{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:HXCUR4UM33BGWUZN23HVBISDBA","short_pith_number":"pith:HXCUR4UM","schema_version":"1.0","canonical_sha256":"3dc548f28cdec26b532dd6cf50a2430823ca214e651e39dd18a21f025e9118be","source":{"kind":"arxiv","id":"1804.03456","version":2},"attestation_state":"computed","paper":{"title":"Some remarks about disjointly homogeneous symmetric spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"S. Astashkin","submitted_at":"2018-04-10T11:18:25Z","abstract_excerpt":"Let $1\\le p<\\infty$. A symmetric space $X$ on $[0,1]$ is said to be $p$-disjointly homogeneous (resp. restricted $p$-disjointly homogeneous) if every sequence of normalized pairwise disjoint functions from $X$ (resp. characteristic functions) contains a subsequence equivalent in $X$ to the unit vector basis of $l_p$. Answering a question posed recently, we construct, for each $1\\le p<\\infty$, a restricted $p$-disjointly homogeneous symmetric space, which is not $p$-disjointly homogeneous. Moreover, we prove that the property of $p$-disjoint homogeneity is preserved under Banach isomorphisms."},"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":"1804.03456","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-04-10T11:18:25Z","cross_cats_sorted":[],"title_canon_sha256":"e88761a0b8c5e08dcb6cbcc881538ec9cd665c7ed7482c07ddeb289342b9747b","abstract_canon_sha256":"fa34464170b30f27b498e2ca490e7fe8f841ff8e8dfa05b254b33022a954ee67"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:05.932403Z","signature_b64":"1zwHU3T+DMwXLbB7RsYE0gmAisl/nQ/2fkHNGOlBIdg19EeIlEQ1w7d7y6qyCV6QcJuNFzIS8eYzUVPtb79WDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3dc548f28cdec26b532dd6cf50a2430823ca214e651e39dd18a21f025e9118be","last_reissued_at":"2026-05-17T23:51:05.931944Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:05.931944Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Some remarks about disjointly homogeneous symmetric spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"S. Astashkin","submitted_at":"2018-04-10T11:18:25Z","abstract_excerpt":"Let $1\\le p<\\infty$. A symmetric space $X$ on $[0,1]$ is said to be $p$-disjointly homogeneous (resp. restricted $p$-disjointly homogeneous) if every sequence of normalized pairwise disjoint functions from $X$ (resp. characteristic functions) contains a subsequence equivalent in $X$ to the unit vector basis of $l_p$. Answering a question posed recently, we construct, for each $1\\le p<\\infty$, a restricted $p$-disjointly homogeneous symmetric space, which is not $p$-disjointly homogeneous. Moreover, we prove that the property of $p$-disjoint homogeneity is preserved under Banach isomorphisms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.03456","kind":"arxiv","version":2},"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":"1804.03456","created_at":"2026-05-17T23:51:05.932007+00:00"},{"alias_kind":"arxiv_version","alias_value":"1804.03456v2","created_at":"2026-05-17T23:51:05.932007+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.03456","created_at":"2026-05-17T23:51:05.932007+00:00"},{"alias_kind":"pith_short_12","alias_value":"HXCUR4UM33BG","created_at":"2026-05-18T12:32:28.185984+00:00"},{"alias_kind":"pith_short_16","alias_value":"HXCUR4UM33BGWUZN","created_at":"2026-05-18T12:32:28.185984+00:00"},{"alias_kind":"pith_short_8","alias_value":"HXCUR4UM","created_at":"2026-05-18T12:32:28.185984+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/HXCUR4UM33BGWUZN23HVBISDBA","json":"https://pith.science/pith/HXCUR4UM33BGWUZN23HVBISDBA.json","graph_json":"https://pith.science/api/pith-number/HXCUR4UM33BGWUZN23HVBISDBA/graph.json","events_json":"https://pith.science/api/pith-number/HXCUR4UM33BGWUZN23HVBISDBA/events.json","paper":"https://pith.science/paper/HXCUR4UM"},"agent_actions":{"view_html":"https://pith.science/pith/HXCUR4UM33BGWUZN23HVBISDBA","download_json":"https://pith.science/pith/HXCUR4UM33BGWUZN23HVBISDBA.json","view_paper":"https://pith.science/paper/HXCUR4UM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1804.03456&json=true","fetch_graph":"https://pith.science/api/pith-number/HXCUR4UM33BGWUZN23HVBISDBA/graph.json","fetch_events":"https://pith.science/api/pith-number/HXCUR4UM33BGWUZN23HVBISDBA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HXCUR4UM33BGWUZN23HVBISDBA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HXCUR4UM33BGWUZN23HVBISDBA/action/storage_attestation","attest_author":"https://pith.science/pith/HXCUR4UM33BGWUZN23HVBISDBA/action/author_attestation","sign_citation":"https://pith.science/pith/HXCUR4UM33BGWUZN23HVBISDBA/action/citation_signature","submit_replication":"https://pith.science/pith/HXCUR4UM33BGWUZN23HVBISDBA/action/replication_record"}},"created_at":"2026-05-17T23:51:05.932007+00:00","updated_at":"2026-05-17T23:51:05.932007+00:00"}