{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:WZRA7FPRV7CYFP575GJ7HCNJSX","short_pith_number":"pith:WZRA7FPR","schema_version":"1.0","canonical_sha256":"b6620f95f1afc582bfbfe993f389a995f0433de4291eb8f256326741ed8e3c8c","source":{"kind":"arxiv","id":"1703.07707","version":2},"attestation_state":"computed","paper":{"title":"Existence of Stein Kernels under a Spectral Gap, and Discrepancy Bound","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.FA","math.IT"],"primary_cat":"math.PR","authors_text":"Ashwin Pananjady, Max Fathi, Thomas A. Courtade","submitted_at":"2017-03-22T15:33:33Z","abstract_excerpt":"We establish existence of Stein kernels for probability measures on $\\mathbb{R}^d$ satisfying a Poincar\\'e inequality, and obtain bounds on the Stein discrepancy of such measures. Applications to quantitative central limit theorems are discussed, including a new CLT in Wasserstein distance $W_2$ with optimal rate and dependence on the dimension. As a byproduct, we obtain a stability version of an estimate of the Poincar\\'e constant of probability measures under a second moment constraint. The results extend more generally to the setting of converse weighted Poincar\\'e inequalities. The proof i"},"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":"1703.07707","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-03-22T15:33:33Z","cross_cats_sorted":["cs.IT","math.FA","math.IT"],"title_canon_sha256":"01f13eb3dc3fb4a40e999de5360aad5920026d5b865a6696e94ceb3d8aa6563b","abstract_canon_sha256":"1078fec1be2a4274898b0bf6e71ceb9c3ca8538e711edc945da4feef3dd88fce"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:21:46.488357Z","signature_b64":"CoYy86zI6oUmGO1dX3aVwzqXSMHN6F1HovDNxEg618LXKj5kHaiQYqLxAfpeXTpX2qWnAgEw+vQGr376zRoeCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b6620f95f1afc582bfbfe993f389a995f0433de4291eb8f256326741ed8e3c8c","last_reissued_at":"2026-05-18T00:21:46.487690Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:21:46.487690Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Existence of Stein Kernels under a Spectral Gap, and Discrepancy Bound","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.FA","math.IT"],"primary_cat":"math.PR","authors_text":"Ashwin Pananjady, Max Fathi, Thomas A. Courtade","submitted_at":"2017-03-22T15:33:33Z","abstract_excerpt":"We establish existence of Stein kernels for probability measures on $\\mathbb{R}^d$ satisfying a Poincar\\'e inequality, and obtain bounds on the Stein discrepancy of such measures. Applications to quantitative central limit theorems are discussed, including a new CLT in Wasserstein distance $W_2$ with optimal rate and dependence on the dimension. As a byproduct, we obtain a stability version of an estimate of the Poincar\\'e constant of probability measures under a second moment constraint. The results extend more generally to the setting of converse weighted Poincar\\'e inequalities. The proof i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.07707","kind":"arxiv","version":2},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1703.07707","created_at":"2026-05-18T00:21:46.487797+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.07707v2","created_at":"2026-05-18T00:21:46.487797+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.07707","created_at":"2026-05-18T00:21:46.487797+00:00"},{"alias_kind":"pith_short_12","alias_value":"WZRA7FPRV7CY","created_at":"2026-05-18T12:31:53.515858+00:00"},{"alias_kind":"pith_short_16","alias_value":"WZRA7FPRV7CYFP57","created_at":"2026-05-18T12:31:53.515858+00:00"},{"alias_kind":"pith_short_8","alias_value":"WZRA7FPR","created_at":"2026-05-18T12:31:53.515858+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1906.08372","citing_title":"First order covariance inequalities via Stein's method","ref_index":28,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WZRA7FPRV7CYFP575GJ7HCNJSX","json":"https://pith.science/pith/WZRA7FPRV7CYFP575GJ7HCNJSX.json","graph_json":"https://pith.science/api/pith-number/WZRA7FPRV7CYFP575GJ7HCNJSX/graph.json","events_json":"https://pith.science/api/pith-number/WZRA7FPRV7CYFP575GJ7HCNJSX/events.json","paper":"https://pith.science/paper/WZRA7FPR"},"agent_actions":{"view_html":"https://pith.science/pith/WZRA7FPRV7CYFP575GJ7HCNJSX","download_json":"https://pith.science/pith/WZRA7FPRV7CYFP575GJ7HCNJSX.json","view_paper":"https://pith.science/paper/WZRA7FPR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.07707&json=true","fetch_graph":"https://pith.science/api/pith-number/WZRA7FPRV7CYFP575GJ7HCNJSX/graph.json","fetch_events":"https://pith.science/api/pith-number/WZRA7FPRV7CYFP575GJ7HCNJSX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WZRA7FPRV7CYFP575GJ7HCNJSX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WZRA7FPRV7CYFP575GJ7HCNJSX/action/storage_attestation","attest_author":"https://pith.science/pith/WZRA7FPRV7CYFP575GJ7HCNJSX/action/author_attestation","sign_citation":"https://pith.science/pith/WZRA7FPRV7CYFP575GJ7HCNJSX/action/citation_signature","submit_replication":"https://pith.science/pith/WZRA7FPRV7CYFP575GJ7HCNJSX/action/replication_record"}},"created_at":"2026-05-18T00:21:46.487797+00:00","updated_at":"2026-05-18T00:21:46.487797+00:00"}