{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:KLPOAKR5ODZKB7DXD7QRSLHBAI","short_pith_number":"pith:KLPOAKR5","canonical_record":{"source":{"id":"1312.0216","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-12-01T13:19:42Z","cross_cats_sorted":[],"title_canon_sha256":"1cfaa4099afe89169694f5879f5003370194ddc51a7e700000a0414ad6ad54ad","abstract_canon_sha256":"732d2542dcedb0a474473b9bc4d6b45f00f42897fa4179961a1f9211f28e5704"},"schema_version":"1.0"},"canonical_sha256":"52dee02a3d70f2a0fc771fe1192ce10234036e5bd220c7b28b071a3762c42599","source":{"kind":"arxiv","id":"1312.0216","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.0216","created_at":"2026-05-18T03:05:46Z"},{"alias_kind":"arxiv_version","alias_value":"1312.0216v1","created_at":"2026-05-18T03:05:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.0216","created_at":"2026-05-18T03:05:46Z"},{"alias_kind":"pith_short_12","alias_value":"KLPOAKR5ODZK","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"KLPOAKR5ODZKB7DX","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"KLPOAKR5","created_at":"2026-05-18T12:27:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:KLPOAKR5ODZKB7DXD7QRSLHBAI","target":"record","payload":{"canonical_record":{"source":{"id":"1312.0216","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-12-01T13:19:42Z","cross_cats_sorted":[],"title_canon_sha256":"1cfaa4099afe89169694f5879f5003370194ddc51a7e700000a0414ad6ad54ad","abstract_canon_sha256":"732d2542dcedb0a474473b9bc4d6b45f00f42897fa4179961a1f9211f28e5704"},"schema_version":"1.0"},"canonical_sha256":"52dee02a3d70f2a0fc771fe1192ce10234036e5bd220c7b28b071a3762c42599","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:05:46.354097Z","signature_b64":"Ur4rB9vLCD0Fw/ZkcCJSKmx3J6rsmJLDA752SbfjZilVyFdbuDGzPx7m/6j+j6S3fVyxg5mdUYrPDQxiOrtJDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"52dee02a3d70f2a0fc771fe1192ce10234036e5bd220c7b28b071a3762c42599","last_reissued_at":"2026-05-18T03:05:46.353498Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:05:46.353498Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.0216","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:05:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AvXcw8sGaOkN1GQSeF1Do9BsbILbwPRZKGodLF5J8WP0dc5LlrsIdoCgGivnC9+jNWT6okThflKVEdB4HHMLCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T03:37:24.898267Z"},"content_sha256":"71db8128dc23a4b6d7aee4a15665838a4cf496d68aeb8b041cdbb444df5fc11a","schema_version":"1.0","event_id":"sha256:71db8128dc23a4b6d7aee4a15665838a4cf496d68aeb8b041cdbb444df5fc11a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:KLPOAKR5ODZKB7DXD7QRSLHBAI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the absolute stability regions corresponding to partial sums of the exponential function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"David Ketcheson, Lajos L\\'oczi, Tiham\\'er A. Kocsis","submitted_at":"2013-12-01T13:19:42Z","abstract_excerpt":"Certain numerical methods for initial value problems have as stability function the nth partial sum of the exponential function. We study the stability region, i.e., the set in the complex plane over which the nth partial sum has at most unit modulus. It is known that the asymptotic shape of the part of the stability region in the left half-plane is a semi-disk. We quantify this by providing disks that enclose or are enclosed by the stability region or its left half-plane part. The radius of the smallest disk centered at the origin that contains the stability region (or its portion in the left"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.0216","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T03:05:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vVbJNDs7NndD7Lo1eLvBLcQxN79m03O5VOE3af3DxUs5SzLSJoxQxs51/I9IanhaBT2Om+r7G63s60M/gc2VAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T03:37:24.898624Z"},"content_sha256":"93f9a29b67359674dcb88db51b46f141b77bec16c25fb1aee75456a83cf5eec9","schema_version":"1.0","event_id":"sha256:93f9a29b67359674dcb88db51b46f141b77bec16c25fb1aee75456a83cf5eec9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KLPOAKR5ODZKB7DXD7QRSLHBAI/bundle.json","state_url":"https://pith.science/pith/KLPOAKR5ODZKB7DXD7QRSLHBAI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KLPOAKR5ODZKB7DXD7QRSLHBAI/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":"2026-05-31T03:37:24Z","links":{"resolver":"https://pith.science/pith/KLPOAKR5ODZKB7DXD7QRSLHBAI","bundle":"https://pith.science/pith/KLPOAKR5ODZKB7DXD7QRSLHBAI/bundle.json","state":"https://pith.science/pith/KLPOAKR5ODZKB7DXD7QRSLHBAI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KLPOAKR5ODZKB7DXD7QRSLHBAI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:KLPOAKR5ODZKB7DXD7QRSLHBAI","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":"732d2542dcedb0a474473b9bc4d6b45f00f42897fa4179961a1f9211f28e5704","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-12-01T13:19:42Z","title_canon_sha256":"1cfaa4099afe89169694f5879f5003370194ddc51a7e700000a0414ad6ad54ad"},"schema_version":"1.0","source":{"id":"1312.0216","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.0216","created_at":"2026-05-18T03:05:46Z"},{"alias_kind":"arxiv_version","alias_value":"1312.0216v1","created_at":"2026-05-18T03:05:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.0216","created_at":"2026-05-18T03:05:46Z"},{"alias_kind":"pith_short_12","alias_value":"KLPOAKR5ODZK","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"KLPOAKR5ODZKB7DX","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"KLPOAKR5","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:93f9a29b67359674dcb88db51b46f141b77bec16c25fb1aee75456a83cf5eec9","target":"graph","created_at":"2026-05-18T03:05:46Z","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":"Certain numerical methods for initial value problems have as stability function the nth partial sum of the exponential function. We study the stability region, i.e., the set in the complex plane over which the nth partial sum has at most unit modulus. It is known that the asymptotic shape of the part of the stability region in the left half-plane is a semi-disk. We quantify this by providing disks that enclose or are enclosed by the stability region or its left half-plane part. The radius of the smallest disk centered at the origin that contains the stability region (or its portion in the left","authors_text":"David Ketcheson, Lajos L\\'oczi, Tiham\\'er A. Kocsis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-12-01T13:19:42Z","title":"On the absolute stability regions corresponding to partial sums of the exponential function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.0216","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":"sha256:71db8128dc23a4b6d7aee4a15665838a4cf496d68aeb8b041cdbb444df5fc11a","target":"record","created_at":"2026-05-18T03:05:46Z","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":"732d2542dcedb0a474473b9bc4d6b45f00f42897fa4179961a1f9211f28e5704","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-12-01T13:19:42Z","title_canon_sha256":"1cfaa4099afe89169694f5879f5003370194ddc51a7e700000a0414ad6ad54ad"},"schema_version":"1.0","source":{"id":"1312.0216","kind":"arxiv","version":1}},"canonical_sha256":"52dee02a3d70f2a0fc771fe1192ce10234036e5bd220c7b28b071a3762c42599","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"52dee02a3d70f2a0fc771fe1192ce10234036e5bd220c7b28b071a3762c42599","first_computed_at":"2026-05-18T03:05:46.353498Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:05:46.353498Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ur4rB9vLCD0Fw/ZkcCJSKmx3J6rsmJLDA752SbfjZilVyFdbuDGzPx7m/6j+j6S3fVyxg5mdUYrPDQxiOrtJDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:05:46.354097Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.0216","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:71db8128dc23a4b6d7aee4a15665838a4cf496d68aeb8b041cdbb444df5fc11a","sha256:93f9a29b67359674dcb88db51b46f141b77bec16c25fb1aee75456a83cf5eec9"],"state_sha256":"1566599410f656551e7d674f8117a8a8ed6d9e65dd358d8bc31ff3dacfd18e51"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R/yCLtBPM0d9leeTyq2Uk/0UhSmqAlr3XD7PFK/tFOdxjYTnDZUumeX3rJoTI/3iMh716GociV8ALeGwbRBEBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T03:37:24.900651Z","bundle_sha256":"4806c7a1450b102ce99bff9ba95f3e6f9f54fb03f5105960a60d6acc0cf08687"}}