{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:YZPKZIGO5JRT2XLKOFF7YMOOS6","short_pith_number":"pith:YZPKZIGO","canonical_record":{"source":{"id":"1808.01836","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-08-06T12:00:04Z","cross_cats_sorted":[],"title_canon_sha256":"ab681beae3c326992f91862bc11e1a80c34bd2a5833cc24c6e15d568e332d0da","abstract_canon_sha256":"19769feadd57342dd9b52f93c488728018309c7699d237001d453d5299e959d9"},"schema_version":"1.0"},"canonical_sha256":"c65eaca0ceea633d5d6a714bfc31ce97814449a73dd28ca98d2d61abaf470d84","source":{"kind":"arxiv","id":"1808.01836","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.01836","created_at":"2026-05-18T00:08:49Z"},{"alias_kind":"arxiv_version","alias_value":"1808.01836v1","created_at":"2026-05-18T00:08:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.01836","created_at":"2026-05-18T00:08:49Z"},{"alias_kind":"pith_short_12","alias_value":"YZPKZIGO5JRT","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"YZPKZIGO5JRT2XLK","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"YZPKZIGO","created_at":"2026-05-18T12:33:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:YZPKZIGO5JRT2XLKOFF7YMOOS6","target":"record","payload":{"canonical_record":{"source":{"id":"1808.01836","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-08-06T12:00:04Z","cross_cats_sorted":[],"title_canon_sha256":"ab681beae3c326992f91862bc11e1a80c34bd2a5833cc24c6e15d568e332d0da","abstract_canon_sha256":"19769feadd57342dd9b52f93c488728018309c7699d237001d453d5299e959d9"},"schema_version":"1.0"},"canonical_sha256":"c65eaca0ceea633d5d6a714bfc31ce97814449a73dd28ca98d2d61abaf470d84","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:49.545094Z","signature_b64":"cHZj3wz/wdADJs/IpWO4F8dVFkoAN4BJxmty5D4Cxn354NPsTz16ECea9f0WVu4kUI+e4vV5lOO7p35ekseZAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c65eaca0ceea633d5d6a714bfc31ce97814449a73dd28ca98d2d61abaf470d84","last_reissued_at":"2026-05-18T00:08:49.544439Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:49.544439Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1808.01836","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":"2026-05-18T00:08:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6q8TlwqDVEiQ/px8IIQF59UBWLgVBWvIAu9fyGereJd3fFtsGvDBiRAcCoeygwqF9LOpVEmvY0XhcikJkWUTDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T23:44:39.074180Z"},"content_sha256":"9c9b29f061a9582e2294167832161e935b3f83265dc292c4c937e46012f12919","schema_version":"1.0","event_id":"sha256:9c9b29f061a9582e2294167832161e935b3f83265dc292c4c937e46012f12919"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:YZPKZIGO5JRT2XLKOFF7YMOOS6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fourth moment theorems on the Poisson space: analytic statements via product formulae","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Christian D\\\"obler, Giovanni Peccati","submitted_at":"2018-08-06T12:00:04Z","abstract_excerpt":"We prove necessary and sufficient conditions for the asymptotic normality of multiple integrals with respect to a Poisson measure on a general measure space, expressed both in terms of norms of contraction kernels and of variances of carr\\'e-du-champ operators. Our results substantially complete the fourth moment theorems recently obtained by D\\\"obler and Peccati (2018) and D\\\"obler, Vidotto and Zheng (2018). An important tool for achieving our goals is a novel product formula for multiple integrals under minimal conditions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.01836","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":"2026-05-18T00:08:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u0bHE4ycy8ypz0RQL2eB+s3XquXy6Obi6/I5UGEGxLV5+3uPVuzaEutsnDwFfPSYWgX/B/1WEbNQpXlq1qemBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T23:44:39.074718Z"},"content_sha256":"2d60becec5f82aa417713f3811b09ab727eb8e2727ad61ffe81958cccbb64443","schema_version":"1.0","event_id":"sha256:2d60becec5f82aa417713f3811b09ab727eb8e2727ad61ffe81958cccbb64443"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YZPKZIGO5JRT2XLKOFF7YMOOS6/bundle.json","