{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:JT6E2UV6PR43P2ROFMMPCXFA5Q","short_pith_number":"pith:JT6E2UV6","schema_version":"1.0","canonical_sha256":"4cfc4d52be7c79b7ea2e2b18f15ca0ec1a66cad762e22c6557c895e86cdaeef6","source":{"kind":"arxiv","id":"2605.23292","version":1},"attestation_state":"computed","paper":{"title":"Second-order Poincar\\'e inequalities and localization on the Poisson space","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"J. E. Yukich, Tara Trauthwein","submitted_at":"2026-05-22T07:05:41Z","abstract_excerpt":"Given a mean zero functional $F$ of a Poisson measure on a metric space, we apply the Malliavin-Stein method to establish sharpened second-order Poincar\\'e inequalities for $F/\\sqrt{\\operatorname{Var} (F)}$ in terms of fourth moments of difference operators. The rates of normal approximation are expressed in the Kolmogorov and Wasserstein distances and require fewer error terms than corresponding previous results. When $F$ is expressible as a sum of score functions which are distributionally close to scores having short-range structure, then we deduce that $F/\\sqrt{\\operatorname{Var}(F)}$ sati"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2605.23292","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-05-22T07:05:41Z","cross_cats_sorted":[],"title_canon_sha256":"4ae766f1ee7d6890eb4756a5ab55af22bfa9eb66684aaa73d653c5b3465cedab","abstract_canon_sha256":"0fb32eba8f401e74ac0520e8e54dcb4a5c4891bde189316c2b1bcee9b9c3da1e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-25T02:01:47.519955Z","signature_b64":"LQXIJuRb2Qc7ihsrmkHC+KKIYWcYBRdD8i890rL9mx4S5peLtq2K+wM9B+9BXqLr5GggwrGGY95cXikvCgSDDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4cfc4d52be7c79b7ea2e2b18f15ca0ec1a66cad762e22c6557c895e86cdaeef6","last_reissued_at":"2026-05-25T02:01:47.519216Z","signature_status":"signed_v1","first_computed_at":"2026-05-25T02:01:47.519216Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Second-order Poincar\\'e inequalities and localization on the Poisson space","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"J. E. Yukich, Tara Trauthwein","submitted_at":"2026-05-22T07:05:41Z","abstract_excerpt":"Given a mean zero functional $F$ of a Poisson measure on a metric space, we apply the Malliavin-Stein method to establish sharpened second-order Poincar\\'e inequalities for $F/\\sqrt{\\operatorname{Var} (F)}$ in terms of fourth moments of difference operators. The rates of normal approximation are expressed in the Kolmogorov and Wasserstein distances and require fewer error terms than corresponding previous results. When $F$ is expressible as a sum of score functions which are distributionally close to scores having short-range structure, then we deduce that $F/\\sqrt{\\operatorname{Var}(F)}$ sati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.23292","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.23292/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2605.23292","created_at":"2026-05-25T02:01:47.519343+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.23292v1","created_at":"2026-05-25T02:01:47.519343+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.23292","created_at":"2026-05-25T02:01:47.519343+00:00"},{"alias_kind":"pith_short_12","alias_value":"JT6E2UV6PR43","created_at":"2026-05-25T02:01:47.519343+00:00"},{"alias_kind":"pith_short_16","alias_value":"JT6E2UV6PR43P2RO","created_at":"2026-05-25T02:01:47.519343+00:00"},{"alias_kind":"pith_short_8","alias_value":"JT6E2UV6","created_at":"2026-05-25T02:01:47.519343+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/JT6E2UV6PR43P2ROFMMPCXFA5Q","json":"https://pith.science/pith/JT6E2UV6PR43P2ROFMMPCXFA5Q.json","graph_json":"https://pith.science/api/pith-number/JT6E2UV6PR43P2ROFMMPCXFA5Q/graph.json","events_json":"https://pith.science/api/pith-number/JT6E2UV6PR43P2ROFMMPCXFA5Q/events.json","paper":"https://pith.science/paper/JT6E2UV6"},"agent_actions":{"view_html":"https://pith.science/pith/JT6E2UV6PR43P2ROFMMPCXFA5Q","download_json":"https://pith.science/pith/JT6E2UV6PR43P2ROFMMPCXFA5Q.json","view_paper":"https://pith.science/paper/JT6E2UV6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.23292&json=true","fetch_graph":"https://pith.science/api/pith-number/JT6E2UV6PR43P2ROFMMPCXFA5Q/graph.json","fetch_events":"https://pith.science/api/pith-number/JT6E2UV6PR43P2ROFMMPCXFA5Q/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JT6E2UV6PR43P2ROFMMPCXFA5Q/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JT6E2UV6PR43P2ROFMMPCXFA5Q/action/storage_attestation","attest_author":"https://pith.science/pith/JT6E2UV6PR43P2ROFMMPCXFA5Q/action/author_attestation","sign_citation":"https://pith.science/pith/JT6E2UV6PR43P2ROFMMPCXFA5Q/action/citation_signature","submit_replication":"https://pith.science/pith/JT6E2UV6PR43P2ROFMMPCXFA5Q/action/replication_record"}},"created_at":"2026-05-25T02:01:47.519343+00:00","updated_at":"2026-05-25T02:01:47.519343+00:00"}