{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:M2IZ47ZOR3NP4X6JBJ5BCB6TMM","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":"61df1c2dca6b456995d83b93213d123bc59615ad453cb3d55e5795a56540b5cc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-06-04T14:01:27Z","title_canon_sha256":"52af53b9412d62bd2d1b151b2bfa8f00b260db8f3582d1d03c5e3dcae054a333"},"schema_version":"1.0","source":{"id":"1906.01448","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.01448","created_at":"2026-05-17T23:44:16Z"},{"alias_kind":"arxiv_version","alias_value":"1906.01448v1","created_at":"2026-05-17T23:44:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.01448","created_at":"2026-05-17T23:44:16Z"},{"alias_kind":"pith_short_12","alias_value":"M2IZ47ZOR3NP","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"M2IZ47ZOR3NP4X6J","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"M2IZ47ZO","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:728c2a2aa138b47cfdcf17cf84c3b59ae4f97f39fc99cc6a7fbc8e9e4c858279","target":"graph","created_at":"2026-05-17T23:44:16Z","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":"We prove a weighted version of a classical inequality of Johnson and Schechtman from which we derive a decomposition theorem for $p$-th moments ($0<p\\leq 1$) of nonnegative generalized $U$-statistics with constant not dependent on $p$. In particular, for $1\\leq p\\leq 2$, the norm in the subspace $U^p_{\\leq m}\\left(\\Omega^\\infty\\right)$ of $L^p\\left(\\Omega^\\infty\\right)$ spanned by functions dependent on at most $m$ variables is equivalent to the norm in a suitable interpolation sum of $L^p\\left(L^2\\right)$ spaces. As a consequence, we obtain some interpolation properties of $U^1_m\\left(\\Omega^","authors_text":"Maciej Rzeszut","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-06-04T14:01:27Z","title":"Weighted and multivariate Johnson--Schechtman inequalities with application to interpolation theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.01448","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":"sha256:956196575d27238a7d0f74c4f28012f16559c597dcfa8ca4f05143423903d400","target":"record","created_at":"2026-05-17T23:44:16Z","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":"61df1c2dca6b456995d83b93213d123bc59615ad453cb3d55e5795a56540b5cc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-06-04T14:01:27Z","title_canon_sha256":"52af53b9412d62bd2d1b151b2bfa8f00b260db8f3582d1d03c5e3dcae054a333"},"schema_version":"1.0","source":{"id":"1906.01448","kind":"arxiv","version":1}},"canonical_sha256":"66919e7f2e8edafe5fc90a7a1107d36302ee22ce9dffe6338e8b48ffa4b57a59","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"66919e7f2e8edafe5fc90a7a1107d36302ee22ce9dffe6338e8b48ffa4b57a59","first_computed_at":"2026-05-17T23:44:16.569233Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:44:16.569233Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"R5vY9mxbY7YvxJAfiSRj48+fyqwQA1hCg8eYQslTIUN3N6aAr9gErMHyXbyRqwCaZ4wh81m//aW6Ny6V6kIWDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:44:16.569899Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.01448","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:956196575d27238a7d0f74c4f28012f16559c597dcfa8ca4f05143423903d400","sha256:728c2a2aa138b47cfdcf17cf84c3b59ae4f97f39fc99cc6a7fbc8e9e4c858279"],"state_sha256":"b83c02d026ad8f2f3f1c1585a54aafc3ed39ecd9f118cdb4297dae773ab01b01"}