state_url":"https://pith.science/pith/YZPKZIGO5JRT2XLKOFF7YMOOS6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YZPKZIGO5JRT2XLKOFF7YMOOS6/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":"2026-05-27T23:44:39Z","links":{"resolver":"https://pith.science/pith/YZPKZIGO5JRT2XLKOFF7YMOOS6","bundle":"https://pith.science/pith/YZPKZIGO5JRT2XLKOFF7YMOOS6/bundle.json","state":"https://pith.science/pith/YZPKZIGO5JRT2XLKOFF7YMOOS6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YZPKZIGO5JRT2XLKOFF7YMOOS6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:YZPKZIGO5JRT2XLKOFF7YMOOS6","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":"19769feadd57342dd9b52f93c488728018309c7699d237001d453d5299e959d9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-08-06T12:00:04Z","title_canon_sha256":"ab681beae3c326992f91862bc11e1a80c34bd2a5833cc24c6e15d568e332d0da"},"schema_version":"1.0","source":{"id":"1808.01836","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.01836","created_at":"2026-05-18T00:08:49Z"},{"alias_kind":"arxiv_version","alias_value":"1808.01836v1","created_at":"2026-05-18T00:08:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.01836","created_at":"2026-05-18T00:08:49Z"},{"alias_kind":"pith_short_12","alias_value":"YZPKZIGO5JRT","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"YZPKZIGO5JRT2XLK","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"YZPKZIGO","created_at":"2026-05-18T12:33:04Z"}],"graph_snapshots":[{"event_id":"sha256:2d60becec5f82aa417713f3811b09ab727eb8e2727ad61ffe81958cccbb64443","target":"graph","created_at":"2026-05-18T00:08:49Z","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 prove necessary and sufficient conditions for the asymptotic normality of multiple integrals with respect to a Poisson measure on a general measure space, expressed both in terms of norms of contraction kernels and of variances of carr\\'e-du-champ operators. Our results substantially complete the fourth moment theorems recently obtained by D\\\"obler and Peccati (2018) and D\\\"obler, Vidotto and Zheng (2018). An important tool for achieving our goals is a novel product formula for multiple integrals under minimal conditions.","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":"2018-08-06T12:00:04Z","title":"Fourth moment theorems on the Poisson space: analytic statements via product formulae"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.01836","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":"sha256:9c9b29f061a9582e2294167832161e935b3f83265dc292c4c937e46012f12919","target":"record","created_at":"2026-05-18T00:08:49Z","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":"19769feadd57342dd9b52f93c488728018309c7699d237001d453d5299e959d9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-08-06T12:00:04Z","title_canon_sha256":"ab681beae3c326992f91862bc11e1a80c34bd2a5833cc24c6e15d568e332d0da"},"schema_version":"1.0","source":{"id":"1808.01836","kind":"arxiv","version":1}},"canonical_sha256":"c65eaca0ceea633d5d6a714bfc31ce97814449a73dd28ca98d2d61abaf470d84","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c65eaca0ceea633d5d6a714bfc31ce97814449a73dd28ca98d2d61abaf470d84","first_computed_at":"2026-05-18T00:08:49.544439Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:08:49.544439Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cHZj3wz/wdADJs/IpWO4F8dVFkoAN4BJxmty5D4Cxn354NPsTz16ECea9f0WVu4kUI+e4vV5lOO7p35ekseZAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:08:49.545094Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.01836","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9c9b29f061a9582e2294167832161e935b3f83265dc292c4c937e46012f12919","sha256:2d60becec5f82aa417713f3811b09ab727eb8e2727ad61ffe81958cccbb64443"],"state_sha256":"53adea51d378a0f866c8d7334a02e8c070d30aa36e7f53778c9a95352f3dc51f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hMFeYPf4uTqUQaZpt0gcDGM0ERYf7CKqGZRppAUCt7uxxgnVYPHuDjWGzA7ZfAS01znct8TOoEUNBrGjFzxnDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T23:44:39.077389Z","bundle_sha256":"34faf1263038b397fd5aa2e01052ad01e4902b3754cc99add7c14d9317d787cf"}}