{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:OD6T34Q7VJSHBF7BS4FCAHFC7R","short_pith_number":"pith:OD6T34Q7","schema_version":"1.0","canonical_sha256":"70fd3df21faa647097e1970a201ca2fc51cc62d676762aa7a09e43b5bc96608f","source":{"kind":"arxiv","id":"1102.1953","version":2},"attestation_state":"computed","paper":{"title":"A relation between some special centro-skew, near-Toeplitz, tridiagonal matrices and circulant matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Kenneth R. Driessel","submitted_at":"2011-02-09T19:46:28Z","abstract_excerpt":"Let $n\\ge 2$ be an integer. Let $R_n$ denote the $n\\times n$ tridiagonal matrix with -1's on the sub-diagonal, 1's on the super-diagonal, -1 in the (1,1) entry, 1 in the (n,n) entry and zeros elsewhere. This paper shows that $R_n$ is closely related to a certain circulant matrix and a certain skew-circulant matrix. More precisely, let $E_n$ denote the exchange matrix which is defined by $E_n(i,j):=\\delta(i+j,n+1)$. Let $E_+$ (respectively, $E_-$) be the projection defined by $x\\mapsto (1/2)(x + E_n x)$ (respectively, $x\\mapsto (1/2)(x - E_n x)$). Then $R_n = (\\pi_n - \\pi_n^T) E_+ + (\\eta_n - \\"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1102.1953","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-02-09T19:46:28Z","cross_cats_sorted":[],"title_canon_sha256":"7be198fcfb9273e930006f14dc5a133d32d53dcbcb9f817ab50d877df3396902","abstract_canon_sha256":"244683a89d5bf1af5f08442c31b38c6edb95e23852405ad0f9c1f5d94e2dc773"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:27:37.655248Z","signature_b64":"ZsjXN7KUi1RG2CFGG6064fyNGG/mu4QCrLbj33C9wpsZ9c3jYnEN3Eo5Ej+BBLN+vt5ayhXQ8fzNk1UU2Yn6CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"70fd3df21faa647097e1970a201ca2fc51cc62d676762aa7a09e43b5bc96608f","last_reissued_at":"2026-05-18T04:27:37.654600Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:27:37.654600Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A relation between some special centro-skew, near-Toeplitz, tridiagonal matrices and circulant matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Kenneth R. Driessel","submitted_at":"2011-02-09T19:46:28Z","abstract_excerpt":"Let $n\\ge 2$ be an integer. Let $R_n$ denote the $n\\times n$ tridiagonal matrix with -1's on the sub-diagonal, 1's on the super-diagonal, -1 in the (1,1) entry, 1 in the (n,n) entry and zeros elsewhere. This paper shows that $R_n$ is closely related to a certain circulant matrix and a certain skew-circulant matrix. More precisely, let $E_n$ denote the exchange matrix which is defined by $E_n(i,j):=\\delta(i+j,n+1)$. Let $E_+$ (respectively, $E_-$) be the projection defined by $x\\mapsto (1/2)(x + E_n x)$ (respectively, $x\\mapsto (1/2)(x - E_n x)$). Then $R_n = (\\pi_n - \\pi_n^T) E_+ + (\\eta_n - \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.1953","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1102.1953","created_at":"2026-05-18T04:27:37.654704+00:00"},{"alias_kind":"arxiv_version","alias_value":"1102.1953v2","created_at":"2026-05-18T04:27:37.654704+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.1953","created_at":"2026-05-18T04:27:37.654704+00:00"},{"alias_kind":"pith_short_12","alias_value":"OD6T34Q7VJSH","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_16","alias_value":"OD6T34Q7VJSHBF7B","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_8","alias_value":"OD6T34Q7","created_at":"2026-05-18T12:26:37.096874+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/OD6T34Q7VJSHBF7BS4FCAHFC7R","json":"https://pith.science/pith/OD6T34Q7VJSHBF7BS4FCAHFC7R.json","graph_json":"https://pith.science/api/pith-number/OD6T34Q7VJSHBF7BS4FCAHFC7R/graph.json","events_json":"https://pith.science/api/pith-number/OD6T34Q7VJSHBF7BS4FCAHFC7R/events.json","paper":"https://pith.science/paper/OD6T34Q7"},"agent_actions":{"view_html":"https://pith.science/pith/OD6T34Q7VJSHBF7BS4FCAHFC7R","download_json":"https://pith.science/pith/OD6T34Q7VJSHBF7BS4FCAHFC7R.json","view_paper":"https://pith.science/paper/OD6T34Q7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1102.1953&json=true","fetch_graph":"https://pith.science/api/pith-number/OD6T34Q7VJSHBF7BS4FCAHFC7R/graph.json","fetch_events":"https://pith.science/api/pith-number/OD6T34Q7VJSHBF7BS4FCAHFC7R/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OD6T34Q7VJSHBF7BS4FCAHFC7R/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OD6T34Q7VJSHBF7BS4FCAHFC7R/action/storage_attestation","attest_author":"https://pith.science/pith/OD6T34Q7VJSHBF7BS4FCAHFC7R/action/author_attestation","sign_citation":"https://pith.science/pith/OD6T34Q7VJSHBF7BS4FCAHFC7R/action/citation_signature","submit_replication":"https://pith.science/pith/OD6T34Q7VJSHBF7BS4FCAHFC7R/action/replication_record"}},"created_at":"2026-05-18T04:27:37.654704+00:00","updated_at":"2026-05-18T04:27:37.654704+00:00"}