{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2002:B2KZM6O3C6AGXLEHBZBSQ4JRIS","short_pith_number":"pith:B2KZM6O3","canonical_record":{"source":{"id":"math/0205064","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CA","submitted_at":"2002-05-07T10:40:03Z","cross_cats_sorted":[],"title_canon_sha256":"cb7110c533a5cdaabb245eff7b79df9f4e9c3e022c663d7508d99639f1212798","abstract_canon_sha256":"590c02f02f90f4681b2222c44afc233f100bce22fb9e53d006e0f4dd6e9c601b"},"schema_version":"1.0"},"canonical_sha256":"0e959679db17806bac870e43287131449f6b051a2b7a1dd844c2a483bae3c29c","source":{"kind":"arxiv","id":"math/0205064","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0205064","created_at":"2026-07-04T14:36:11Z"},{"alias_kind":"arxiv_version","alias_value":"math/0205064v1","created_at":"2026-07-04T14:36:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0205064","created_at":"2026-07-04T14:36:11Z"},{"alias_kind":"pith_short_12","alias_value":"B2KZM6O3C6AG","created_at":"2026-07-04T14:36:11Z"},{"alias_kind":"pith_short_16","alias_value":"B2KZM6O3C6AGXLEH","created_at":"2026-07-04T14:36:11Z"},{"alias_kind":"pith_short_8","alias_value":"B2KZM6O3","created_at":"2026-07-04T14:36:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2002:B2KZM6O3C6AGXLEHBZBSQ4JRIS","target":"record","payload":{"canonical_record":{"source":{"id":"math/0205064","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CA","submitted_at":"2002-05-07T10:40:03Z","cross_cats_sorted":[],"title_canon_sha256":"cb7110c533a5cdaabb245eff7b79df9f4e9c3e022c663d7508d99639f1212798","abstract_canon_sha256":"590c02f02f90f4681b2222c44afc233f100bce22fb9e53d006e0f4dd6e9c601b"},"schema_version":"1.0"},"canonical_sha256":"0e959679db17806bac870e43287131449f6b051a2b7a1dd844c2a483bae3c29c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:36:11.246672Z","signature_b64":"AaEE6vXseK53Xw3f7J6+2Y6wGC+jbORQlgsOPCLjWjXamVpEw0tgnjC+RrK+LzvscwnjNcXDZMtZWByefIKIDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0e959679db17806bac870e43287131449f6b051a2b7a1dd844c2a483bae3c29c","last_reissued_at":"2026-07-04T14:36:11.246287Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:36:11.246287Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0205064","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":"2026-07-04T14:36:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eoyBx+fbzEs1UQxlMD3JkZx+hf1dV4BDAHKielx2m6aGtYWAVFZNC6zpUZaiRJkmnwTeBBgT6lXgM0P7IbHlDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T14:40:21.097141Z"},"content_sha256":"298feb90725f34a31caa9b510f3ab95b103e3ed6f2b30f815737031a8879d5a1","schema_version":"1.0","event_id":"sha256:298feb90725f34a31caa9b510f3ab95b103e3ed6f2b30f815737031a8879d5a1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2002:B2KZM6O3C6AGXLEHBZBSQ4JRIS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Two-point Taylor Expansions of Analytic Functions","license":"","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"(2) CWI, Amsterdam), Jose L. Lopez (1), Nico M. Temme (2) ((1) Universidad Publica de Navarra, Pamplona","submitted_at":"2002-05-07T10:40:03Z","abstract_excerpt":"Taylor expansions of analytic functions are considered with respect to two points. Cauchy-type formulas are given for coefficients and remainders in the expansions, and the regions of convergence are indicated. It is explained how these expansions can be used in deriving uniform asymptotic expansions of integrals. The method is also used for obtaining Laurent expansions in two points."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0205064","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0205064/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":"2026-07-04T14:36:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uQAco5YDbp0EGgGeALZritsVHfC9LedrqthJjSB/PhQB97QIXhYOONeW6ZQ2FiDlHGLs9FjAjEghBR7jXTs2CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T14:40:21.097681Z"},"content_sha256":"a8ba0c81673de1b2a132c19b421fdfda8cc87364f889a325a2a59b8badeadd3c","schema_version":"1.0","event_id":"sha256:a8ba0c81673de1b2a132c19b421fdfda8cc87364f889a325a2a59b8badeadd3c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/B2KZM6O3C6AGXLEHBZBSQ4JRIS/bundle.json","state_url":"https://pith.science/pith