{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:WTTMW5SRQRRNTYHNPY3K6ETYPT","short_pith_number":"pith:WTTMW5SR","canonical_record":{"source":{"id":"1405.2474","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-05-10T21:13:33Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"8430208a47321e3111bc15b53d42cda45b26dcd404141143d24fc2df8b4d25a1","abstract_canon_sha256":"974c70576dd51f1850c5875e4b118b4d17bfb15dab01753832920b0d01965995"},"schema_version":"1.0"},"canonical_sha256":"b4e6cb76518462d9e0ed7e36af12787cec0e6c4167dc72846af9d25a46f20c56","source":{"kind":"arxiv","id":"1405.2474","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.2474","created_at":"2026-05-18T02:52:05Z"},{"alias_kind":"arxiv_version","alias_value":"1405.2474v1","created_at":"2026-05-18T02:52:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.2474","created_at":"2026-05-18T02:52:05Z"},{"alias_kind":"pith_short_12","alias_value":"WTTMW5SRQRRN","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"WTTMW5SRQRRNTYHN","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"WTTMW5SR","created_at":"2026-05-18T12:28:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:WTTMW5SRQRRNTYHNPY3K6ETYPT","target":"record","payload":{"canonical_record":{"source":{"id":"1405.2474","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-05-10T21:13:33Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"8430208a47321e3111bc15b53d42cda45b26dcd404141143d24fc2df8b4d25a1","abstract_canon_sha256":"974c70576dd51f1850c5875e4b118b4d17bfb15dab01753832920b0d01965995"},"schema_version":"1.0"},"canonical_sha256":"b4e6cb76518462d9e0ed7e36af12787cec0e6c4167dc72846af9d25a46f20c56","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:52:05.436690Z","signature_b64":"Ijms5A7BuC8oI45Er3WhBe4bgVd+BRBsLPoSIqSFkiKDHOrnWExp2EXfN2LlVtSj5ov+NrzsHJzD1sJovBT6CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b4e6cb76518462d9e0ed7e36af12787cec0e6c4167dc72846af9d25a46f20c56","last_reissued_at":"2026-05-18T02:52:05.436204Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:52:05.436204Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.2474","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":"2026-05-18T02:52:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bF2y4+TEgSfSXa1NU2tW9BvzvKK+vL06HKIFC337pphauz7UaNyy0VFjCp/377GePFyS7pbcjGx9pSmEIy7WDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T16:26:54.955015Z"},"content_sha256":"9815574959ef8bf46c4fc2e924461ee55f41db3fa784b115d4f9d4354ea3c7a8","schema_version":"1.0","event_id":"sha256:9815574959ef8bf46c4fc2e924461ee55f41db3fa784b115d4f9d4354ea3c7a8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:WTTMW5SRQRRNTYHNPY3K6ETYPT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Convergence Analysis of the Summation of the Euler Series by Pad\\'e Approximants and the Delta Transformation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"(2) Institut f\\\"ur Physikalische und Theoretische Chemie, Ernst Joachim Weniger (2) ((1) Dipartimento di Ingegneria, Germany), Italy, Riccardo Borghi (1), Universit\\`a \"Roma Tre\", Universit\\\"at Regensburg","submitted_at":"2014-05-10T21:13:33Z","abstract_excerpt":"Sequence transformations are valuable numerical tools that have been used with considerable success for the acceleration of convergence and the summation of diverging series. However, our understanding of their theoretical properties is far from satisfactory. The Euler series $\\mathcal{E}(z) \\sim \\sum_{n=0}^{\\infty} (-1)^n n! z^n$ is a very important model for the ubiquitous factorially divergent perturbation expansions in physics. In this article, we analyze the summation of the Euler series by Pad\\'e approximants and the delta transformation [E. J. Weniger, Comput. Phys. Rep. Vol.10, 189 (19"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.2474","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":"2026-05-18T02:52:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UihRYP41qR5k69GnpIWGuVO4nOIb2O1H0JI867dGZdz8IMDQ46jtodQYn7+7jV3VP6e1bTgAdhKKbKo4sycIAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T16:26:54.955394Z"},"content_sha256":"eab291e92f570aa4d3dac06d29a47b93ac58fe7eca6625d8b76a7a1477d56284","schema_version":"1.0","event_id":"sha256:eab291e92f570aa4d3dac06d29a47b93ac58fe7eca6625d8b76a7a1477d56284"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WTTMW5SRQRRNTYHNPY3K6ETYPT/bundle.json","state_url":"https://pith.science/pith/WTTMW5SRQRRNTYHNPY3K6ETYPT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WTTMW5SRQRRNTYHNPY3K6ETYPT/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":"2026-06-01T16:26:54Z","links":{"resolver":"https://pith.science/pith/WTTMW5SRQRRNTYHNPY3K6ETYPT","bundle":"https://pith.science/pith/WTTMW5SRQRRNTYHNPY3K6ETYPT/bundle.json","state":"https://pith.science/pith/WTTMW5SRQRRNTYHNPY3K6ETYPT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WTTMW5SRQRRNTYHNPY3K6ETYPT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:WTTMW5SRQRRNTYHNPY3K6ETYPT","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":"974c70576dd51f1850c5875e4b118b4d17bfb15dab01753832920b0d01965995","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-05-10T21:13:33Z","title_canon_sha256":"8430208a47321e3111bc15b53d42cda45b26dcd404141143d24fc2df8b4d25a1"},"schema_version":"1.0","source":{"id":"1405.2474","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.2474","created_at":"2026-05-18T02:52:05Z"},{"alias_kind":"arxiv_version","alias_value":"1405.2474v1","created_at":"2026-05-18T02:52:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.2474","created_at":"2026-05-18T02:52:05Z"},{"alias_kind":"pith_short_12","alias_value":"WTTMW5SRQRRN","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"WTTMW5SRQRRNTYHN","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"WTTMW5SR","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:eab291e92f570aa4d3dac06d29a47b93ac58fe7eca6625d8b76a7a1477d56284","target":"graph","created_at":"2026-05-18T02:52:05Z","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":"Sequence transformations are valuable numerical tools that have been used with considerable success for the acceleration of convergence and the summation of diverging series. However, our understanding of their theoretical properties is far from satisfactory. The Euler series $\\mathcal{E}(z) \\sim \\sum_{n=0}^{\\infty} (-1)^n n! z^n$ is a very important model for the ubiquitous factorially divergent perturbation expansions in physics. In this article, we analyze the summation of the Euler series by Pad\\'e approximants and the delta transformation [E. J. Weniger, Comput. Phys. Rep. Vol.10, 189 (19","authors_text":"(2) Institut f\\\"ur Physikalische und Theoretische Chemie, Ernst Joachim Weniger (2) ((1) Dipartimento di Ingegneria, Germany), Italy, Riccardo Borghi (1), Universit\\`a \"Roma Tre\", Universit\\\"at Regensburg","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-05-10T21:13:33Z","title":"Convergence Analysis of the Summation of the Euler Series by Pad\\'e Approximants and the Delta Transformation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.2474","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":"sha256:9815574959ef8bf46c4fc2e924461ee55f41db3fa784b115d4f9d4354ea3c7a8","target":"record","created_at":"2026-05-18T02:52:05Z","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":"974c70576dd51f1850c5875e4b118b4d17bfb15dab01753832920b0d01965995","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-05-10T21:13:33Z","title_canon_sha256":"8430208a47321e3111bc15b53d42cda45b26dcd404141143d24fc2df8b4d25a1"},"schema_version":"1.0","source":{"id":"1405.2474","kind":"arxiv","version":1}},"canonical_sha256":"b4e6cb76518462d9e0ed7e36af12787cec0e6c4167dc72846af9d25a46f20c56","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b4e6cb76518462d9e0ed7e36af12787cec0e6c4167dc72846af9d25a46f20c56","first_computed_at":"2026-05-18T02:52:05.436204Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:52:05.436204Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ijms5A7BuC8oI45Er3WhBe4bgVd+BRBsLPoSIqSFkiKDHOrnWExp2EXfN2LlVtSj5ov+NrzsHJzD1sJovBT6CA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:52:05.436690Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.2474","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9815574959ef8bf46c4fc2e924461ee55f41db3fa784b115d4f9d4354ea3c7a8","sha256:eab291e92f570aa4d3dac06d29a47b93ac58fe7eca6625d8b76a7a1477d56284"],"state_sha256":"69283bbf71db16d50529dfc075d3acd498af86d866211c7f03b03ede53efbab9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3Ci15fwH9HdIa/mlXBH+DGGQZJGSc50+YCXVlzONxZTiwCGm8mtd8o0vZpTnN3ccjg7+kRR/sVNOURnl+MOvBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T16:26:54.957378Z","bundle_sha256":"1ff0eae9ad4f7f799158efef726332ff268df70a95ff4ea0ce42b2ce7c21f28a"}}