{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:IRS6I7WWQA6BUQXKUF7X3FMWRB","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":"4488f79f653db7442c2dac91ecd8ce75c518c780d29439926966dbe139f76401","cross_cats_sorted":[],"license":"","primary_cat":"math.PR","submitted_at":"2001-02-28T23:19:32Z","title_canon_sha256":"b21dc79bdbb8c7ffa65de25ac86ed0124b2405a1b1a9fc83ddfd0138d2145546"},"schema_version":"1.0","source":{"id":"math/0102227","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0102227","created_at":"2026-05-18T03:09:23Z"},{"alias_kind":"arxiv_version","alias_value":"math/0102227v1","created_at":"2026-05-18T03:09:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0102227","created_at":"2026-05-18T03:09:23Z"},{"alias_kind":"pith_short_12","alias_value":"IRS6I7WWQA6B","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"IRS6I7WWQA6BUQXK","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"IRS6I7WW","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:8758569aa90478626024950b438a5bb7dc5ede48630a0c03b5aafb3fd4be91f2","target":"graph","created_at":"2026-05-18T03:09:23Z","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":"The aim of this note is to connect a reversed form of the Gross logarithmic Sobolev inequality with the Gaussian maximum of Shannon's entropy power. There is thus a complete parallel with the well-known link between logarithmic Sobolev inequalities and their information theoretic counterparts. We moreover provide an elementary proof of the reversed Gross inequality via a two-point inequality and the Central Limit Theorem.","authors_text":"Djalil Chafai","cross_cats":[],"headline":"","license":"","primary_cat":"math.PR","submitted_at":"2001-02-28T23:19:32Z","title":"Gaussian maximum of entropy and reversed log-Sobolev inequality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0102227","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":"sha256:50cffccb54f927e193372ee9384c0a22c09b7c8df3af67dcc3f187069e043e3d","target":"record","created_at":"2026-05-18T03:09:23Z","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":"4488f79f653db7442c2dac91ecd8ce75c518c780d29439926966dbe139f76401","cross_cats_sorted":[],"license":"","primary_cat":"math.PR","submitted_at":"2001-02-28T23:19:32Z","title_canon_sha256":"b21dc79bdbb8c7ffa65de25ac86ed0124b2405a1b1a9fc83ddfd0138d2145546"},"schema_version":"1.0","source":{"id":"math/0102227","kind":"arxiv","version":1}},"canonical_sha256":"4465e47ed6803c1a42eaa17f7d959688455fed14dada534a7a5d9e46ed0a6cfb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4465e47ed6803c1a42eaa17f7d959688455fed14dada534a7a5d9e46ed0a6cfb","first_computed_at":"2026-05-18T03:09:23.400171Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:09:23.400171Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"h+htIt2t6hWKy1P+WHD3BYoVUi/slMzk5B7KDpHQO/uHikSy/1cC5sbUtyPQowHy/XKi1j6E3RMgsTIpIm5XBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:09:23.400898Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0102227","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:50cffccb54f927e193372ee9384c0a22c09b7c8df3af67dcc3f187069e043e3d","sha256:8758569aa90478626024950b438a5bb7dc5ede48630a0c03b5aafb3fd4be91f2"],"state_sha256":"bf9b06189cdf90246e9e83f16dddfc9aba11fd4832cb3e6e96629d2a40bce106"}