{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:4SHGQSNXTBGSWJUR7RQEELFZRR","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":"f1607e7da018a57e247046b69a45733dd4cbb30623f69494d0cb495c5f8aba8e","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-05-17T21:44:43Z","title_canon_sha256":"f0230cc9c29bd458d3fea84e12e6cecee3185f11e6951d78bc8c4975a2c3ea23"},"schema_version":"1.0","source":{"id":"1605.05377","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.05377","created_at":"2026-05-18T01:03:11Z"},{"alias_kind":"arxiv_version","alias_value":"1605.05377v2","created_at":"2026-05-18T01:03:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.05377","created_at":"2026-05-18T01:03:11Z"},{"alias_kind":"pith_short_12","alias_value":"4SHGQSNXTBGS","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4SHGQSNXTBGSWJUR","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4SHGQSNX","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:31047ab855611602209c1f1248c960c6b6c27fe1e00fc0eb0d02098751a47b09","target":"graph","created_at":"2026-05-18T01:03:11Z","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":"Let $p>1$ and $1/p+1/q=1$. Consider H\\\"older's inequality $$ \\|ab^*\\|_1\\le \\|a\\|_p\\|b\\|_q $$ for the $p$-norms of some trace ($a,b$ are matrices, compact operators, elements of a finite $C^*$-algebra or a semi-finite von Neumann algebra). This note contains a simple proof (based on the case $p=2$) of the fact that equality holds iff $|a|^p=\\lambda |b|^q$ for some $\\lambda\\ge 0$.","authors_text":"Gabriel Larotonda","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-05-17T21:44:43Z","title":"The case of equality in H\\\"older's inequality for matrices and operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.05377","kind":"arxiv","version":2},"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":"sha256:734433fac2ad82200f014eb2012eba2e747522ecb1ceb2084b64198f31f9d544","target":"record","created_at":"2026-05-18T01:03:11Z","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":"f1607e7da018a57e247046b69a45733dd4cbb30623f69494d0cb495c5f8aba8e","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-05-17T21:44:43Z","title_canon_sha256":"f0230cc9c29bd458d3fea84e12e6cecee3185f11e6951d78bc8c4975a2c3ea23"},"schema_version":"1.0","source":{"id":"1605.05377","kind":"arxiv","version":2}},"canonical_sha256":"e48e6849b7984d2b2691fc60422cb98c6e019bffc83905103df9b973e295d451","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e48e6849b7984d2b2691fc60422cb98c6e019bffc83905103df9b973e295d451","first_computed_at":"2026-05-18T01:03:11.824359Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:11.824359Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/cn6fMmM9hVVy7bISwHQILtQYzx7p9oqKnkccQueDa6831wCaVjr7a7ZnAXVO8bQ4lxB2CLBlrtHj2vkGkOaCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:11.825012Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.05377","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:734433fac2ad82200f014eb2012eba2e747522ecb1ceb2084b64198f31f9d544","sha256:31047ab855611602209c1f1248c960c6b6c27fe1e00fc0eb0d02098751a47b09"],"state_sha256":"4f2a2f12244f3d5bca5a817bf2031ac222932dfe19f831162d5d6603c55a9aa1"}