{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:IK6FHB3DZAHFNZAM2ZFY3VTUOU","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":"a69e2044d20633f46e0a6fbf57edd48c25214bab8cb8de8d926a9a8937e1e065","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-04-03T17:18:08Z","title_canon_sha256":"8e054991a26f5d54b89df8f53c459d7063306c143d57716b3322e8e8221d880c"},"schema_version":"1.0","source":{"id":"1104.0408","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.0408","created_at":"2026-05-18T01:31:21Z"},{"alias_kind":"arxiv_version","alias_value":"1104.0408v2","created_at":"2026-05-18T01:31:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.0408","created_at":"2026-05-18T01:31:21Z"},{"alias_kind":"pith_short_12","alias_value":"IK6FHB3DZAHF","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"IK6FHB3DZAHFNZAM","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"IK6FHB3D","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:c99c0ca6d9fcc1518573b4b7ff2e536c638a02ebf635a816384b36a66758a650","target":"graph","created_at":"2026-05-18T01:31:21Z","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 study Hermitian unitary matrices $\\mathcal{S}\\in\\mathbb{C}^{n,n}$ with the following property: There exist $r\\geq0$ and $t>0$ such that the entries of $\\mathcal{S}$ satisfy $|\\mathcal{S}_{jj}|=r$ and $|\\mathcal{S}_{jk}|=t$ for all $j,k=1,\\ldots,n$, $j\\neq k$. We derive necessary conditions on the ratio $d:=r/t$ and show that these conditions are very restrictive except for the case when $n$ is even and the sum of the diagonal elements of $\\S$ is zero. Examples of families of matrices $\\mathcal{S}$ are constructed for $d$ belonging to certain intervals. The case of real matrices $\\mathcal{S}","authors_text":"Ondrej Turek, Taksu Cheon","cross_cats":["math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-04-03T17:18:08Z","title":"Hermitian unitary matrices with modular permutation symmetry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.0408","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":"sha256:1f1da2f1728096d401f3f3f30d2fa74c8854c3c4e9b38215490a7f826776c742","target":"record","created_at":"2026-05-18T01:31:21Z","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":"a69e2044d20633f46e0a6fbf57edd48c25214bab8cb8de8d926a9a8937e1e065","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-04-03T17:18:08Z","title_canon_sha256":"8e054991a26f5d54b89df8f53c459d7063306c143d57716b3322e8e8221d880c"},"schema_version":"1.0","source":{"id":"1104.0408","kind":"arxiv","version":2}},"canonical_sha256":"42bc538763c80e56e40cd64b8dd674751886c6d35aab3e2ba68914ba6d237b09","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"42bc538763c80e56e40cd64b8dd674751886c6d35aab3e2ba68914ba6d237b09","first_computed_at":"2026-05-18T01:31:21.717915Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:31:21.717915Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vqXq9P4uRk8FXeq7FuosH/h2Ej0+oh/hyGchsRAWqiCocbV7cvL6+T9p8Ude80x+a0eZOXJvCw8xcp534SnXDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:31:21.718496Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.0408","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1f1da2f1728096d401f3f3f30d2fa74c8854c3c4e9b38215490a7f826776c742","sha256:c99c0ca6d9fcc1518573b4b7ff2e536c638a02ebf635a816384b36a66758a650"],"state_sha256":"515dc93ca11e7f5f5d12e9904ce83c9a3743a5bfc3c564be787ea7b0004deac7"}