{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:G5KO3ZF5CRRQFOCHO4DWUJEI7A","short_pith_number":"pith:G5KO3ZF5","canonical_record":{"source":{"id":"1101.4894","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-01-25T18:46:14Z","cross_cats_sorted":[],"title_canon_sha256":"d9c6af989418f4af3bfa1f5743703c4c2e6823bebdb98ecb6fc0c71e7f808610","abstract_canon_sha256":"0b1b5d431fc3bc7431ae894bde51e7205a12a4643def28339565938c4555f1ea"},"schema_version":"1.0"},"canonical_sha256":"3754ede4bd146302b84777076a2488f80731f12eb9f85a7e9976aad062907466","source":{"kind":"arxiv","id":"1101.4894","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.4894","created_at":"2026-05-18T04:30:58Z"},{"alias_kind":"arxiv_version","alias_value":"1101.4894v1","created_at":"2026-05-18T04:30:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.4894","created_at":"2026-05-18T04:30:58Z"},{"alias_kind":"pith_short_12","alias_value":"G5KO3ZF5CRRQ","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"G5KO3ZF5CRRQFOCH","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"G5KO3ZF5","created_at":"2026-05-18T12:26:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:G5KO3ZF5CRRQFOCHO4DWUJEI7A","target":"record","payload":{"canonical_record":{"source":{"id":"1101.4894","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-01-25T18:46:14Z","cross_cats_sorted":[],"title_canon_sha256":"d9c6af989418f4af3bfa1f5743703c4c2e6823bebdb98ecb6fc0c71e7f808610","abstract_canon_sha256":"0b1b5d431fc3bc7431ae894bde51e7205a12a4643def28339565938c4555f1ea"},"schema_version":"1.0"},"canonical_sha256":"3754ede4bd146302b84777076a2488f80731f12eb9f85a7e9976aad062907466","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:30:58.805117Z","signature_b64":"UzQUmwk43RkId+WK4qJPIHL6eIH4Ev3QmynKy1pLWNj755rX1BpBWmCW6DO2cImc/ADiJYFt9I/QvAtAsMolAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3754ede4bd146302b84777076a2488f80731f12eb9f85a7e9976aad062907466","last_reissued_at":"2026-05-18T04:30:58.804121Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:30:58.804121Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1101.4894","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":"2026-05-18T04:30:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N7OrQuTflU7aseCSRK6tkUM/Cp4aryfQe1x17JLg0gfjgwqYUgxRkGtI/Yh0GPw2TC/Vgj/HfD0oO0TiIaK+DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T03:48:08.449758Z"},"content_sha256":"b93ad3fda2d60f89164b34ae3be01ad3a2c053332d53c99d4055a2c4fc0f23d0","schema_version":"1.0","event_id":"sha256:b93ad3fda2d60f89164b34ae3be01ad3a2c053332d53c99d4055a2c4fc0f23d0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:G5KO3ZF5CRRQFOCHO4DWUJEI7A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Large Degree Asymptotics of Generalized Bessel Polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Jos\\'e Luis L\\'opez, Nico M. Temme","submitted_at":"2011-01-25T18:46:14Z","abstract_excerpt":"Asymptotic expansions are given for large values of $n$ of the generalized Bessel polynomials $Y_n^\\mu(z)$. The analysis is based on integrals that follow from the generating functions of the polynomials. A new simple expansion is given that is valid outside a compact neighborhood of the origin in the $z-$plane. New forms of expansions in terms of elementary functions valid in sectors not containing the turning points $z=\\pm i/n$ are derived, and a new expansion in terms of modified Bessel functions is given. Earlier asymptotic expansions of the generalized Bessel polynomials by Wong and Zhang"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.4894","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":"2026-05-18T04:30:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P9AidyECWA8lpmaZvpimz1ggeKN76A61W0Nn+aXCC7DaNPKW9dit85r1iE6g0sF+LP6VPqCXlZTPkTjE5SyWDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T03:48:08.450108Z"},"content_sha256":"d9f29758e1b026e8677352264ae1539f0182c0fc5d63e2b839c5407222df7c4a","schema_version":"1.0","event_id":"sha256:d9f29758e1b026e8677352264ae1539f0182c0fc5d63e2b839c5407222df7c4a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G5KO3ZF5CRRQFOCHO4DWUJEI7A/bundle.json","state_url":