{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:LXRSHR5AXSSMWJVIT6DW5N653Q","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":"dd94ff0ec5ceb33ee417f83b1dc34092d1949e4c4e07c719d4e0b9b8dc10596b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-08-19T18:57:16Z","title_canon_sha256":"10e168b59b5ce6b8cec1df7a86a6734b1d71a6816cad573788c09e8af9306410"},"schema_version":"1.0","source":{"id":"1908.07024","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.07024","created_at":"2026-07-04T23:58:30Z"},{"alias_kind":"arxiv_version","alias_value":"1908.07024v1","created_at":"2026-07-04T23:58:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.07024","created_at":"2026-07-04T23:58:30Z"},{"alias_kind":"pith_short_12","alias_value":"LXRSHR5AXSSM","created_at":"2026-07-04T23:58:30Z"},{"alias_kind":"pith_short_16","alias_value":"LXRSHR5AXSSMWJVI","created_at":"2026-07-04T23:58:30Z"},{"alias_kind":"pith_short_8","alias_value":"LXRSHR5A","created_at":"2026-07-04T23:58:30Z"}],"graph_snapshots":[{"event_id":"sha256:a59d39a4a866763773b2d0ccc9cae0a4447a383250282924be813e0437e59ed7","target":"graph","created_at":"2026-07-04T23:58:30Z","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/1908.07024/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $\\mathcal{H}$ be a complex, separable Hilbert space, and $\\mathcal{B}(\\mathcal{H})$ denote the set of all bounded linear operators on $\\mathcal{H}$. Given an orthogonal projection $P \\in \\mathcal{B}(\\mathcal{H})$ and an operator $D \\in \\mathcal{B}(\\mathcal{H})$, we may write $D=\\begin{bmatrix} D_1& D_2 D_3 & D_4 \\end{bmatrix}$ relative to the decomposition $\\mathcal{H} = \\mathrm{ran}\\, P \\oplus \\mathrm{ran}\\, (I-P)$. In this paper we study the question: for which non-negative integers $j, k$ can we find a normal operator $D$ and an orthogonal projection $P$ such that $\\mathrm{rank}\\, D_2 =","authors_text":"Heydar Radjavi, Laurent W. Marcoux, Yuanhang Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-08-19T18:57:16Z","title":"Normal operators with highly incompatible off-diagonal corners"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.07024","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":"sha256:5de3455fa72c1491a9eec1f58c90c643b7789aaf6215e67cf39025f01b666e53","target":"record","created_at":"2026-07-04T23:58:30Z","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":"dd94ff0ec5ceb33ee417f83b1dc34092d1949e4c4e07c719d4e0b9b8dc10596b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-08-19T18:57:16Z","title_canon_sha256":"10e168b59b5ce6b8cec1df7a86a6734b1d71a6816cad573788c09e8af9306410"},"schema_version":"1.0","source":{"id":"1908.07024","kind":"arxiv","version":1}},"canonical_sha256":"5de323c7a0bca4cb26a89f876eb7dddc07043eba8a10ae48ca1ee04baf4b4745","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5de323c7a0bca4cb26a89f876eb7dddc07043eba8a10ae48ca1ee04baf4b4745","first_computed_at":"2026-07-04T23:58:30.215355Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:58:30.215355Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ezuIGp6x3D6r8uIIQUiq+mwwgDCRbBDYcDlaOD77I7r5bX4e6+WRB+XCANAeoTbWYE1FdjZJGHgYPkNwLwsmDg==","signature_status":"signed_v1","signed_at":"2026-07-04T23:58:30.215791Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.07024","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5de3455fa72c1491a9eec1f58c90c643b7789aaf6215e67cf39025f01b666e53","sha256:a59d39a4a866763773b2d0ccc9cae0a4447a383250282924be813e0437e59ed7"],"state_sha256":"95556e9ad63f3729d8799bef0650b50b912bad83ef5d1f581f3eaf1b421de138"}