{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:2AWR34HWX3DJJBFLEPK2TKAAVB","short_pith_number":"pith:2AWR34HW","canonical_record":{"source":{"id":"1812.02703","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-12-06T18:37:36Z","cross_cats_sorted":["math.FA","math.ST","stat.TH"],"title_canon_sha256":"43f9d86a838e99154e8db59ec3726f50e2533e00c8845f733500bb79402028a4","abstract_canon_sha256":"9d783e4ed6a55e7d68249b0c20d2b39046a0acfce897cef3a28b30a86c432b68"},"schema_version":"1.0"},"canonical_sha256":"d02d1df0f6bec69484ab23d5a9a800a84285fe4822c251e78a3567f7b883af66","source":{"kind":"arxiv","id":"1812.02703","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.02703","created_at":"2026-05-17T23:58:55Z"},{"alias_kind":"arxiv_version","alias_value":"1812.02703v1","created_at":"2026-05-17T23:58:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.02703","created_at":"2026-05-17T23:58:55Z"},{"alias_kind":"pith_short_12","alias_value":"2AWR34HWX3DJ","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"2AWR34HWX3DJJBFL","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"2AWR34HW","created_at":"2026-05-18T12:31:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:2AWR34HWX3DJJBFLEPK2TKAAVB","target":"record","payload":{"canonical_record":{"source":{"id":"1812.02703","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-12-06T18:37:36Z","cross_cats_sorted":["math.FA","math.ST","stat.TH"],"title_canon_sha256":"43f9d86a838e99154e8db59ec3726f50e2533e00c8845f733500bb79402028a4","abstract_canon_sha256":"9d783e4ed6a55e7d68249b0c20d2b39046a0acfce897cef3a28b30a86c432b68"},"schema_version":"1.0"},"canonical_sha256":"d02d1df0f6bec69484ab23d5a9a800a84285fe4822c251e78a3567f7b883af66","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:55.166017Z","signature_b64":"h80B6ew87fcYHUepo0AnuqKJo0wzx2ED0Wa9yqWYv5A4eFrI1Zp6/BIeHmtZtiF7H5SKifvHybVaSHiXU8rYDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d02d1df0f6bec69484ab23d5a9a800a84285fe4822c251e78a3567f7b883af66","last_reissued_at":"2026-05-17T23:58:55.165495Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:55.165495Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.02703","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":"2026-05-17T23:58:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c/6+90z3hIK6DigSv3QQn7EKi0tMedqRiEFPeUJM5xrSttfOx6zG+BySLncNLtadaVt7r3BuclXLjSbe2ROBDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T12:17:20.916213Z"},"content_sha256":"f31d153443d0bf13470476fe606ca9e8847e2c424eb086b4edae9996ebc810f2","schema_version":"1.0","event_id":"sha256:f31d153443d0bf13470476fe606ca9e8847e2c424eb086b4edae9996ebc810f2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:2AWR34HWX3DJJBFLEPK2TKAAVB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Higher-order Stein kernels for Gaussian approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Max Fathi","submitted_at":"2018-12-06T18:37:36Z","abstract_excerpt":"We introduce higher-order Stein kernels relative to the standard Gaussian measure, which generalize the usual Stein kernels by involving higher-order derivatives of test functions. We relate the associated discrepancies to various metrics on the space of probability measures and prove new functional inequalities involving them. As an application, we obtain new explicit improved rates of convergence in the classical multidimensional CLT under higher moment and regularity assumptions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.02703","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":"2026-05-17T23:58:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sDtoinl6bGWLmEp3hBX8jF9F8YykejaN2SSydcCyHWw4HX9YUGkrlZqD0Y08XLkjpAH5K2FXpFPMZQGhmGeaCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T12:17:20.916906Z"},"content_sha256":"235590e55e80a89a79a190f33a31c4b0988256e784817fec3a400dccb4c4af3f","schema_version":"1.0","event_id":"sha256:235590e55e80a89a79a190f33a31c4b0988256e784817fec3a400dccb4c4af3f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2AWR34HWX3DJJBFLEPK2TKAAVB/bundle.json","state_url":"https://pith.science/pith