{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:YW5PUYCTOTUTO7ZPDEOSSSXCKM","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":"7ae35f88989dbb6e57e8838bc6542c2d45863e74d7a4e62cb1efbf2626c7c4f1","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-06-22T08:11:51Z","title_canon_sha256":"b667835ca499264fc9014ea7682255ab16299345b8125c4e2fd3b44bbedc66cc"},"schema_version":"1.0","source":{"id":"1206.5080","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.5080","created_at":"2026-05-18T03:32:17Z"},{"alias_kind":"arxiv_version","alias_value":"1206.5080v3","created_at":"2026-05-18T03:32:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.5080","created_at":"2026-05-18T03:32:17Z"},{"alias_kind":"pith_short_12","alias_value":"YW5PUYCTOTUT","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"YW5PUYCTOTUTO7ZP","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"YW5PUYCT","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:dc0ed94aae4d85c4a8fd3d07b47020a4a6d9fc4e3c63c002ea09d7d42c3c4e5b","target":"graph","created_at":"2026-05-18T03:32:17Z","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":"We show that every self--adjoint matrix B of trace 0 can be realized as B=T+T^* for a nilpotent matrix T of norm no greater than K times the norm of B, for a constant K that is independent of matrix size. More particularly, if D is a diagonal, self--adjoint n-by-n matrix of trace 0, then there is a unitary matrix V=XU_n, where X is an n-by-n permutation matrix and U_n is the n-by-n Fourier matrix, such that the upper triangular part, T, of the conjugate V^*DV of D has norm no greater than K times the norm of D. This matrix T is a strictly upper triangular Toeplitz matrix such that T+T^*=V^*DV.","authors_text":"Anna Skripka, Junsheng Fang, Ken Dykema","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-06-22T08:11:51Z","title":"Upper triangular Toeplitz matrices and real parts of quasinilpotent operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.5080","kind":"arxiv","version":3},"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:c3de3833000876927a2e0de5fc598b88525dc59ddb24b970ec3a0d8c5d727f6f","target":"record","created_at":"2026-05-18T03:32:17Z","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":"7ae35f88989dbb6e57e8838bc6542c2d45863e74d7a4e62cb1efbf2626c7c4f1","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-06-22T08:11:51Z","title_canon_sha256":"b667835ca499264fc9014ea7682255ab16299345b8125c4e2fd3b44bbedc66cc"},"schema_version":"1.0","source":{"id":"1206.5080","kind":"arxiv","version":3}},"canonical_sha256":"c5bafa605374e9377f2f191d294ae2533577ed94a20ecf27e177e83447d4c049","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c5bafa605374e9377f2f191d294ae2533577ed94a20ecf27e177e83447d4c049","first_computed_at":"2026-05-18T03:32:17.049978Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:32:17.049978Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AhlZQCxK8eUonmIlvaCZ+r2JnMPvzeCAPMY5/vuBU8jKVYxA/yo8RyUObRNc93DSR701QY6JV+jhFGFWV5yJBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:32:17.050672Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.5080","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c3de3833000876927a2e0de5fc598b88525dc59ddb24b970ec3a0d8c5d727f6f","sha256:dc0ed94aae4d85c4a8fd3d07b47020a4a6d9fc4e3c63c002ea09d7d42c3c4e5b"],"state_sha256":"2b259b0aab1dbbb8351976f8f9cc83711421cea8737f0984efacb50ffe431802"}