{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:GXSZJGGFFKFTV3VPRDFBH4JIAT","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":"e311fd4208dad541547094bffe4701417e6f2d254d3e3fedc7f5e0e93f3a37b2","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-06-13T12:10:20Z","title_canon_sha256":"27d0e5a21e46e4981d096c44b991863f4d255dc052c1736014e3f680e1685e45"},"schema_version":"1.0","source":{"id":"1606.03913","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.03913","created_at":"2026-05-18T01:12:32Z"},{"alias_kind":"arxiv_version","alias_value":"1606.03913v1","created_at":"2026-05-18T01:12:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.03913","created_at":"2026-05-18T01:12:32Z"},{"alias_kind":"pith_short_12","alias_value":"GXSZJGGFFKFT","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GXSZJGGFFKFTV3VP","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GXSZJGGF","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:3901feaf5482838cc69ee97e241d4c70a71020ad06537f5e310121fc8ee31225","target":"graph","created_at":"2026-05-18T01:12:32Z","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 $A,\\;B$ be the positive semidefinite matrices. A matrix version of the famous Powers-St{\\o}rmer's inequality $$2Tr(A^\\alpha B^{1-\\alpha})\\geq Tr(A+B-|A-B|),\\;\\;\\;0\\leq\\alpha\\leq 1,$$ was proven by Audenaert et. al. We establish a comparison of eigenvalues for the matrices $A^\\alpha B^{1-\\alpha}$ and $A+B-|A-B|, \\; 0 \\leq \\alpha \\leq 1,$ subsuming the Powers-St{\\o}rmer's inequality. We also prove several related norm inequalities.","authors_text":"Anchal Aggarwal, Mandeep Singh","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-06-13T12:10:20Z","title":"A generalization of POWERS-ST{\\O}RMER inequality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.03913","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:c5a2194b87e0986687d93437db13f8afb88092a317cee25c8eeda4c4197e8ce8","target":"record","created_at":"2026-05-18T01:12:32Z","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":"e311fd4208dad541547094bffe4701417e6f2d254d3e3fedc7f5e0e93f3a37b2","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-06-13T12:10:20Z","title_canon_sha256":"27d0e5a21e46e4981d096c44b991863f4d255dc052c1736014e3f680e1685e45"},"schema_version":"1.0","source":{"id":"1606.03913","kind":"arxiv","version":1}},"canonical_sha256":"35e59498c52a8b3aeeaf88ca13f12804ca39c9fffcb53cc2e5cfec80403ab2f7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"35e59498c52a8b3aeeaf88ca13f12804ca39c9fffcb53cc2e5cfec80403ab2f7","first_computed_at":"2026-05-18T01:12:32.816957Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:32.816957Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xLs27zE+SUrBhvZ0BtGana1905n8tabS8paCGINhJig/T0ek9Fra8DqJo0vMslCDjhyZveTsBr3BzwSwbmrZBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:32.817371Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.03913","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c5a2194b87e0986687d93437db13f8afb88092a317cee25c8eeda4c4197e8ce8","sha256:3901feaf5482838cc69ee97e241d4c70a71020ad06537f5e310121fc8ee31225"],"state_sha256":"666e7298b33d6b4e9209d109490b762ae1738d013d4ab0e23c3d0d71622303a2"}