{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:JALTZI7JUMDAKHRCDADXTZFTDH","short_pith_number":"pith:JALTZI7J","schema_version":"1.0","canonical_sha256":"48173ca3e9a306051e22180779e4b319ddcb62faa4e2b02224f9c7d44f3f0f58","source":{"kind":"arxiv","id":"1610.07969","version":1},"attestation_state":"computed","paper":{"title":"Wasserstein Stability of the Entropy Power Inequality for Log-Concave Densities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.IT","math.PR"],"primary_cat":"cs.IT","authors_text":"Ashwin Pananjady, Max Fathi, Thomas A. Courtade","submitted_at":"2016-10-25T17:15:48Z","abstract_excerpt":"We establish quantitative stability results for the entropy power inequality (EPI). Specifically, we show that if uniformly log-concave densities nearly saturate the EPI, then they must be close to Gaussian densities in the quadratic Wasserstein distance. Further, if one of the densities is log-concave and the other is Gaussian, then the deficit in the EPI can be controlled in terms of the $L^1$-Wasserstein distance. As a counterpoint, an example shows that the EPI can be unstable with respect to the quadratic Wasserstein distance when densities are uniformly log-concave on sets of measure arb"},"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":"1610.07969","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-10-25T17:15:48Z","cross_cats_sorted":["math.FA","math.IT","math.PR"],"title_canon_sha256":"10b86eaa96085d5844a1bbeffc74b24291213bfdd80109408fb62a346da2babc","abstract_canon_sha256":"b365626de73809e4b0dcacc190d808c1eafe630dfbdd7c50f3f38c5b597c1dae"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:01:17.074224Z","signature_b64":"jzH/h4F4j/eK4/vNPcir02guRC5Xa3uecLuQHWGvz+5ec7gSFIFT/3ChE9oJtHFsgZ3Z/7Ra640TDmKwox8hCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"48173ca3e9a306051e22180779e4b319ddcb62faa4e2b02224f9c7d44f3f0f58","last_reissued_at":"2026-05-18T01:01:17.073575Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:01:17.073575Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Wasserstein Stability of the Entropy Power Inequality for Log-Concave Densities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.IT","math.PR"],"primary_cat":"cs.IT","authors_text":"Ashwin Pananjady, Max Fathi, Thomas A. Courtade","submitted_at":"2016-10-25T17:15:48Z","abstract_excerpt":"We establish quantitative stability results for the entropy power inequality (EPI). Specifically, we show that if uniformly log-concave densities nearly saturate the EPI, then they must be close to Gaussian densities in the quadratic Wasserstein distance. Further, if one of the densities is log-concave and the other is Gaussian, then the deficit in the EPI can be controlled in terms of the $L^1$-Wasserstein distance. As a counterpoint, an example shows that the EPI can be unstable with respect to the quadratic Wasserstein distance when densities are uniformly log-concave on sets of measure arb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.07969","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1610.07969","created_at":"2026-05-18T01:01:17.073669+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.07969v1","created_at":"2026-05-18T01:01:17.073669+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.07969","created_at":"2026-05-18T01:01:17.073669+00:00"},{"alias_kind":"pith_short_12","alias_value":"JALTZI7JUMDA","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_16","alias_value":"JALTZI7JUMDAKHRC","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_8","alias_value":"JALTZI7J","created_at":"2026-05-18T12:30:22.444734+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/JALTZI7JUMDAKHRCDADXTZFTDH","json":"https://pith.science/pith/JALTZI7JUMDAKHRCDADXTZFTDH.json","graph_json":"https://pith.science/api/pith-number/JALTZI7JUMDAKHRCDADXTZFTDH/graph.json","events_json":"https://pith.science/api/pith-number/JALTZI7JUMDAKHRCDADXTZFTDH/events.json","paper":"https://pith.science/paper/JALTZI7J"},"agent_actions":{"view_html":"https://pith.science/pith/JALTZI7JUMDAKHRCDADXTZFTDH","download_json":"https://pith.science/pith/JALTZI7JUMDAKHRCDADXTZFTDH.json","view_paper":"https://pith.science/paper/JALTZI7J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.07969&json=true","fetch_graph":"https://pith.science/api/pith-number/JALTZI7JUMDAKHRCDADXTZFTDH/graph.json","fetch_events":"https://pith.science/api/pith-number/JALTZI7JUMDAKHRCDADXTZFTDH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JALTZI7JUMDAKHRCDADXTZFTDH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JALTZI7JUMDAKHRCDADXTZFTDH/action/storage_attestation","attest_author":"https://pith.science/pith/JALTZI7JUMDAKHRCDADXTZFTDH/action/author_attestation","sign_citation":"https://pith.science/pith/JALTZI7JUMDAKHRCDADXTZFTDH/action/citation_signature","submit_replication":"https://pith.science/pith/JALTZI7JUMDAKHRCDADXTZFTDH/action/replication_record"}},"created_at":"2026-05-18T01:01:17.073669+00:00","updated_at":"2026-05-18T01:01:17.073669+00:00"}