"https://pith.science/pith/G5KO3ZF5CRRQFOCHO4DWUJEI7A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G5KO3ZF5CRRQFOCHO4DWUJEI7A/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":"2026-06-22T03:48:08Z","links":{"resolver":"https://pith.science/pith/G5KO3ZF5CRRQFOCHO4DWUJEI7A","bundle":"https://pith.science/pith/G5KO3ZF5CRRQFOCHO4DWUJEI7A/bundle.json","state":"https://pith.science/pith/G5KO3ZF5CRRQFOCHO4DWUJEI7A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G5KO3ZF5CRRQFOCHO4DWUJEI7A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:G5KO3ZF5CRRQFOCHO4DWUJEI7A","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":"0b1b5d431fc3bc7431ae894bde51e7205a12a4643def28339565938c4555f1ea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-01-25T18:46:14Z","title_canon_sha256":"d9c6af989418f4af3bfa1f5743703c4c2e6823bebdb98ecb6fc0c71e7f808610"},"schema_version":"1.0","source":{"id":"1101.4894","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.4894","created_at":"2026-05-18T04:30:58Z"},{"alias_kind":"arxiv_version","alias_value":"1101.4894v1","created_at":"2026-05-18T04:30:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.4894","created_at":"2026-05-18T04:30:58Z"},{"alias_kind":"pith_short_12","alias_value":"G5KO3ZF5CRRQ","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"G5KO3ZF5CRRQFOCH","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"G5KO3ZF5","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:d9f29758e1b026e8677352264ae1539f0182c0fc5d63e2b839c5407222df7c4a","target":"graph","created_at":"2026-05-18T04:30:58Z","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":"Asymptotic expansions are given for large values of $n$ of the generalized Bessel polynomials $Y_n^\\mu(z)$. The analysis is based on integrals that follow from the generating functions of the polynomials. A new simple expansion is given that is valid outside a compact neighborhood of the origin in the $z-$plane. New forms of expansions in terms of elementary functions valid in sectors not containing the turning points $z=\\pm i/n$ are derived, and a new expansion in terms of modified Bessel functions is given. Earlier asymptotic expansions of the generalized Bessel polynomials by Wong and Zhang","authors_text":"Jos\\'e Luis L\\'opez, Nico M. Temme","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-01-25T18:46:14Z","title":"Large Degree Asymptotics of Generalized Bessel Polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.4894","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:b93ad3fda2d60f89164b34ae3be01ad3a2c053332d53c99d4055a2c4fc0f23d0","target":"record","created_at":"2026-05-18T04:30:58Z","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":"0b1b5d431fc3bc7431ae894bde51e7205a12a4643def28339565938c4555f1ea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-01-25T18:46:14Z","title_canon_sha256":"d9c6af989418f4af3bfa1f5743703c4c2e6823bebdb98ecb6fc0c71e7f808610"},"schema_version":"1.0","source":{"id":"1101.4894","kind":"arxiv","version":1}},"canonical_sha256":"3754ede4bd146302b84777076a2488f80731f12eb9f85a7e9976aad062907466","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3754ede4bd146302b84777076a2488f80731f12eb9f85a7e9976aad062907466","first_computed_at":"2026-05-18T04:30:58.804121Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:30:58.804121Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UzQUmwk43RkId+WK4qJPIHL6eIH4Ev3QmynKy1pLWNj755rX1BpBWmCW6DO2cImc/ADiJYFt9I/QvAtAsMolAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:30:58.805117Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.4894","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b93ad3fda2d60f89164b34ae3be01ad3a2c053332d53c99d4055a2c4fc0f23d0","sha256:d9f29758e1b026e8677352264ae1539f0182c0fc5d63e2b839c5407222df7c4a"],"state_sha256":"531d2fa0d41c08532038ed89fa5f2248879c94c929a758de58a1c4793ea6c6e7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lE02NQlL11HZp8HpxQaGWgBJM57x1Q/JiqKIUrIsrzzLXMLq9j8VjETsCqrhHid5fRPSH0LCzKIsr59Mo132DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T03:48:08.452066Z","bundle_sha256":"7204364414e7952d0e46aa71246c610d35fe9713a5653f6012fef4f5a0454c3d"}}