{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:BZS2UVP5PFWETJSIOD37HBE4CX","short_pith_number":"pith:BZS2UVP5","canonical_record":{"source":{"id":"1805.08830","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-05-22T19:40:19Z","cross_cats_sorted":[],"title_canon_sha256":"dfd7e29ebd5f19066e462510f021acdb56dc28991d3eb9a55ca4878634ff5461","abstract_canon_sha256":"45f59016eb2833bbe51caa4a0d6fd1ca016a9ba0a9dd644bcae33ae531185817"},"schema_version":"1.0"},"canonical_sha256":"0e65aa55fd796c49a64870f7f3849c15c068133668dc9138beb7b2d1803804c3","source":{"kind":"arxiv","id":"1805.08830","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.08830","created_at":"2026-05-18T00:04:39Z"},{"alias_kind":"arxiv_version","alias_value":"1805.08830v3","created_at":"2026-05-18T00:04:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.08830","created_at":"2026-05-18T00:04:39Z"},{"alias_kind":"pith_short_12","alias_value":"BZS2UVP5PFWE","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"BZS2UVP5PFWETJSI","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"BZS2UVP5","created_at":"2026-05-18T12:32:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:BZS2UVP5PFWETJSIOD37HBE4CX","target":"record","payload":{"canonical_record":{"source":{"id":"1805.08830","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-05-22T19:40:19Z","cross_cats_sorted":[],"title_canon_sha256":"dfd7e29ebd5f19066e462510f021acdb56dc28991d3eb9a55ca4878634ff5461","abstract_canon_sha256":"45f59016eb2833bbe51caa4a0d6fd1ca016a9ba0a9dd644bcae33ae531185817"},"schema_version":"1.0"},"canonical_sha256":"0e65aa55fd796c49a64870f7f3849c15c068133668dc9138beb7b2d1803804c3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:39.349426Z","signature_b64":"P0B1uRPuwrqmJF2IkX0IZwE7rg7b9BCUmRpJmpzIKlyN2pIeqCByXvCe9Lpp6vZjSe+ir1VPsbtija3CNsgzCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0e65aa55fd796c49a64870f7f3849c15c068133668dc9138beb7b2d1803804c3","last_reissued_at":"2026-05-18T00:04:39.349023Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:39.349023Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.08830","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":"2026-05-18T00:04:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iWMS0mnJlpB6+Sa0d4rDfGThPr16ZMVsG3CwVpHUYhkly2Wy5SWnoyljVoescUnICamTdeBF7Ydn3WtleUViCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T17:53:32.723338Z"},"content_sha256":"3dd77c8f0c6efd207da31dcc714598fd979ea78590eeb57c4f2ac18de5f307af","schema_version":"1.0","event_id":"sha256:3dd77c8f0c6efd207da31dcc714598fd979ea78590eeb57c4f2ac18de5f307af"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:BZS2UVP5PFWETJSIOD37HBE4CX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stein operators for variables form the third and fourth Wiener chaoses","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Robert E. Gaunt","submitted_at":"2018-05-22T19:40:19Z","abstract_excerpt":"Let $Z$ be a standard normal random variable and let $H_n$ denote the $n$-th Hermite polynomial. In this note, we obtain Stein equations for the random variables $H_3(Z)$ and $H_4(Z)$, which represents a first step towards developing Stein's method for distributional limits from the third and fourth Wiener chaoses. Perhaps surprisingly, these Stein equations are fifth and third order linear ordinary differential equations, respectively. As a warm up, we obtain a Stein equation for the random variable $aZ^2+bZ+c$, $a,b,c\\in\\mathbb{R}$, which leads us to a Stein equation for the non-central chi-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.08830","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":"2026-05-18T00:04:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vvmj7ZlRU6I+FstC7fS5RgdtnjYyZIalklxhOigxbclrySQtA+NuyuJ1zeSy08eC1KeEVn/NVYdBjr32Gw95DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T17:53:32.723783Z"},"content_sha256":"bf266e1394c3823dc1df91925c095128ac52169cf9dfd57645b231b68b379e01","schema_version":"1.0","event_id":"sha256:bf266e1394c3823dc1df91925c095128ac52169cf9dfd57645b231b68b379e01"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BZS2UVP5PFWETJSIOD37HBE4CX/bundle.json","state_url":"https://