{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:KEGS27ZB3SHZ26NCF7YFRIFCUR","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":"ace234b0634c4225ebf4907c13c4d91297f6d8962eb63fd9bc9b467e6d69702b","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-01-18T15:39:17Z","title_canon_sha256":"e59d374f26d51740d7fae15ef460f2374bd87a2a9b31da6e88983b65a791fc38"},"schema_version":"1.0","source":{"id":"1301.4406","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.4406","created_at":"2026-05-18T03:36:05Z"},{"alias_kind":"arxiv_version","alias_value":"1301.4406v1","created_at":"2026-05-18T03:36:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.4406","created_at":"2026-05-18T03:36:05Z"},{"alias_kind":"pith_short_12","alias_value":"KEGS27ZB3SHZ","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"KEGS27ZB3SHZ26NC","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"KEGS27ZB","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:079b23f7cfed4e763c787c6e22415fbfb24b8e7cf60254a025d27583ecdb03ab","target":"graph","created_at":"2026-05-18T03:36:05Z","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":"By functional calculus methods, we obtain optimal convergence rates in Euler's approximation formula for C_0-semigroups restricted to ranges of generalized Stieltjes functions. Our results include a number of partial cases studied in the literature and cannot essentially be improved.","authors_text":"Alexander Gomilko, Yuri Tomilov","cross_cats":["math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-01-18T15:39:17Z","title":"On rates in Euler's formula for C_0-semigroups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.4406","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:a316802b1b9d65b56eef8ec35b84b19f2ef7b017e902997f198fe7d6c6fdeb08","target":"record","created_at":"2026-05-18T03:36:05Z","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":"ace234b0634c4225ebf4907c13c4d91297f6d8962eb63fd9bc9b467e6d69702b","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-01-18T15:39:17Z","title_canon_sha256":"e59d374f26d51740d7fae15ef460f2374bd87a2a9b31da6e88983b65a791fc38"},"schema_version":"1.0","source":{"id":"1301.4406","kind":"arxiv","version":1}},"canonical_sha256":"510d2d7f21dc8f9d79a22ff058a0a2a44fe6894951934086281b131fae3a2bf6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"510d2d7f21dc8f9d79a22ff058a0a2a44fe6894951934086281b131fae3a2bf6","first_computed_at":"2026-05-18T03:36:05.477104Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:36:05.477104Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eDOUo1jF0/z7wP1BW8CueHE3Jnsma+tNF+UFIhZU5HxPfuar0Z2cEoQmm48K21Wsa5Rqbmxeq/+0k6qtbxSgBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:36:05.477549Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.4406","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a316802b1b9d65b56eef8ec35b84b19f2ef7b017e902997f198fe7d6c6fdeb08","sha256:079b23f7cfed4e763c787c6e22415fbfb24b8e7cf60254a025d27583ecdb03ab"],"state_sha256":"c81942b1025622e6c7b332ed035f3189ef4ba3ee43700fabd42deae29698d555"}