{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:TKODDQ4BOYWGMXVFAC7RA47OKC","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":"8bbc6d251074d973359ab7cd234d2cd5a406956f1daa2ce187dea30a2772aed2","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-12-13T13:40:36Z","title_canon_sha256":"26d9ddaab71c8c6b2a944dcd9f559f92823e857fa7bb231674a50abdb6566a1f"},"schema_version":"1.0","source":{"id":"1112.2887","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.2887","created_at":"2026-05-18T04:06:32Z"},{"alias_kind":"arxiv_version","alias_value":"1112.2887v1","created_at":"2026-05-18T04:06:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.2887","created_at":"2026-05-18T04:06:32Z"},{"alias_kind":"pith_short_12","alias_value":"TKODDQ4BOYWG","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"TKODDQ4BOYWGMXVF","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"TKODDQ4B","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:73d02d4f6ddc8ef33f5884784875ed73b7d06ac9ba40d1720dd2c8bb05e55e30","target":"graph","created_at":"2026-05-18T04:06:32Z","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":"We consider sequences of rational interpolants $r_n(z)$ of degree $n$ to the exponential function $e^z$ associated to a triangular scheme of complex points $\\{z_{j}^{(2n)}\\}_{j=0}^{2n}$, $n>0$, such that, for all $n$, $|z_{j}^{(2n)}|\\leq cn^{1-\\alpha}$, $j=0,...,2n$, with $0<\\alpha\\leq 1$ and $c>0$. We prove the local uniform convergence of $r_{n}(z)$ to $e^{z}$ in the complex plane, as $n$ tends to infinity, and show that the limit distributions of the conveniently scaled zeros and poles of $r_{n}$ are identical to the corresponding distributions of the classical Pad\\'e approximants. This ext","authors_text":"F. Wielonsky, T. Claeys","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-12-13T13:40:36Z","title":"On sequences of rational interpolants of the exponential function with unbounded interpolation points"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.2887","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:be9e113c755fbcda98e17b7c88b32e6639e5c4696847897b24f45ad3a1355b63","target":"record","created_at":"2026-05-18T04:06:32Z","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":"8bbc6d251074d973359ab7cd234d2cd5a406956f1daa2ce187dea30a2772aed2","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-12-13T13:40:36Z","title_canon_sha256":"26d9ddaab71c8c6b2a944dcd9f559f92823e857fa7bb231674a50abdb6566a1f"},"schema_version":"1.0","source":{"id":"1112.2887","kind":"arxiv","version":1}},"canonical_sha256":"9a9c31c381762c665ea500bf1073ee509e96f1e6feaca5884d0f10bb17c1b8ea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9a9c31c381762c665ea500bf1073ee509e96f1e6feaca5884d0f10bb17c1b8ea","first_computed_at":"2026-05-18T04:06:32.152212Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:06:32.152212Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"F6v5aGbx4jNBNWzKeft9XzAoNGaoc5i+y+KPYrtDo3q3Xf/HhUcW8zRGIkSwK3QO+1j6EgGQ9XbP9/qbw3BmDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:06:32.153043Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.2887","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:be9e113c755fbcda98e17b7c88b32e6639e5c4696847897b24f45ad3a1355b63","sha256:73d02d4f6ddc8ef33f5884784875ed73b7d06ac9ba40d1720dd2c8bb05e55e30"],"state_sha256":"a6f8e1e14a8744424ffd085e74cdfc9580f53f9af4af820ec53eb92c7d0076fe"}