{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:RLFWO4IAGA7WBFKJUYEIXAHEMR","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":"82feeba5582d097a175733f9705638ec5bf53470f417f95d8182e63cfd06affc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-04-05T07:36:17Z","title_canon_sha256":"5b169b8a8dc67379f147724a8d719c62debc897940ba6cd07ffcaa396f2a403f"},"schema_version":"1.0","source":{"id":"1004.0581","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.0581","created_at":"2026-05-18T04:27:15Z"},{"alias_kind":"arxiv_version","alias_value":"1004.0581v3","created_at":"2026-05-18T04:27:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.0581","created_at":"2026-05-18T04:27:15Z"},{"alias_kind":"pith_short_12","alias_value":"RLFWO4IAGA7W","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"RLFWO4IAGA7WBFKJ","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"RLFWO4IA","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:416db222b48a0c89717f199f03b3a4c32baeec68dd93aa09861196337ca952d7","target":"graph","created_at":"2026-05-18T04:27:15Z","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 this paper, we show that the $\\nu$-weighted arithmetic mean is greater than the product of the $\\nu$-weighted geometric mean and Specht's ratio. As a corollary, we also show that the $\\nu$-weighted geometric mean is greater than the product of the $\\nu$-weighted harmonic mean and Specht's ratio. These results give the improvements for the classical Young inequalities, since Specht's ratio is generally greater than 1. In addition, we give an operator inequality for positive operators, applying our refined Young inequality.","authors_text":"Shigeru Furuichi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-04-05T07:36:17Z","title":"Refined Young inequalities with Specht's ratio"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.0581","kind":"arxiv","version":3},"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:b7f1f3b86e34bedededfe7f49138f3c50e4b096b4f90658ceaabdfa4a574f429","target":"record","created_at":"2026-05-18T04:27:15Z","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":"82feeba5582d097a175733f9705638ec5bf53470f417f95d8182e63cfd06affc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-04-05T07:36:17Z","title_canon_sha256":"5b169b8a8dc67379f147724a8d719c62debc897940ba6cd07ffcaa396f2a403f"},"schema_version":"1.0","source":{"id":"1004.0581","kind":"arxiv","version":3}},"canonical_sha256":"8acb677100303f609549a6088b80e46466a39b399a9fccf7bc1ab719b54398d3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8acb677100303f609549a6088b80e46466a39b399a9fccf7bc1ab719b54398d3","first_computed_at":"2026-05-18T04:27:15.050162Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:27:15.050162Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WibmaGKbZZLNzFvxeAu0juQCjIMBX9Izw2+JQwvNsJ5Hu4amnYcccEeKgsRlkv7IsIK0jl1jr7vw6+WKFhjWAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:27:15.050765Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.0581","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b7f1f3b86e34bedededfe7f49138f3c50e4b096b4f90658ceaabdfa4a574f429","sha256:416db222b48a0c89717f199f03b3a4c32baeec68dd93aa09861196337ca952d7"],"state_sha256":"8feabf4179b0f83efcbf5a3b0bfaebcc92cc469b381bc17045fa4a178d55c7ea"}