{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:AOMJU4YW3EN6E4K75SREWVYHCQ","short_pith_number":"pith:AOMJU4YW","canonical_record":{"source":{"id":"1611.06380","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-11-19T15:20:02Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"2d6de8763bba3399d9accd9f8bc816f0b80d753f28fe5701b153b275e49e6878","abstract_canon_sha256":"3f4bc29278569876ef8218f6c0c0b86859ba0ca5ed9814d12dc0bc8dafb52449"},"schema_version":"1.0"},"canonical_sha256":"03989a7316d91be2715feca24b57071413031869227d89e6a3c2612c4edd180e","source":{"kind":"arxiv","id":"1611.06380","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.06380","created_at":"2026-06-04T18:10:16Z"},{"alias_kind":"arxiv_version","alias_value":"1611.06380v2","created_at":"2026-06-04T18:10:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.06380","created_at":"2026-06-04T18:10:16Z"},{"alias_kind":"pith_short_12","alias_value":"AOMJU4YW3EN6","created_at":"2026-06-04T18:10:16Z"},{"alias_kind":"pith_short_16","alias_value":"AOMJU4YW3EN6E4K7","created_at":"2026-06-04T18:10:16Z"},{"alias_kind":"pith_short_8","alias_value":"AOMJU4YW","created_at":"2026-06-04T18:10:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:AOMJU4YW3EN6E4K75SREWVYHCQ","target":"record","payload":{"canonical_record":{"source":{"id":"1611.06380","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-11-19T15:20:02Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"2d6de8763bba3399d9accd9f8bc816f0b80d753f28fe5701b153b275e49e6878","abstract_canon_sha256":"3f4bc29278569876ef8218f6c0c0b86859ba0ca5ed9814d12dc0bc8dafb52449"},"schema_version":"1.0"},"canonical_sha256":"03989a7316d91be2715feca24b57071413031869227d89e6a3c2612c4edd180e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T18:10:16.663072Z","signature_b64":"58CQLyffFmf3u9L60RRMqecSQnesLwnNrQ4KyCbKl423ZchH9tbLEg0AV5rh605Q52Uhs2oO1qb6iz2LnAVKCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"03989a7316d91be2715feca24b57071413031869227d89e6a3c2612c4edd180e","last_reissued_at":"2026-06-04T18:10:16.662650Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T18:10:16.662650Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.06380","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":"2026-06-04T18:10:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uQR4k3pj4kAoosaeBaRbKsxmH67EQ66vc6XChoyC3rwONwbKmm3o4s/yMLDyXh7iWvdrJEuv8iSsXdhWG4jrCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T23:23:41.751670Z"},"content_sha256":"d9a9bd9deb7117d3b14a0cde67da7bb53a9782754a648d3e6a7d06c3cd125fbc","schema_version":"1.0","event_id":"sha256:d9a9bd9deb7117d3b14a0cde67da7bb53a9782754a648d3e6a7d06c3cd125fbc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:AOMJU4YW3EN6E4K75SREWVYHCQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the exponential of semi-infinite quasi-Toeplitz matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Beatrice Meini, Dario A. Bini","submitted_at":"2016-11-19T15:20:02Z","abstract_excerpt":"Let $a(z)=\\sum_{i\\in\\mathbb Z}a_iz^i$ be a complex valued function defined for $|z|=1$, such that $\\sum_{i\\in\\mathbb Z}|ia_i|<\\infty$, and let $E=(e_{i,j})_{i,j\\in\\mathbb {Z}^+}$ be such that $\\sum_{i,j\\in\\mathbb{Z}^+}|e_{i,j}|<\\infty$. A semi-infinite quasi-Toeplitz matrix is a matrix of the kind $A=T(a)+E$, where $T(a)=(t_{i,j})_{i,j\\in\\mathbb{Z}^+}$ is the semi-infinite Toeplitz matrix associated with the symbol $a(z)$, that is, $t_{i,j}=a_{j-i}$ for $i,j\\in\\mathbb Z^+$. We analyze theoretical and computational properties of the exponential of $A$. More specifically, it is shown that $\\exp("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.06380","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/1611.06380/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":"2026-06-04T18:10:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cYwrXeQH51+JCgo+SqEYNHQnaCEmcnFc8DspyvyB3Ul/VC+ylEMHIsFBffSZrTa47QOxjEVFjvsXnuVKwx22DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T23:23:41.752044Z"},"content_sha256":"c323b303e073ab5b9dbd7293925861ec68e8f1abc4a88e7d9c267525de044434","schema_version":"1.0","event_id":"sha256:c323b303e073ab5b9dbd7293925861ec68e8f1abc4a88e7d9c267525de044434"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AOMJU4YW3EN6E4K75SREWVYHCQ/bundle.json","state_url":"https://pith