{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:Q34VKV4G63I3VP3XEQXP5EKSLL","short_pith_number":"pith:Q34VKV4G","canonical_record":{"source":{"id":"1405.0164","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-05-01T14:07:44Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"bde5e588ca9e8bdd63cf0cb098ebc7e0b089bf4f902e6f6f95eb1f7eb13cbbb1","abstract_canon_sha256":"f8b00be19e43e627e9ab80f33ffcd3fa6a7eea0718788d79fdfcea979569c35c"},"schema_version":"1.0"},"canonical_sha256":"86f9555786f6d1babf77242efe91525af29227e383444729a83f968e22344ef0","source":{"kind":"arxiv","id":"1405.0164","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.0164","created_at":"2026-05-18T01:27:38Z"},{"alias_kind":"arxiv_version","alias_value":"1405.0164v1","created_at":"2026-05-18T01:27:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.0164","created_at":"2026-05-18T01:27:38Z"},{"alias_kind":"pith_short_12","alias_value":"Q34VKV4G63I3","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"Q34VKV4G63I3VP3X","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"Q34VKV4G","created_at":"2026-05-18T12:28:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:Q34VKV4G63I3VP3XEQXP5EKSLL","target":"record","payload":{"canonical_record":{"source":{"id":"1405.0164","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-05-01T14:07:44Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"bde5e588ca9e8bdd63cf0cb098ebc7e0b089bf4f902e6f6f95eb1f7eb13cbbb1","abstract_canon_sha256":"f8b00be19e43e627e9ab80f33ffcd3fa6a7eea0718788d79fdfcea979569c35c"},"schema_version":"1.0"},"canonical_sha256":"86f9555786f6d1babf77242efe91525af29227e383444729a83f968e22344ef0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:27:38.662055Z","signature_b64":"3dCCUIsV5GVTWswZlizGcEaudBpirNJoKDUye2ZSUPJohYdz+QkuS9mzPXV9AmILiXeXk3HvqZWV7dNrwdc+Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"86f9555786f6d1babf77242efe91525af29227e383444729a83f968e22344ef0","last_reissued_at":"2026-05-18T01:27:38.661434Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:27:38.661434Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.0164","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:27:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wXL749jwZHm3M3gIP5k/DKcENoAZ+VTuw8qb1awuP3MjX29DzPb5OoWFZwzocS9jGqMDFifnRdicei1N2+noDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T17:23:45.848360Z"},"content_sha256":"89081bde1e87bf98ce7a415f209041ef5abe90dbaa5b633becc60ef6c610f952","schema_version":"1.0","event_id":"sha256:89081bde1e87bf98ce7a415f209041ef5abe90dbaa5b633becc60ef6c610f952"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:Q34VKV4G63I3VP3XEQXP5EKSLL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Reverses and variations of Heinz inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Mohammad Sal Moslehian, Mojtaba Bakherad","submitted_at":"2014-05-01T14:07:44Z","abstract_excerpt":"Let $A, B$ be positive definite $n\\times n$ matrices. We present several reverse Heinz type inequalities, in particular \\begin{align*} \\|AX+XB\\|_2^2+ 2(\\nu-1) \\|AX-XB\\|_2^2\\leq \\|A^{\\nu}XB^{1-\\nu}+A^{1-\\nu}XB^{\\nu}\\|_2^2,\n  \\end{align*} where $X$ is an arbitrary $n \\times n$ matrix, $\\|\\cdot\\|_2$ is Hilbert-Schmidt norm and $\\nu>1$. We also establish a Heinz type inequality involving the Hadamard product of the form \\begin{align*} 2|||A^{1\\over2}\\circ B^{1\\over2}|||\\leq|||A^{s}\\circ B^{1-t}+A^{1-s}\\circ B^{t}||| \\leq\\max\\{|||(A+B)\\circ I|||,|||(A\\circ B)+I|||\\}, \\end{align*} in which $s, t\\in "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.0164","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:27:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lHiX20eT/0j1D2O11zs6Dz2gNWdFicbz+4GdgwyGU3XUIa0r5foJFqBqfSK+QAniK9rm0eBbUI2wOja17NyxAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T17:23:45.849006Z"},"content_sha256":"59f7408bc37a25eb019962e28b077493931c41eb20f1b0986f6641663c3ab650","schema_version":"1.0","event_id":"sha256:59f7408bc37a25eb019962e28b077493931c41eb20f1b0986f6641663c3ab650"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q34VKV4G63I3VP3XEQXP5EKSLL/bundle.json","state_url":"https://