{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:QYJI5DFQ73JUYGIJSKEAZCT7G2","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":"dcf725fa494e02c3188a26bf89327230c78f3fe25cf221637a58a29a8cdf4eff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-04-01T04:30:04Z","title_canon_sha256":"cda7afdcaa9a4b73ba8ec3221d76c9e9953cfaa97e83e683a1aa9d21ca7bcaab"},"schema_version":"1.0","source":{"id":"1304.0295","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.0295","created_at":"2026-05-18T03:29:17Z"},{"alias_kind":"arxiv_version","alias_value":"1304.0295v1","created_at":"2026-05-18T03:29:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.0295","created_at":"2026-05-18T03:29:17Z"},{"alias_kind":"pith_short_12","alias_value":"QYJI5DFQ73JU","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QYJI5DFQ73JUYGIJ","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QYJI5DFQ","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:d44cc15e883f799e3a1cb452ebdff0aefc017d6503db5ee23d87adae6fc83cf0","target":"graph","created_at":"2026-05-18T03:29:17Z","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":"A KMS matrix is one of the form $$J_n(a)=[{array}{ccccc} 0 & a & a^2 &... & a^{n-1} & 0 & a & \\ddots & \\vdots & & \\ddots & \\ddots & a^2 & & & \\ddots & a 0 & & & & 0{array}]$$ for $n\\ge 1$ and $a$ in $\\mathbb{C}$. Among other things, we prove the following properties of its numerical range: (1) $W(J_n(a))$ is a circular disc if and only if $n=2$ and $a\\neq 0$, (2) its boundary $\\partial W(J_n(a))$ contains a line segment if and only if $n\\ge 3$ and $|a|=1$, and (3) the intersection of the boundaries $\\partial W(J_n(a))$ and $\\partial W(J_n(a)[j])$ is either the singleton $\\{\\min\\sigma(\\re J_n(a","authors_text":"Hwa-Long Gau, Pei Yuan Wu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-04-01T04:30:04Z","title":"Numerical Ranges of KMS Matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0295","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":"sha256:74562483b2527b0b07fb5a8a34e53a794e4d28539744ed6ed01b029ea06c0213","target":"record","created_at":"2026-05-18T03:29:17Z","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":"dcf725fa494e02c3188a26bf89327230c78f3fe25cf221637a58a29a8cdf4eff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-04-01T04:30:04Z","title_canon_sha256":"cda7afdcaa9a4b73ba8ec3221d76c9e9953cfaa97e83e683a1aa9d21ca7bcaab"},"schema_version":"1.0","source":{"id":"1304.0295","kind":"arxiv","version":1}},"canonical_sha256":"86128e8cb0fed34c190992880c8a7f3693b91785895c4580d8fce7a8c587ac5f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"86128e8cb0fed34c190992880c8a7f3693b91785895c4580d8fce7a8c587ac5f","first_computed_at":"2026-05-18T03:29:17.364246Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:29:17.364246Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mROWL5y+XrbWr/x88wNiKYjDjzdi0HAV3ULoum0aDDwss7EnPH+sTN2IW/RLKlUy4YKNHvznb8WlNH0mppFtAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:29:17.364797Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.0295","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:74562483b2527b0b07fb5a8a34e53a794e4d28539744ed6ed01b029ea06c0213","sha256:d44cc15e883f799e3a1cb452ebdff0aefc017d6503db5ee23d87adae6fc83cf0"],"state_sha256":"f939e08cd558f82703e555cb731a30882e9deb5912361656a9b8754b082a1609"}