pith.science/pith/BZS2UVP5PFWETJSIOD37HBE4CX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BZS2UVP5PFWETJSIOD37HBE4CX/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":"2026-05-29T17:53:32Z","links":{"resolver":"https://pith.science/pith/BZS2UVP5PFWETJSIOD37HBE4CX","bundle":"https://pith.science/pith/BZS2UVP5PFWETJSIOD37HBE4CX/bundle.json","state":"https://pith.science/pith/BZS2UVP5PFWETJSIOD37HBE4CX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BZS2UVP5PFWETJSIOD37HBE4CX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:BZS2UVP5PFWETJSIOD37HBE4CX","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":"45f59016eb2833bbe51caa4a0d6fd1ca016a9ba0a9dd644bcae33ae531185817","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-05-22T19:40:19Z","title_canon_sha256":"dfd7e29ebd5f19066e462510f021acdb56dc28991d3eb9a55ca4878634ff5461"},"schema_version":"1.0","source":{"id":"1805.08830","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.08830","created_at":"2026-05-18T00:04:39Z"},{"alias_kind":"arxiv_version","alias_value":"1805.08830v3","created_at":"2026-05-18T00:04:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.08830","created_at":"2026-05-18T00:04:39Z"},{"alias_kind":"pith_short_12","alias_value":"BZS2UVP5PFWE","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"BZS2UVP5PFWETJSI","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"BZS2UVP5","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:bf266e1394c3823dc1df91925c095128ac52169cf9dfd57645b231b68b379e01","target":"graph","created_at":"2026-05-18T00:04:39Z","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":"Let $Z$ be a standard normal random variable and let $H_n$ denote the $n$-th Hermite polynomial. In this note, we obtain Stein equations for the random variables $H_3(Z)$ and $H_4(Z)$, which represents a first step towards developing Stein's method for distributional limits from the third and fourth Wiener chaoses. Perhaps surprisingly, these Stein equations are fifth and third order linear ordinary differential equations, respectively. As a warm up, we obtain a Stein equation for the random variable $aZ^2+bZ+c$, $a,b,c\\in\\mathbb{R}$, which leads us to a Stein equation for the non-central chi-","authors_text":"Robert E. Gaunt","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-05-22T19:40:19Z","title":"Stein operators for variables form the third and fourth Wiener chaoses"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.08830","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":"sha256:3dd77c8f0c6efd207da31dcc714598fd979ea78590eeb57c4f2ac18de5f307af","target":"record","created_at":"2026-05-18T00:04:39Z","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":"45f59016eb2833bbe51caa4a0d6fd1ca016a9ba0a9dd644bcae33ae531185817","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-05-22T19:40:19Z","title_canon_sha256":"dfd7e29ebd5f19066e462510f021acdb56dc28991d3eb9a55ca4878634ff5461"},"schema_version":"1.0","source":{"id":"1805.08830","kind":"arxiv","version":3}},"canonical_sha256":"0e65aa55fd796c49a64870f7f3849c15c068133668dc9138beb7b2d1803804c3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0e65aa55fd796c49a64870f7f3849c15c068133668dc9138beb7b2d1803804c3","first_computed_at":"2026-05-18T00:04:39.349023Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:39.349023Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"P0B1uRPuwrqmJF2IkX0IZwE7rg7b9BCUmRpJmpzIKlyN2pIeqCByXvCe9Lpp6vZjSe+ir1VPsbtija3CNsgzCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:39.349426Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.08830","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3dd77c8f0c6efd207da31dcc714598fd979ea78590eeb57c4f2ac18de5f307af","sha256:bf266e1394c3823dc1df91925c095128ac52169cf9dfd57645b231b68b379e01"],"state_sha256":"2652c87c2d58d872e74425cbd711255d3b6b1a316694a19e3f29b0343814d46e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kRP3KU/0U8PSDQ5Wv28mRrW6IayJ4WeQ0GHqTztBko64FqBr/pinMOH0AoWDWcnIQyXfw4OaeOX+B7mu52IUBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T17:53:32.727173Z","bundle_sha256":"43e27c58286b457a8b491e67a6ae6e6a7873fb810cbdb320b73c15c588c52572"}}