{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1994:MBO4U27IIKLDWVCKC23SQ3R4IZ","short_pith_number":"pith:MBO4U27I","schema_version":"1.0","canonical_sha256":"605dca6be842963b544a16b7286e3c465858a32a01f0327a5d07a188a5340424","source":{"kind":"arxiv","id":"math/9402204","version":1},"attestation_state":"computed","paper":{"title":"On the embedding of 2-concave Orlicz spaces into $L^1$","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Carsten Sch\\\"utt","submitted_at":"1994-02-01T16:01:49Z","abstract_excerpt":"In [K--S 1] it was shown that\n  $$ \\underset {\\pi} \\to {\\text{Ave}} (\\sum_{i=1}^{n}|x_i a_{\\pi(i)}|^2)^{\\frac {1}{2}} $$\n  is equivalent to an Orlicz norm whose Orlicz function is 2-concave. Here we give a formula for the sequence $a_1, a_2,....,a_n$ so that the above expression is equivalent to a given Orlicz norm."},"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/9402204","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.FA","submitted_at":"1994-02-01T16:01:49Z","cross_cats_sorted":[],"title_canon_sha256":"b29222b1307063c252d999b297aae98ab08216d117c4d792ed75c7ca2a2e43b0","abstract_canon_sha256":"d0ce942b17d85ca831f81ce83a21fa807698dd347b59c004c4c11d844622f8dc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:51.669634Z","signature_b64":"NRfH41In/S1f7P5EOgfMloUpa2XbSjkv59/QgKms8hrvoqrComVJQ1Nbgg+DJkUgzYVqU+HfSA0B8fozfG0kCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"605dca6be842963b544a16b7286e3c465858a32a01f0327a5d07a188a5340424","last_reissued_at":"2026-05-18T01:05:51.669195Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:51.669195Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the embedding of 2-concave Orlicz spaces into $L^1$","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Carsten Sch\\\"utt","submitted_at":"1994-02-01T16:01:49Z","abstract_excerpt":"In [K--S 1] it was shown that\n  $$ \\underset {\\pi} \\to {\\text{Ave}} (\\sum_{i=1}^{n}|x_i a_{\\pi(i)}|^2)^{\\frac {1}{2}} $$\n  is equivalent to an Orlicz norm whose Orlicz function is 2-concave. Here we give a formula for the sequence $a_1, a_2,....,a_n$ so that the above expression is equivalent to a given Orlicz norm."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9402204","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":"math/9402204","created_at":"2026-05-18T01:05:51.669266+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/9402204v1","created_at":"2026-05-18T01:05:51.669266+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9402204","created_at":"2026-05-18T01:05:51.669266+00:00"},{"alias_kind":"pith_short_12","alias_value":"MBO4U27IIKLD","created_at":"2026-05-18T12:25:47.102015+00:00"},{"alias_kind":"pith_short_16","alias_value":"MBO4U27IIKLDWVCK","created_at":"2026-05-18T12:25:47.102015+00:00"},{"alias_kind":"pith_short_8","alias_value":"MBO4U27I","created_at":"2026-05-18T12:25:47.102015+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/MBO4U27IIKLDWVCKC23SQ3R4IZ","json":"https://pith.science/pith/MBO4U27IIKLDWVCKC23SQ3R4IZ.json","graph_json":"https://pith.science/api/pith-number/MBO4U27IIKLDWVCKC23SQ3R4IZ/graph.json","events_json":"https://pith.science/api/pith-number/MBO4U27IIKLDWVCKC23SQ3R4IZ/events.json","paper":"https://pith.science/paper/MBO4U27I"},"agent_actions":{"view_html":"https://pith.science/pith/MBO4U27IIKLDWVCKC23SQ3R4IZ","download_json":"https://pith.science/pith/MBO4U27IIKLDWVCKC23SQ3R4IZ.json","view_paper":"https://pith.science/paper/MBO4U27I","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/9402204&json=true","fetch_graph":"https://pith.science/api/pith-number/MBO4U27IIKLDWVCKC23SQ3R4IZ/graph.json","fetch_events":"https://pith.science/api/pith-number/MBO4U27IIKLDWVCKC23SQ3R4IZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MBO4U27IIKLDWVCKC23SQ3R4IZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MBO4U27IIKLDWVCKC23SQ3R4IZ/action/storage_attestation","attest_author":"https://pith.science/pith/MBO4U27IIKLDWVCKC23SQ3R4IZ/action/author_attestation","sign_citation":"https://pith.science/pith/MBO4U27IIKLDWVCKC23SQ3R4IZ/action/citation_signature","submit_replication":"https://pith.science/pith/MBO4U27IIKLDWVCKC23SQ3R4IZ/action/replication_record"}},"created_at":"2026-05-18T01:05:51.669266+00:00","updated_at":"2026-05-18T01:05:51.669266+00:00"}