{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:UEDFGGVKXTRBHYDCZYI45U3T2A","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":"c7495fb94d00feb5a7db740e8dae9e7870ba5b6e723b173e726303bf4a7516c9","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2022-03-21T21:06:33Z","title_canon_sha256":"0213aba89eafc0510c2a2bac09c39f124c31baf9658b9aa8e5c4b49003dcac62"},"schema_version":"1.0","source":{"id":"2203.11338","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2203.11338","created_at":"2026-07-05T04:07:11Z"},{"alias_kind":"arxiv_version","alias_value":"2203.11338v1","created_at":"2026-07-05T04:07:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.11338","created_at":"2026-07-05T04:07:11Z"},{"alias_kind":"pith_short_12","alias_value":"UEDFGGVKXTRB","created_at":"2026-07-05T04:07:11Z"},{"alias_kind":"pith_short_16","alias_value":"UEDFGGVKXTRBHYDC","created_at":"2026-07-05T04:07:11Z"},{"alias_kind":"pith_short_8","alias_value":"UEDFGGVK","created_at":"2026-07-05T04:07:11Z"}],"graph_snapshots":[{"event_id":"sha256:b9415e4b87f3fa9a8127a17aa0b0f47f2f03956135c90a4a9aa0c79ba3cca94b","target":"graph","created_at":"2026-07-05T04:07:11Z","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/2203.11338/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Under appropriate technical assumptions, the simple-loop theory allows to deduce various types of asymptotic expansions for the eigenvalues of Toeplitz matrices $T_{n}(f)$ generated by a function $f$, unfortunately, such a theory is not available in the preconditioning setting, that is for matrices of the form $T_{n}^{-1}(g)T_{n}(l)$ with $l,g$ real-valued, $g$ nonnnegative and not identically zero almost everywhere. Independently and under the milder hypothesis that $f=\\frac{l}{g}$ is even and monotonic over $[0,\\pi]$, matrix-less algorithms have been developed for the fast eigenvalue computa","authors_text":"Manuel Bogoya, Paris Vassalos, Stefano Serra-Cappizano","cross_cats":["cs.NA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2022-03-21T21:06:33Z","title":"Fast Toeplitz eigenvalue computations, joining interpolation-extrapolation matrix-less algorithms and simple-loop conjectures: the preconditioned setting"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.11338","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:bb024a5ad12e68a902efd493cc041a170dc572e950f43262bc3347cd1432718c","target":"record","created_at":"2026-07-05T04:07:11Z","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":"c7495fb94d00feb5a7db740e8dae9e7870ba5b6e723b173e726303bf4a7516c9","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2022-03-21T21:06:33Z","title_canon_sha256":"0213aba89eafc0510c2a2bac09c39f124c31baf9658b9aa8e5c4b49003dcac62"},"schema_version":"1.0","source":{"id":"2203.11338","kind":"arxiv","version":1}},"canonical_sha256":"a106531aaabce213e062ce11ced373d0263b14ef530e3f8e3d01ff0f0afaa755","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a106531aaabce213e062ce11ced373d0263b14ef530e3f8e3d01ff0f0afaa755","first_computed_at":"2026-07-05T04:07:11.024651Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:07:11.024651Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RN0uC08+/xW9hi+DPVzNTFifs0AAENU/0/cT82xQsLuRS8E/2jwFiRITX2IcchUhSpJuiT4/a7lWWcxr2ADMBw==","signature_status":"signed_v1","signed_at":"2026-07-05T04:07:11.025035Z","signed_message":"canonical_sha256_bytes"},"source_id":"2203.11338","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bb024a5ad12e68a902efd493cc041a170dc572e950f43262bc3347cd1432718c","sha256:b9415e4b87f3fa9a8127a17aa0b0f47f2f03956135c90a4a9aa0c79ba3cca94b"],"state_sha256":"d7f9f7b561adce79548aca645609a8384b31398573eee8f767a003a6b360f407"}