{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:JYGEJP6WZEYJCJVGLLTCHYJBHD","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":"f5461ab70b61439aa29b8c78da00360816aa098e6c0744214a5fcea31e701505","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-11-27T19:31:02Z","title_canon_sha256":"f6648fe536ef4f0121099623d231922e2239bdf5b17fbceb42889370e0c6bc4c"},"schema_version":"1.0","source":{"id":"1611.08895","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.08895","created_at":"2026-05-18T00:56:29Z"},{"alias_kind":"arxiv_version","alias_value":"1611.08895v1","created_at":"2026-05-18T00:56:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.08895","created_at":"2026-05-18T00:56:29Z"},{"alias_kind":"pith_short_12","alias_value":"JYGEJP6WZEYJ","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JYGEJP6WZEYJCJVG","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JYGEJP6W","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:52b306f1ff4014b86eeba5e86819304249f4d3c346497ca6f71cf60e83d638f8","target":"graph","created_at":"2026-05-18T00:56:29Z","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 well known numerical task is the inversion of large symmetric tridiagonal Toeplitz matrices, i.e., matrices whose entries equal $a$ on the diagonal and $b$ on the extra diagonals ($a, b\\in \\mathbb R$). The inverses of such matrices are dense and there exist well known explicit formulas by which they can be calculated in $\\mathcal O(n^2)$. In this note we present a simplification of the problem that has proven to be rather useful in everyday practice: If $\\vert a\\vert > 2\\vert b\\vert$, that is, if the matrix is strictly diagonally dominant, its inverse is a band matrix to working precision an","authors_text":"Manuel Radons","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-11-27T19:31:02Z","title":"$\\mathcal O(n)$ working precision inverses for symmetric tridiagonal Toeplitz matrices with $\\mathcal O(1)$ floating point calculations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.08895","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:b0149d2942437de5cc08925a93360ef15d2cb8eeb58800df98a4a959cf83df92","target":"record","created_at":"2026-05-18T00:56:29Z","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":"f5461ab70b61439aa29b8c78da00360816aa098e6c0744214a5fcea31e701505","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-11-27T19:31:02Z","title_canon_sha256":"f6648fe536ef4f0121099623d231922e2239bdf5b17fbceb42889370e0c6bc4c"},"schema_version":"1.0","source":{"id":"1611.08895","kind":"arxiv","version":1}},"canonical_sha256":"4e0c44bfd6c9309126a65ae623e12138f0b6bf2b8828001aadda9a3c8c74d98f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4e0c44bfd6c9309126a65ae623e12138f0b6bf2b8828001aadda9a3c8c74d98f","first_computed_at":"2026-05-18T00:56:29.914628Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:56:29.914628Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bekXSDE50yUdAM0r1jRKuuYppuEK8hZQqccsi1AC8L8aFoAy2JhHQPY/jmKr1kyOk60B/1JMsqzkI1Q19DZRBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:56:29.915200Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.08895","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b0149d2942437de5cc08925a93360ef15d2cb8eeb58800df98a4a959cf83df92","sha256:52b306f1ff4014b86eeba5e86819304249f4d3c346497ca6f71cf60e83d638f8"],"state_sha256":"35771ddd186ce88047cba82d75108cec49fb99234ec6dba96452cf5a1ae0afaa"}