{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:N7NM6KBPNRYZNRD55EUUADMCHC","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":"377b7eee781c6d7b8efacfcc7d5469a4eee315b45b11f130105464ede4327a44","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-12-07T15:07:10Z","title_canon_sha256":"03cec73be88081dabdbd1fb785a469fc6ee26180ea1c97a5c866c0e8f23edb3d"},"schema_version":"1.0","source":{"id":"1612.02279","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.02279","created_at":"2026-05-18T00:48:53Z"},{"alias_kind":"arxiv_version","alias_value":"1612.02279v2","created_at":"2026-05-18T00:48:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.02279","created_at":"2026-05-18T00:48:53Z"},{"alias_kind":"pith_short_12","alias_value":"N7NM6KBPNRYZ","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"N7NM6KBPNRYZNRD5","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"N7NM6KBP","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:70b624ef4785123837442a3306bc1c5b71ea6271aee5a105c0bde2c5a22d597f","target":"graph","created_at":"2026-05-18T00:48:53Z","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 study the Stein equation associated with the one-dimensional Gamma distribution, and provide novel bounds, allowing one to effectively deal with test functions supported by the whole real line. We apply our estimates to derive new quantitative results involving random variables that are non-linear functionals of random fields, namely: (i) a non-central quantitative de Jong theorem for sequences of degenerate U-statistics satisfying minimal uniform integrability conditions, significantly extending previous findings by de Jong (1990), Nourdin, Peccati and Reinert (2010) and D\\\"obler and Pecca","authors_text":"Christian D\\\"obler, Giovanni Peccati","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-12-07T15:07:10Z","title":"The Gamma Stein equation and non-central de Jong theorems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.02279","kind":"arxiv","version":2},"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":"sha256:2bd9b9512a0feea03d472c751dcd48f633e009ca64141237cd7b28371641b217","target":"record","created_at":"2026-05-18T00:48:53Z","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":"377b7eee781c6d7b8efacfcc7d5469a4eee315b45b11f130105464ede4327a44","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-12-07T15:07:10Z","title_canon_sha256":"03cec73be88081dabdbd1fb785a469fc6ee26180ea1c97a5c866c0e8f23edb3d"},"schema_version":"1.0","source":{"id":"1612.02279","kind":"arxiv","version":2}},"canonical_sha256":"6fdacf282f6c7196c47de929400d823881d5f6b4db12c3cf4d82c6b5385f6162","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6fdacf282f6c7196c47de929400d823881d5f6b4db12c3cf4d82c6b5385f6162","first_computed_at":"2026-05-18T00:48:53.622828Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:53.622828Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oKhVfAILo9BZ5baCnqimz/0lg6vjPVpa4NhBWYTh2tYVYM2XcUHWubBZdR/zBQziWjfUG85WSxWzgac1+DGYCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:53.623523Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.02279","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2bd9b9512a0feea03d472c751dcd48f633e009ca64141237cd7b28371641b217","sha256:70b624ef4785123837442a3306bc1c5b71ea6271aee5a105c0bde2c5a22d597f"],"state_sha256":"5b490c765bd1b140930a1a96cbfed4dd23d2e2bc1cb430fd9ba8ff5791ee7432"}