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If $\\weakLp\\msp$ is isomorphic, as a Banach space, to $\\weakLp\\mspp$ for some purely atomic measure space $\\mspp$, then there is a measurable partition $\\Omega = \\Omega_1\\cup\\Omega_2$ such that $(\\Omega_1,\\Sigma\\cap\\Omega_1,\\mu_{|\\Sigma\\cap\\Omega_1})$ is countably generated and $\\sigma$-finite, and that $\\mu(\\sigma) = 0$ or $\\infty$ for every measurable $\\sigma \\subseteq \\Omega_2$. In particular, $\\weakLp\\msp$ is isomorphic to $\\ell^{p,\\infty}$."},"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":"math/9607208","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.FA","submitted_at":"1996-07-12T00:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"5ba0c18edf12cec5b1fa9cb6987dbff18ba6f7a7d87cca998fa0ffcf08e89187","abstract_canon_sha256":"800129808dc9908686504905eacd05226e1945252c46f3a4213df384fead9030"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:47.245481Z","signature_b64":"SLC4NM2iwYHLMQ5zA6yz6BYZXGqWbQ0JoKHQqW6AigTm5EMGNFz/aZMCJzn5Eq8DyaHrCXBrXqVG8HzT67yiCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4c060fe6d1bcc73c7fb392eee7813f91305367f9ae8d509167540268ecb396a5","last_reissued_at":"2026-05-18T01:05:47.244952Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:47.244952Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Purely non-atomic weak L^p spaces","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Denny H. 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