signature","submit_replication":"https://pith.science/pith/7ZL3KDAYVZEZK6NBZAICVFEQEB/action/replication_record"}},"created_at":"2026-05-18T01:12:58.778308+00:00","updated_at":"2026-05-18T01:12:58.778308+00:00"}