{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:T4QHMP6NJGAWAXS3ZTVDRPCTTT","short_pith_number":"pith:T4QHMP6N","canonical_record":{"source":{"id":"2203.06992","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2022-03-14T10:55:43Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"afe4bd2526cb412feed56d705bdcf77b734b93e8e2f5c82029d546a0e18e40a1","abstract_canon_sha256":"c24a46b8b2b0dceb0dce55a3c731267bc68ab77f02566f29fea7255e549919fd"},"schema_version":"1.0"},"canonical_sha256":"9f20763fcd4981605e5bccea38bc539cfea8142fc50b75a09123760e823226cd","source":{"kind":"arxiv","id":"2203.06992","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2203.06992","created_at":"2026-07-05T04:41:11Z"},{"alias_kind":"arxiv_version","alias_value":"2203.06992v2","created_at":"2026-07-05T04:41:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.06992","created_at":"2026-07-05T04:41:11Z"},{"alias_kind":"pith_short_12","alias_value":"T4QHMP6NJGAW","created_at":"2026-07-05T04:41:11Z"},{"alias_kind":"pith_short_16","alias_value":"T4QHMP6NJGAWAXS3","created_at":"2026-07-05T04:41:11Z"},{"alias_kind":"pith_short_8","alias_value":"T4QHMP6N","created_at":"2026-07-05T04:41:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:T4QHMP6NJGAWAXS3ZTVDRPCTTT","target":"record","payload":{"canonical_record":{"source":{"id":"2203.06992","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2022-03-14T10:55:43Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"afe4bd2526cb412feed56d705bdcf77b734b93e8e2f5c82029d546a0e18e40a1","abstract_canon_sha256":"c24a46b8b2b0dceb0dce55a3c731267bc68ab77f02566f29fea7255e549919fd"},"schema_version":"1.0"},"canonical_sha256":"9f20763fcd4981605e5bccea38bc539cfea8142fc50b75a09123760e823226cd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:41:11.701775Z","signature_b64":"klgESc5zmu7yMbJ7TXw/XnsoM5IAy3hji7w/s7CUjOSUYkve9Wc9Qw4zTA2Xrp+aptoI7p2CSjmqs/tnSxlJBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9f20763fcd4981605e5bccea38bc539cfea8142fc50b75a09123760e823226cd","last_reissued_at":"2026-07-05T04:41:11.701284Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:41:11.701284Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2203.06992","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:41:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ih/qwExKAPEcDohRugaE1AAkCWs6436OoMlozIn7imkzBO7g553XyOHGfo3sSEzpVoyU6crNBZXf14hRxLQNAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-10T12:35:11.748501Z"},"content_sha256":"3e0f85c78e58804f05140f314ea6a53d39a32ddffdecccca9b0b045610812df1","schema_version":"1.0","event_id":"sha256:3e0f85c78e58804f05140f314ea6a53d39a32ddffdecccca9b0b045610812df1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:T4QHMP6NJGAWAXS3ZTVDRPCTTT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Theoretical results for eigenvalues, singular values, and eigenvectors of (flipped) Toeplitz matrices and related computational proposals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Giovanni Barbarino, Paris Vassalos, Stefano Serra-Capizzano, Sven-Erik Ekstr\\\"om","submitted_at":"2022-03-14T10:55:43Z","abstract_excerpt":"In a series of recent papers the spectral behavior of the matrix sequence $\\{Y_nT_n(f)\\}$ is studied in the sense of the spectral distribution, where $Y_n$ is the main antidiagonal (or flip matrix) and $T_n(f)$ is the Toeplitz matrix generated by the function $f$, with $f$ being Lebesgue integrable and with real Fourier coefficients. This kind of study is also motivated by computational purposes for the solution of the related large linear systems using the (preconditioned) MINRES algorithm. Here we complement the spectral study with more results holding both asymptotically and for a fixed dim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.06992","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2203.06992/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:41:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vNw00noB60zvaI95C32WmFRgpDu7yjB2czhMJ79xIE6ULYQMqvmyF1ANt4BJHgy1R4hE2nHne3HngbqNtymvAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-10T12:35:11.748882Z"},"content_sha256":"440667e6a215d8b3b856f5164e4222751838f21a7db6e9695042cda95ed03212","schema_version":"1.0","event_id":"sha256:440667e6a215d8b3b856f5164e4222751838f21a7db6e9695042cda95ed03212"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T4QHMP6NJGAWAXS3ZTVDRPCTTT/bundle.json","state_url":"https://pith.science/pith/T4QHMP6NJGAWAXS3ZTVDRPCTTT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T4QHMP6NJGAWAXS3ZTVDRPCTTT/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-10T12:35:11Z","links":{"resolver":"https://pith.science/pith/T4QHMP6NJGAWAXS3ZTVDRPCTTT","bundle":"https://pith.science/pith/T4QHMP6NJGAWAXS3ZTVDRPCTTT/bundle.json","state":"https://pith.science/pith/T4QHMP6NJGAWAXS3ZTVDRPCTTT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T4QHMP6NJGAWAXS3ZTVDRPCTTT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:T4QHMP6NJGAWAXS3ZTVDRPCTTT","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":"c24a46b8b2b0dceb0dce55a3c731267bc68ab77f02566f29fea7255e549919fd","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2022-03-14T10:55:43Z","title_canon_sha256":"afe4bd2526cb412feed56d705bdcf77b734b93e8e2f5c82029d546a0e18e40a1"},"schema_version":"1.0","source":{"id":"2203.06992","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2203.06992","created_at":"2026-07-05T04:41:11Z"},{"alias_kind":"arxiv_version","alias_value":"2203.06992v2","created_at":"2026-07-05T04:41:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.06992","created_at":"2026-07-05T04:41:11Z"},{"alias_kind":"pith_short_12","alias_value":"T4QHMP6NJGAW","created_at":"2026-07-05T04:41:11Z"},{"alias_kind":"pith_short_16","alias_value":"T4QHMP6NJGAWAXS3","created_at":"2026-07-05T04:41:11Z"},{"alias_kind":"pith_short_8","alias_value":"T4QHMP6N","created_at":"2026-07-05T04:41:11Z"}],"graph_snapshots":[{"event_id":"sha256:440667e6a215d8b3b856f5164e4222751838f21a7db6e9695042cda95ed03212","target":"graph","created_at":"2026-07-05T04:41:11Z","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/2203.06992/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In a series of recent papers the spectral behavior of the matrix sequence $\\{Y_nT_n(f)\\}$ is studied in the sense of the spectral distribution, where $Y_n$ is the main antidiagonal (or flip matrix) and $T_n(f)$ is the Toeplitz matrix generated by the function $f$, with $f$ being Lebesgue integrable and with real Fourier coefficients. This kind of study is also motivated by computational purposes for the solution of the related large linear systems using the (preconditioned) MINRES algorithm. Here we complement the spectral study with more results holding both asymptotically and for a fixed dim","authors_text":"Giovanni Barbarino, Paris Vassalos, Stefano Serra-Capizzano, Sven-Erik Ekstr\\\"om","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2022-03-14T10:55:43Z","title":"Theoretical results for eigenvalues, singular values, and eigenvectors of (flipped) Toeplitz matrices and related computational proposals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.06992","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":"sha256:3e0f85c78e58804f05140f314ea6a53d39a32ddffdecccca9b0b045610812df1","target":"record","created_at":"2026-07-05T04:41:11Z","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":"c24a46b8b2b0dceb0dce55a3c731267bc68ab77f02566f29fea7255e549919fd","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2022-03-14T10:55:43Z","title_canon_sha256":"afe4bd2526cb412feed56d705bdcf77b734b93e8e2f5c82029d546a0e18e40a1"},"schema_version":"1.0","source":{"id":"2203.06992","kind":"arxiv","version":2}},"canonical_sha256":"9f20763fcd4981605e5bccea38bc539cfea8142fc50b75a09123760e823226cd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9f20763fcd4981605e5bccea38bc539cfea8142fc50b75a09123760e823226cd","first_computed_at":"2026-07-05T04:41:11.701284Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:41:11.701284Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"klgESc5zmu7yMbJ7TXw/XnsoM5IAy3hji7w/s7CUjOSUYkve9Wc9Qw4zTA2Xrp+aptoI7p2CSjmqs/tnSxlJBA==","signature_status":"signed_v1","signed_at":"2026-07-05T04:41:11.701775Z","signed_message":"canonical_sha256_bytes"},"source_id":"2203.06992","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3e0f85c78e58804f05140f314ea6a53d39a32ddffdecccca9b0b045610812df1","sha256:440667e6a215d8b3b856f5164e4222751838f21a7db6e9695042cda95ed03212"],"state_sha256":"9c37c7bf3fe01cb49396f8685d232b89508b68750369f6c456e59e3dd5f82ad9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V42NwW0KL01u2GzevzoL0lOg0fIDWpRUqsQgcAx/C4QlrDc0z7IKDbzX/O+kunBsEEDfRyD/AJEdVck5MUpEDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-10T12:35:11.750941Z","bundle_sha256":"68113c0e2fab207759051dc91cb49f402ce3983dc18c779b94c34812833c64e1"}}