{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1994:MBO4U27IIKLDWVCKC23SQ3R4IZ","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":"d0ce942b17d85ca831f81ce83a21fa807698dd347b59c004c4c11d844622f8dc","cross_cats_sorted":[],"license":"","primary_cat":"math.FA","submitted_at":"1994-02-01T16:01:49Z","title_canon_sha256":"b29222b1307063c252d999b297aae98ab08216d117c4d792ed75c7ca2a2e43b0"},"schema_version":"1.0","source":{"id":"math/9402204","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9402204","created_at":"2026-05-18T01:05:51Z"},{"alias_kind":"arxiv_version","alias_value":"math/9402204v1","created_at":"2026-05-18T01:05:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9402204","created_at":"2026-05-18T01:05:51Z"},{"alias_kind":"pith_short_12","alias_value":"MBO4U27IIKLD","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"MBO4U27IIKLDWVCK","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"MBO4U27I","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:9b2edeaa6b48f7c8364d14a2eda8ac5a9967f7ca2fab24c5060df61af453e21f","target":"graph","created_at":"2026-05-18T01:05:51Z","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":"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.","authors_text":"Carsten Sch\\\"utt","cross_cats":[],"headline":"","license":"","primary_cat":"math.FA","submitted_at":"1994-02-01T16:01:49Z","title":"On the embedding of 2-concave Orlicz spaces into $L^1$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9402204","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:caa2663f2d1134e474e10d031c1c16e3c6a9e01d8a37e6ff71de0c0a66f7c281","target":"record","created_at":"2026-05-18T01:05:51Z","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":"d0ce942b17d85ca831f81ce83a21fa807698dd347b59c004c4c11d844622f8dc","cross_cats_sorted":[],"license":"","primary_cat":"math.FA","submitted_at":"1994-02-01T16:01:49Z","title_canon_sha256":"b29222b1307063c252d999b297aae98ab08216d117c4d792ed75c7ca2a2e43b0"},"schema_version":"1.0","source":{"id":"math/9402204","kind":"arxiv","version":1}},"canonical_sha256":"605dca6be842963b544a16b7286e3c465858a32a01f0327a5d07a188a5340424","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"605dca6be842963b544a16b7286e3c465858a32a01f0327a5d07a188a5340424","first_computed_at":"2026-05-18T01:05:51.669195Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:51.669195Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NRfH41In/S1f7P5EOgfMloUpa2XbSjkv59/QgKms8hrvoqrComVJQ1Nbgg+DJkUgzYVqU+HfSA0B8fozfG0kCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:51.669634Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9402204","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:caa2663f2d1134e474e10d031c1c16e3c6a9e01d8a37e6ff71de0c0a66f7c281","sha256:9b2edeaa6b48f7c8364d14a2eda8ac5a9967f7ca2fab24c5060df61af453e21f"],"state_sha256":"1a27ca6fda367c0247b33596ceb9b49462cdcdbd73f7803105944cef92f9ae31"}