{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:4VLEY7JD6Q4SKCE7TNWDAJ5LTN","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":"3c6c63456346a00340d04f7d32a35803d544244d96530f3f4c8271b2d8fcd996","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2025-07-20T12:29:14Z","title_canon_sha256":"a2b56a1436a8039c47c16de47ea1fa12431841041c82fce4e297683785abb65f"},"schema_version":"1.0","source":{"id":"2507.14940","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.14940","created_at":"2026-07-05T11:40:15Z"},{"alias_kind":"arxiv_version","alias_value":"2507.14940v1","created_at":"2026-07-05T11:40:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.14940","created_at":"2026-07-05T11:40:15Z"},{"alias_kind":"pith_short_12","alias_value":"4VLEY7JD6Q4S","created_at":"2026-07-05T11:40:15Z"},{"alias_kind":"pith_short_16","alias_value":"4VLEY7JD6Q4SKCE7","created_at":"2026-07-05T11:40:15Z"},{"alias_kind":"pith_short_8","alias_value":"4VLEY7JD","created_at":"2026-07-05T11:40:15Z"}],"graph_snapshots":[{"event_id":"sha256:e75b556a25728ad54257e36cdef9794c0e597ec2312e3b545483b5c2f3fdac57","target":"graph","created_at":"2026-07-05T11:40:15Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2507.14940/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Leveraging tools from convex analysis and incorporating additional singular value information of matrices, we completely resolve the problem of establishing perturbation bounds for the Frobenius norm of subunitary and positive polar factors. We derive corresponding sharp upper and lower bounds. As corollaries, we refine the results of Li and Sun [SIAM J. Matrix Anal. Appl., 23 (2002), pp. 1183--1193] and strengthen the classical Araki-Yamagami inequality [Comm. Math. Phys., 81 (1981), no. 1, pp. 89--96]. The versatility of our method also allows us to strengthen Lee's conjecture, providing a s","authors_text":"Teng Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2025-07-20T12:29:14Z","title":"Sharp perturbation bounds on the Frobenius norm of subunitary and positive polar factor"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.14940","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:de980c5c91f0f213305ce0a79a80279168cc1040a40d262cb3a9fb62290e0fd4","target":"record","created_at":"2026-07-05T11:40:15Z","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":"3c6c63456346a00340d04f7d32a35803d544244d96530f3f4c8271b2d8fcd996","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2025-07-20T12:29:14Z","title_canon_sha256":"a2b56a1436a8039c47c16de47ea1fa12431841041c82fce4e297683785abb65f"},"schema_version":"1.0","source":{"id":"2507.14940","kind":"arxiv","version":1}},"canonical_sha256":"e5564c7d23f43925089f9b6c3027ab9b7b5c9542f87f249db4dec8ce732137ea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e5564c7d23f43925089f9b6c3027ab9b7b5c9542f87f249db4dec8ce732137ea","first_computed_at":"2026-07-05T11:40:15.728037Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:40:15.728037Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uE2Vysw5QtBrJn2HJCcuWnVLCAIo+EcOsD76eaWzv5VPXwK7yDclIxlxKFkLPQ14oE2WMJJrZ+wRGEqkw6viBw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:40:15.728526Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.14940","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:de980c5c91f0f213305ce0a79a80279168cc1040a40d262cb3a9fb62290e0fd4","sha256:e75b556a25728ad54257e36cdef9794c0e597ec2312e3b545483b5c2f3fdac57"],"state_sha256":"fcbc014890e1aa79b777a87f0072b5e100febac701f67bbad772bb01b54fce78"}