{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:UCXVYNYVAOFJJYVMJOFDZJSGMF","short_pith_number":"pith:UCXVYNYV","canonical_record":{"source":{"id":"1808.02405","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-08-07T14:48:02Z","cross_cats_sorted":[],"title_canon_sha256":"9a683afda575b116480930ca57198a7fd7b56ea4266a52f8e97e92f1b04cbe40","abstract_canon_sha256":"062d8aa2519b3a7dbf34bcd2c3521a7102b883584873e4766bcef5a7f0804828"},"schema_version":"1.0"},"canonical_sha256":"a0af5c3715038a94e2ac4b8a3ca64661452ebca974160a46b27290ef5fce83e7","source":{"kind":"arxiv","id":"1808.02405","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.02405","created_at":"2026-05-18T00:06:01Z"},{"alias_kind":"arxiv_version","alias_value":"1808.02405v3","created_at":"2026-05-18T00:06:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.02405","created_at":"2026-05-18T00:06:01Z"},{"alias_kind":"pith_short_12","alias_value":"UCXVYNYVAOFJ","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UCXVYNYVAOFJJYVM","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UCXVYNYV","created_at":"2026-05-18T12:32:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:UCXVYNYVAOFJJYVMJOFDZJSGMF","target":"record","payload":{"canonical_record":{"source":{"id":"1808.02405","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-08-07T14:48:02Z","cross_cats_sorted":[],"title_canon_sha256":"9a683afda575b116480930ca57198a7fd7b56ea4266a52f8e97e92f1b04cbe40","abstract_canon_sha256":"062d8aa2519b3a7dbf34bcd2c3521a7102b883584873e4766bcef5a7f0804828"},"schema_version":"1.0"},"canonical_sha256":"a0af5c3715038a94e2ac4b8a3ca64661452ebca974160a46b27290ef5fce83e7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:01.139004Z","signature_b64":"rOC3/OWWLbw3GbM4hB8teQ15ArjpKqwzlCJNIMd2MNCcRB9KzL+/2DEAnyt35DjlaLOLNg4+w6T6zVbfCYYLBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a0af5c3715038a94e2ac4b8a3ca64661452ebca974160a46b27290ef5fce83e7","last_reissued_at":"2026-05-18T00:06:01.138662Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:01.138662Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1808.02405","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:06:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qpTbpbAy7SBKPOJmGmhiZ8YLJe/vJzmnjDO23prJmsyAoZeYHdoRD7GC4aEdVvQhkfh17wLDZ9TkPc/XVOIZDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T15:12:10.341983Z"},"content_sha256":"1d66332649a8bdc988b00fb58043b9ccee3d8dd709c38d916b5b476c97d45734","schema_version":"1.0","event_id":"sha256:1d66332649a8bdc988b00fb58043b9ccee3d8dd709c38d916b5b476c97d45734"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:UCXVYNYVAOFJJYVMJOFDZJSGMF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stein's method for asymmetric $\\alpha$-stable distributions, with application to the stable CLT","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ivan Nourdin, Lihu Xu, Peng Chen","submitted_at":"2018-08-07T14:48:02Z","abstract_excerpt":"This paper is concerned with the Stein's method associated with a (possibly) asymmetric $\\alpha$-stable distribution $Z$, in dimension one. More precisely, its goal is twofold. In the first part, we exhibit a genuine bound for the Wasserstein distance between $Z$ and any integrable random variable $X$, in terms of an operator that reduces to the classical fractional Laplacian in the symmetric case. Then, in the second part we apply the aforementioned bound to compute error rates in the stable central limit theorem, when the entries are in the domain $\\mathcal{D}_\\alpha$ of normal attraction of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.02405","kind":"arxiv","version":3},"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":"2026-05-18T00:06:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z2FGxYjbpFe5qPgpFVQtISBbnOvCqeKWIjSzi1lUegltXff3AQw7BgvJIgM56XLU+iwmnmmqRMIXsPeeSGC0Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T15:12:10.342351Z"},"content_sha256":"b7c7cd8c6d22dc2bf790f784df83973542e00f840eee609b1947aae7615f3129","schema_version":"1.0","event_id":"sha256:b7c7cd8c6d22dc2bf790f784df83973542e00f840eee609b1947aae7615f3129"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UCXVYNYVAOFJJYVMJOFDZJSGMF/bundle.json","state_url":"https://pith.science/pith/UCXVYNYVAOFJJYVMJOFDZJSGMF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UCXVYNYVAOFJJYVMJOFDZJSGMF/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":"2026-05-20T15:12:10Z","links":{"resolver":"https://pith.science/pith/UCXVYNYVAOFJJYVMJOFDZJSGMF","bundle":"https://pith.science/pith/UCXVYNYVAOFJJYVMJOFDZJSGMF/bundle.json","state":"https://pith.science/pith/UCXVYNYVAOFJJYVMJOFDZJSGMF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UCXVYNYVAOFJJYVMJOFDZJSGMF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:UCXVYNYVAOFJJYVMJOFDZJSGMF","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":"062d8aa2519b3a7dbf34bcd2c3521a7102b883584873e4766bcef5a7f0804828","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-08-07T14:48:02Z","title_canon_sha256":"9a683afda575b116480930ca57198a7fd7b56ea4266a52f8e97e92f1b04cbe40"},"schema_version":"1.0","source":{"id":"1808.02405","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.02405","created_at":"2026-05-18T00:06:01Z"},{"alias_kind":"arxiv_version","alias_value":"1808.02405v3","created_at":"2026-05-18T00:06:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.02405","created_at":"2026-05-18T00:06:01Z"},{"alias_kind":"pith_short_12","alias_value":"UCXVYNYVAOFJ","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UCXVYNYVAOFJJYVM","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UCXVYNYV","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:b7c7cd8c6d22dc2bf790f784df83973542e00f840eee609b1947aae7615f3129","target":"graph","created_at":"2026-05-18T00:06:01Z","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":"This paper is concerned with the Stein's method associated with a (possibly) asymmetric $\\alpha$-stable distribution $Z$, in dimension one. More precisely, its goal is twofold. In the first part, we exhibit a genuine bound for the Wasserstein distance between $Z$ and any integrable random variable $X$, in terms of an operator that reduces to the classical fractional Laplacian in the symmetric case. Then, in the second part we apply the aforementioned bound to compute error rates in the stable central limit theorem, when the entries are in the domain $\\mathcal{D}_\\alpha$ of normal attraction of","authors_text":"Ivan Nourdin, Lihu Xu, Peng Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-08-07T14:48:02Z","title":"Stein's method for asymmetric $\\alpha$-stable distributions, with application to the stable CLT"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.02405","kind":"arxiv","version":3},"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":"sha256:1d66332649a8bdc988b00fb58043b9ccee3d8dd709c38d916b5b476c97d45734","target":"record","created_at":"2026-05-18T00:06:01Z","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":"062d8aa2519b3a7dbf34bcd2c3521a7102b883584873e4766bcef5a7f0804828","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-08-07T14:48:02Z","title_canon_sha256":"9a683afda575b116480930ca57198a7fd7b56ea4266a52f8e97e92f1b04cbe40"},"schema_version":"1.0","source":{"id":"1808.02405","kind":"arxiv","version":3}},"canonical_sha256":"a0af5c3715038a94e2ac4b8a3ca64661452ebca974160a46b27290ef5fce83e7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a0af5c3715038a94e2ac4b8a3ca64661452ebca974160a46b27290ef5fce83e7","first_computed_at":"2026-05-18T00:06:01.138662Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:01.138662Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rOC3/OWWLbw3GbM4hB8teQ15ArjpKqwzlCJNIMd2MNCcRB9KzL+/2DEAnyt35DjlaLOLNg4+w6T6zVbfCYYLBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:01.139004Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.02405","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1d66332649a8bdc988b00fb58043b9ccee3d8dd709c38d916b5b476c97d45734","sha256:b7c7cd8c6d22dc2bf790f784df83973542e00f840eee609b1947aae7615f3129"],"state_sha256":"45de8b08a23f764f7717634766ced247e80d8262ddd1f5d3da2b92b4fef47dbb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cHd1KdEdSr5zsaKGQ4KOEHYxm0JI1IMYCNC6zl1hKHNl7Aq06t1AaNwvVOcR4MvLA5HO/fGDx5n2rgx8MGHSAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-20T15:12:10.344496Z","bundle_sha256":"1133af61473c15266868eb68e8c418c7f7111cdd524b516d1e300e1a91eedd78"}}