/B2KZM6O3C6AGXLEHBZBSQ4JRIS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/B2KZM6O3C6AGXLEHBZBSQ4JRIS/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":"2026-08-03T14:40:21Z","links":{"resolver":"https://pith.science/pith/B2KZM6O3C6AGXLEHBZBSQ4JRIS","bundle":"https://pith.science/pith/B2KZM6O3C6AGXLEHBZBSQ4JRIS/bundle.json","state":"https://pith.science/pith/B2KZM6O3C6AGXLEHBZBSQ4JRIS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/B2KZM6O3C6AGXLEHBZBSQ4JRIS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:B2KZM6O3C6AGXLEHBZBSQ4JRIS","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":"590c02f02f90f4681b2222c44afc233f100bce22fb9e53d006e0f4dd6e9c601b","cross_cats_sorted":[],"license":"","primary_cat":"math.CA","submitted_at":"2002-05-07T10:40:03Z","title_canon_sha256":"cb7110c533a5cdaabb245eff7b79df9f4e9c3e022c663d7508d99639f1212798"},"schema_version":"1.0","source":{"id":"math/0205064","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0205064","created_at":"2026-07-04T14:36:11Z"},{"alias_kind":"arxiv_version","alias_value":"math/0205064v1","created_at":"2026-07-04T14:36:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0205064","created_at":"2026-07-04T14:36:11Z"},{"alias_kind":"pith_short_12","alias_value":"B2KZM6O3C6AG","created_at":"2026-07-04T14:36:11Z"},{"alias_kind":"pith_short_16","alias_value":"B2KZM6O3C6AGXLEH","created_at":"2026-07-04T14:36:11Z"},{"alias_kind":"pith_short_8","alias_value":"B2KZM6O3","created_at":"2026-07-04T14:36:11Z"}],"graph_snapshots":[{"event_id":"sha256:a8ba0c81673de1b2a132c19b421fdfda8cc87364f889a325a2a59b8badeadd3c","target":"graph","created_at":"2026-07-04T14:36:11Z","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/math/0205064/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Taylor expansions of analytic functions are considered with respect to two points. Cauchy-type formulas are given for coefficients and remainders in the expansions, and the regions of convergence are indicated. It is explained how these expansions can be used in deriving uniform asymptotic expansions of integrals. The method is also used for obtaining Laurent expansions in two points.","authors_text":"(2) CWI, Amsterdam), Jose L. Lopez (1), Nico M. Temme (2) ((1) Universidad Publica de Navarra, Pamplona","cross_cats":[],"headline":"","license":"","primary_cat":"math.CA","submitted_at":"2002-05-07T10:40:03Z","title":"Two-point Taylor Expansions of Analytic Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0205064","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":"sha256:298feb90725f34a31caa9b510f3ab95b103e3ed6f2b30f815737031a8879d5a1","target":"record","created_at":"2026-07-04T14:36:11Z","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":"590c02f02f90f4681b2222c44afc233f100bce22fb9e53d006e0f4dd6e9c601b","cross_cats_sorted":[],"license":"","primary_cat":"math.CA","submitted_at":"2002-05-07T10:40:03Z","title_canon_sha256":"cb7110c533a5cdaabb245eff7b79df9f4e9c3e022c663d7508d99639f1212798"},"schema_version":"1.0","source":{"id":"math/0205064","kind":"arxiv","version":1}},"canonical_sha256":"0e959679db17806bac870e43287131449f6b051a2b7a1dd844c2a483bae3c29c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0e959679db17806bac870e43287131449f6b051a2b7a1dd844c2a483bae3c29c","first_computed_at":"2026-07-04T14:36:11.246287Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:36:11.246287Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AaEE6vXseK53Xw3f7J6+2Y6wGC+jbORQlgsOPCLjWjXamVpEw0tgnjC+RrK+LzvscwnjNcXDZMtZWByefIKIDw==","signature_status":"signed_v1","signed_at":"2026-07-04T14:36:11.246672Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0205064","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:298feb90725f34a31caa9b510f3ab95b103e3ed6f2b30f815737031a8879d5a1","sha256:a8ba0c81673de1b2a132c19b421fdfda8cc87364f889a325a2a59b8badeadd3c"],"state_sha256":"c98dd679b2aaeb6b61e44406f64e8c01754b602b863f9a5646fdebbc0f9ee893"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BLU3+VHaiEh4svs6a4b7eLNZQEfTrnH4y8XhDQoOR2MfSM/ZrnWMypOu3EP5S+5h5t13rCwMBXMAd8K8Y8JECw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T14:40:21.103248Z","bundle_sha256":"5bf4b301cce0684d319ca7fb3f831c348b70ec259f71552057df3e7e170aea38"}}