/2AWR34HWX3DJJBFLEPK2TKAAVB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2AWR34HWX3DJJBFLEPK2TKAAVB/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":"2026-05-26T12:17:20Z","links":{"resolver":"https://pith.science/pith/2AWR34HWX3DJJBFLEPK2TKAAVB","bundle":"https://pith.science/pith/2AWR34HWX3DJJBFLEPK2TKAAVB/bundle.json","state":"https://pith.science/pith/2AWR34HWX3DJJBFLEPK2TKAAVB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2AWR34HWX3DJJBFLEPK2TKAAVB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:2AWR34HWX3DJJBFLEPK2TKAAVB","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":"9d783e4ed6a55e7d68249b0c20d2b39046a0acfce897cef3a28b30a86c432b68","cross_cats_sorted":["math.FA","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-12-06T18:37:36Z","title_canon_sha256":"43f9d86a838e99154e8db59ec3726f50e2533e00c8845f733500bb79402028a4"},"schema_version":"1.0","source":{"id":"1812.02703","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.02703","created_at":"2026-05-17T23:58:55Z"},{"alias_kind":"arxiv_version","alias_value":"1812.02703v1","created_at":"2026-05-17T23:58:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.02703","created_at":"2026-05-17T23:58:55Z"},{"alias_kind":"pith_short_12","alias_value":"2AWR34HWX3DJ","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"2AWR34HWX3DJJBFL","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"2AWR34HW","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:235590e55e80a89a79a190f33a31c4b0988256e784817fec3a400dccb4c4af3f","target":"graph","created_at":"2026-05-17T23:58:55Z","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":"We introduce higher-order Stein kernels relative to the standard Gaussian measure, which generalize the usual Stein kernels by involving higher-order derivatives of test functions. We relate the associated discrepancies to various metrics on the space of probability measures and prove new functional inequalities involving them. As an application, we obtain new explicit improved rates of convergence in the classical multidimensional CLT under higher moment and regularity assumptions.","authors_text":"Max Fathi","cross_cats":["math.FA","math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-12-06T18:37:36Z","title":"Higher-order Stein kernels for Gaussian approximation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.02703","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:f31d153443d0bf13470476fe606ca9e8847e2c424eb086b4edae9996ebc810f2","target":"record","created_at":"2026-05-17T23:58:55Z","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":"9d783e4ed6a55e7d68249b0c20d2b39046a0acfce897cef3a28b30a86c432b68","cross_cats_sorted":["math.FA","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-12-06T18:37:36Z","title_canon_sha256":"43f9d86a838e99154e8db59ec3726f50e2533e00c8845f733500bb79402028a4"},"schema_version":"1.0","source":{"id":"1812.02703","kind":"arxiv","version":1}},"canonical_sha256":"d02d1df0f6bec69484ab23d5a9a800a84285fe4822c251e78a3567f7b883af66","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d02d1df0f6bec69484ab23d5a9a800a84285fe4822c251e78a3567f7b883af66","first_computed_at":"2026-05-17T23:58:55.165495Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:55.165495Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"h80B6ew87fcYHUepo0AnuqKJo0wzx2ED0Wa9yqWYv5A4eFrI1Zp6/BIeHmtZtiF7H5SKifvHybVaSHiXU8rYDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:55.166017Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.02703","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f31d153443d0bf13470476fe606ca9e8847e2c424eb086b4edae9996ebc810f2","sha256:235590e55e80a89a79a190f33a31c4b0988256e784817fec3a400dccb4c4af3f"],"state_sha256":"e1f35aba31505163f6ef0e4865bab0eb4845fdfefab549e5e259b3e5e8edd01e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T3KS1t/PhOlX4ssm/Czpp211+qiXm0Anuo/oi7+eKlHwoEY+p4pWGIqEdpZrcQZwEYpNiQ8YKPUldvxzx0DnDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T12:17:20.920767Z","bundle_sha256":"d0214d698cbe3a5afbffbac2af9eaa0af9afc4fa2537cc35bd36000b4855c69c"}}