{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:XF442CE4AFD5U24NSBYKO4WIMQ","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":"6050da7b4704244036ee14cf8be1a3c39f7e82c83b4fa3a31f38ab449f78bc88","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-07-19T09:18:30Z","title_canon_sha256":"828907723c48241a0976b9fc0e7a7ceaa98ee8c8680954698c5d5bb28f0b05e1"},"schema_version":"1.0","source":{"id":"1807.07307","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.07307","created_at":"2026-07-05T01:54:39Z"},{"alias_kind":"arxiv_version","alias_value":"1807.07307v2","created_at":"2026-07-05T01:54:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.07307","created_at":"2026-07-05T01:54:39Z"},{"alias_kind":"pith_short_12","alias_value":"XF442CE4AFD5","created_at":"2026-07-05T01:54:39Z"},{"alias_kind":"pith_short_16","alias_value":"XF442CE4AFD5U24N","created_at":"2026-07-05T01:54:39Z"},{"alias_kind":"pith_short_8","alias_value":"XF442CE4","created_at":"2026-07-05T01:54:39Z"}],"graph_snapshots":[{"event_id":"sha256:8ab15ad961a9caee567579f5353880d4a920a7c1ebc30ce2dcb95f7e3f23e1e0","target":"graph","created_at":"2026-07-05T01:54:39Z","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/1807.07307/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we generalize the known DDVV-type inequalities for real (skew-)symmetric and complex (skew-)Hermitian matrices to arbitrary real, complex and quaternionic matrices. Inspired by the Erd\\H{o}s-Mordell inequality, we establish the DDVV-type inequalities for matrices in the subspaces spanned by a Clifford system or a Clifford algebra. We also generalize the B\\\"{o}ttcher-Wenzel inequality to quaternionic matrices.","authors_text":"Fagui Li, Jianquan Ge, Yi Zhou","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-07-19T09:18:30Z","title":"Some generalizations of the DDVV and BW inequalities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.07307","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:ee5ad2efada5878a30aa19604a7efccfcec36b8fc77a9f794fec626e5cb0fbff","target":"record","created_at":"2026-07-05T01:54:39Z","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":"6050da7b4704244036ee14cf8be1a3c39f7e82c83b4fa3a31f38ab449f78bc88","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-07-19T09:18:30Z","title_canon_sha256":"828907723c48241a0976b9fc0e7a7ceaa98ee8c8680954698c5d5bb28f0b05e1"},"schema_version":"1.0","source":{"id":"1807.07307","kind":"arxiv","version":2}},"canonical_sha256":"b979cd089c0147da6b8d9070a772c8642b7cc5bc35787d7f75ac91cd3d501940","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b979cd089c0147da6b8d9070a772c8642b7cc5bc35787d7f75ac91cd3d501940","first_computed_at":"2026-07-05T01:54:39.139679Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:54:39.139679Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"40kugzZsioJv30C+tQtRpbV5pQPhTl6zB3+McLudkiD5FiMSqB0f1cfWTeYao4fTa/VvNs3d3N+H9sj5d9MrCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T01:54:39.140148Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.07307","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ee5ad2efada5878a30aa19604a7efccfcec36b8fc77a9f794fec626e5cb0fbff","sha256:8ab15ad961a9caee567579f5353880d4a920a7c1ebc30ce2dcb95f7e3f23e1e0"],"state_sha256":"bfca19da356f78411475b98960154fbe3c6d9383d54c3f0032f5bd9f1bd98ce7"}