{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:QATEH76CTUIHR4CPBSOPSBWU3I","short_pith_number":"pith:QATEH76C","schema_version":"1.0","canonical_sha256":"802643ffc29d1078f04f0c9cf906d4da0ecf13d4526772e112597d49778c3bf4","source":{"kind":"arxiv","id":"1408.0265","version":1},"attestation_state":"computed","paper":{"title":"The stabilized set of $p$'s in Krivine's theorem can be disconnected","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Daniel Freeman, Kevin Beanland, Pavlos Motakis","submitted_at":"2014-08-01T18:54:39Z","abstract_excerpt":"For any closed subset $F$ of $[1,\\infty]$ which is either finite or consists of the elements of an increasing sequence and its limit, a reflexive Banach space $X$ with a 1-unconditional basis is constructed so that in each block subspace $Y$ of $X$, $\\ell_p$ is finitely block represented in $Y$ if and only if $p \\in F$. In particular, this solves the question as to whether the stabilized Krivine set for a Banach space had to be connected. We also prove that for every infinite dimensional subspace $Y$ of $X$ there is a dense subset $G$ of $F$ such that the spreading models admitted by $Y$ are e"},"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":"1408.0265","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-08-01T18:54:39Z","cross_cats_sorted":[],"title_canon_sha256":"a16c7de919c0b9da869fcfebc0da139a389eb623390675f14bd4841eec5c05bb","abstract_canon_sha256":"e82f2b405d3b58585abd5df838d8e48c889ac7a0cbdf8a23a82e00e1d0358d6c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:42.550107Z","signature_b64":"wVw21TIsBmjn8CA+Ajs4zlYsQYNri8g/HUAUq0Xsw+3wNv19t4tlOCZT8VE+TGHfmsxRWjho6Ux4OvXa5ItxDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"802643ffc29d1078f04f0c9cf906d4da0ecf13d4526772e112597d49778c3bf4","last_reissued_at":"2026-05-18T01:19:42.549440Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:42.549440Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The stabilized set of $p$'s in Krivine's theorem can be disconnected","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Daniel Freeman, Kevin Beanland, Pavlos Motakis","submitted_at":"2014-08-01T18:54:39Z","abstract_excerpt":"For any closed subset $F$ of $[1,\\infty]$ which is either finite or consists of the elements of an increasing sequence and its limit, a reflexive Banach space $X$ with a 1-unconditional basis is constructed so that in each block subspace $Y$ of $X$, $\\ell_p$ is finitely block represented in $Y$ if and only if $p \\in F$. In particular, this solves the question as to whether the stabilized Krivine set for a Banach space had to be connected. We also prove that for every infinite dimensional subspace $Y$ of $X$ there is a dense subset $G$ of $F$ such that the spreading models admitted by $Y$ are e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.0265","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":"1408.0265","created_at":"2026-05-18T01:19:42.549541+00:00"},{"alias_kind":"arxiv_version","alias_value":"1408.0265v1","created_at":"2026-05-18T01:19:42.549541+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.0265","created_at":"2026-05-18T01:19:42.549541+00:00"},{"alias_kind":"pith_short_12","alias_value":"QATEH76CTUIH","created_at":"2026-05-18T12:28:43.426989+00:00"},{"alias_kind":"pith_short_16","alias_value":"QATEH76CTUIHR4CP","created_at":"2026-05-18T12:28:43.426989+00:00"},{"alias_kind":"pith_short_8","alias_value":"QATEH76C","created_at":"2026-05-18T12:28:43.426989+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/QATEH76CTUIHR4CPBSOPSBWU3I","json":"https://pith.science/pith/QATEH76CTUIHR4CPBSOPSBWU3I.json","graph_json":"https://pith.science/api/pith-number/QATEH76CTUIHR4CPBSOPSBWU3I/graph.json","events_json":"https://pith.science/api/pith-number/QATEH76CTUIHR4CPBSOPSBWU3I/events.json","paper":"https://pith.science/paper/QATEH76C"},"agent_actions":{"view_html":"https://pith.science/pith/QATEH76CTUIHR4CPBSOPSBWU3I","download_json":"https://pith.science/pith/QATEH76CTUIHR4CPBSOPSBWU3I.json","view_paper":"https://pith.science/paper/QATEH76C","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1408.0265&json=true","fetch_graph":"https://pith.science/api/pith-number/QATEH76CTUIHR4CPBSOPSBWU3I/graph.json","fetch_events":"https://pith.science/api/pith-number/QATEH76CTUIHR4CPBSOPSBWU3I/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QATEH76CTUIHR4CPBSOPSBWU3I/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QATEH76CTUIHR4CPBSOPSBWU3I/action/storage_attestation","attest_author":"https://pith.science/pith/QATEH76CTUIHR4CPBSOPSBWU3I/action/author_attestation","sign_citation":"https://pith.science/pith/QATEH76CTUIHR4CPBSOPSBWU3I/action/citation_signature","submit_replication":"https://pith.science/pith/QATEH76CTUIHR4CPBSOPSBWU3I/action/replication_record"}},"created_at":"2026-05-18T01:19:42.549541+00:00","updated_at":"2026-05-18T01:19:42.549541+00:00"}