pith.science/pith/Q34VKV4G63I3VP3XEQXP5EKSLL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q34VKV4G63I3VP3XEQXP5EKSLL/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-07T17:23:45Z","links":{"resolver":"https://pith.science/pith/Q34VKV4G63I3VP3XEQXP5EKSLL","bundle":"https://pith.science/pith/Q34VKV4G63I3VP3XEQXP5EKSLL/bundle.json","state":"https://pith.science/pith/Q34VKV4G63I3VP3XEQXP5EKSLL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q34VKV4G63I3VP3XEQXP5EKSLL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:Q34VKV4G63I3VP3XEQXP5EKSLL","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":"f8b00be19e43e627e9ab80f33ffcd3fa6a7eea0718788d79fdfcea979569c35c","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-05-01T14:07:44Z","title_canon_sha256":"bde5e588ca9e8bdd63cf0cb098ebc7e0b089bf4f902e6f6f95eb1f7eb13cbbb1"},"schema_version":"1.0","source":{"id":"1405.0164","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.0164","created_at":"2026-05-18T01:27:38Z"},{"alias_kind":"arxiv_version","alias_value":"1405.0164v1","created_at":"2026-05-18T01:27:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.0164","created_at":"2026-05-18T01:27:38Z"},{"alias_kind":"pith_short_12","alias_value":"Q34VKV4G63I3","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"Q34VKV4G63I3VP3X","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"Q34VKV4G","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:59f7408bc37a25eb019962e28b077493931c41eb20f1b0986f6641663c3ab650","target":"graph","created_at":"2026-05-18T01:27:38Z","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 positive definite $n\\times n$ matrices. We present several reverse Heinz type inequalities, in particular \\begin{align*} \\|AX+XB\\|_2^2+ 2(\\nu-1) \\|AX-XB\\|_2^2\\leq \\|A^{\\nu}XB^{1-\\nu}+A^{1-\\nu}XB^{\\nu}\\|_2^2,\n  \\end{align*} where $X$ is an arbitrary $n \\times n$ matrix, $\\|\\cdot\\|_2$ is Hilbert-Schmidt norm and $\\nu>1$. We also establish a Heinz type inequality involving the Hadamard product of the form \\begin{align*} 2|||A^{1\\over2}\\circ B^{1\\over2}|||\\leq|||A^{s}\\circ B^{1-t}+A^{1-s}\\circ B^{t}||| \\leq\\max\\{|||(A+B)\\circ I|||,|||(A\\circ B)+I|||\\}, \\end{align*} in which $s, t\\in ","authors_text":"Mohammad Sal Moslehian, Mojtaba Bakherad","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-05-01T14:07:44Z","title":"Reverses and variations of Heinz inequality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.0164","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":"sha256:89081bde1e87bf98ce7a415f209041ef5abe90dbaa5b633becc60ef6c610f952","target":"record","created_at":"2026-05-18T01:27:38Z","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":"f8b00be19e43e627e9ab80f33ffcd3fa6a7eea0718788d79fdfcea979569c35c","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-05-01T14:07:44Z","title_canon_sha256":"bde5e588ca9e8bdd63cf0cb098ebc7e0b089bf4f902e6f6f95eb1f7eb13cbbb1"},"schema_version":"1.0","source":{"id":"1405.0164","kind":"arxiv","version":1}},"canonical_sha256":"86f9555786f6d1babf77242efe91525af29227e383444729a83f968e22344ef0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"86f9555786f6d1babf77242efe91525af29227e383444729a83f968e22344ef0","first_computed_at":"2026-05-18T01:27:38.661434Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:27:38.661434Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3dCCUIsV5GVTWswZlizGcEaudBpirNJoKDUye2ZSUPJohYdz+QkuS9mzPXV9AmILiXeXk3HvqZWV7dNrwdc+Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:27:38.662055Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.0164","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:89081bde1e87bf98ce7a415f209041ef5abe90dbaa5b633becc60ef6c610f952","sha256:59f7408bc37a25eb019962e28b077493931c41eb20f1b0986f6641663c3ab650"],"state_sha256":"93241329eb3a441ac67bee0f24fe386eaea0c588c3e9f664b70c80aa725cefba"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dcrDI54/MTouVKKCIo48Bzdfw7t9yjqZ6V8AOLW/fbFS++ITHdKiRTV0sOVGcPnr3PiDUfSwfqMzbcOR+x6+Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T17:23:45.851934Z","bundle_sha256":"c58cdfcaf67c661aa1d14f83ee3b8d8392ff49b04f8ca307758cca2366a21043"}}