.science/pith/AOMJU4YW3EN6E4K75SREWVYHCQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AOMJU4YW3EN6E4K75SREWVYHCQ/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":"2026-06-08T23:23:41Z","links":{"resolver":"https://pith.science/pith/AOMJU4YW3EN6E4K75SREWVYHCQ","bundle":"https://pith.science/pith/AOMJU4YW3EN6E4K75SREWVYHCQ/bundle.json","state":"https://pith.science/pith/AOMJU4YW3EN6E4K75SREWVYHCQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AOMJU4YW3EN6E4K75SREWVYHCQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:AOMJU4YW3EN6E4K75SREWVYHCQ","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":"3f4bc29278569876ef8218f6c0c0b86859ba0ca5ed9814d12dc0bc8dafb52449","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-11-19T15:20:02Z","title_canon_sha256":"2d6de8763bba3399d9accd9f8bc816f0b80d753f28fe5701b153b275e49e6878"},"schema_version":"1.0","source":{"id":"1611.06380","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.06380","created_at":"2026-06-04T18:10:16Z"},{"alias_kind":"arxiv_version","alias_value":"1611.06380v2","created_at":"2026-06-04T18:10:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.06380","created_at":"2026-06-04T18:10:16Z"},{"alias_kind":"pith_short_12","alias_value":"AOMJU4YW3EN6","created_at":"2026-06-04T18:10:16Z"},{"alias_kind":"pith_short_16","alias_value":"AOMJU4YW3EN6E4K7","created_at":"2026-06-04T18:10:16Z"},{"alias_kind":"pith_short_8","alias_value":"AOMJU4YW","created_at":"2026-06-04T18:10:16Z"}],"graph_snapshots":[{"event_id":"sha256:c323b303e073ab5b9dbd7293925861ec68e8f1abc4a88e7d9c267525de044434","target":"graph","created_at":"2026-06-04T18:10:16Z","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/1611.06380/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $a(z)=\\sum_{i\\in\\mathbb Z}a_iz^i$ be a complex valued function defined for $|z|=1$, such that $\\sum_{i\\in\\mathbb Z}|ia_i|<\\infty$, and let $E=(e_{i,j})_{i,j\\in\\mathbb {Z}^+}$ be such that $\\sum_{i,j\\in\\mathbb{Z}^+}|e_{i,j}|<\\infty$. A semi-infinite quasi-Toeplitz matrix is a matrix of the kind $A=T(a)+E$, where $T(a)=(t_{i,j})_{i,j\\in\\mathbb{Z}^+}$ is the semi-infinite Toeplitz matrix associated with the symbol $a(z)$, that is, $t_{i,j}=a_{j-i}$ for $i,j\\in\\mathbb Z^+$. We analyze theoretical and computational properties of the exponential of $A$. More specifically, it is shown that $\\exp(","authors_text":"Beatrice Meini, Dario A. Bini","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-11-19T15:20:02Z","title":"On the exponential of semi-infinite quasi-Toeplitz matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.06380","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:d9a9bd9deb7117d3b14a0cde67da7bb53a9782754a648d3e6a7d06c3cd125fbc","target":"record","created_at":"2026-06-04T18:10:16Z","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":"3f4bc29278569876ef8218f6c0c0b86859ba0ca5ed9814d12dc0bc8dafb52449","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-11-19T15:20:02Z","title_canon_sha256":"2d6de8763bba3399d9accd9f8bc816f0b80d753f28fe5701b153b275e49e6878"},"schema_version":"1.0","source":{"id":"1611.06380","kind":"arxiv","version":2}},"canonical_sha256":"03989a7316d91be2715feca24b57071413031869227d89e6a3c2612c4edd180e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"03989a7316d91be2715feca24b57071413031869227d89e6a3c2612c4edd180e","first_computed_at":"2026-06-04T18:10:16.662650Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-04T18:10:16.662650Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"58CQLyffFmf3u9L60RRMqecSQnesLwnNrQ4KyCbKl423ZchH9tbLEg0AV5rh605Q52Uhs2oO1qb6iz2LnAVKCA==","signature_status":"signed_v1","signed_at":"2026-06-04T18:10:16.663072Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.06380","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d9a9bd9deb7117d3b14a0cde67da7bb53a9782754a648d3e6a7d06c3cd125fbc","sha256:c323b303e073ab5b9dbd7293925861ec68e8f1abc4a88e7d9c267525de044434"],"state_sha256":"4fd7e1f23dfe7b1d07619394f504087271740f5d2f895f91016fc98310ae12d2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DsrfBjrJ8fRekkVqYUi6LkFr2wliLRhHIbwFsJeBUc4hKJCDxfZV46OH3Ney245eHxSo/p1Z59RzIrRYea2oDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T23:23:41.753999Z","bundle_sha256":"2baa884ee17ac24e8443df363e82c4dd8a6bb522350c79c38522060d65a26ad1"}}