{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:34IOBQO7VRFR5FDMHMTKYIFPEA","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":"136c9176b6169d83cd6475221efd7c3307f8a63be07970bb0b86eecf7863ed5b","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2021-02-23T03:57:04Z","title_canon_sha256":"bfaec15b629a4e99719d2cbdbb344ccc6cc4da7179b2ed1cc43bb8d294d29993"},"schema_version":"1.0","source":{"id":"2102.11476","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2102.11476","created_at":"2026-07-05T02:20:32Z"},{"alias_kind":"arxiv_version","alias_value":"2102.11476v2","created_at":"2026-07-05T02:20:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.11476","created_at":"2026-07-05T02:20:32Z"},{"alias_kind":"pith_short_12","alias_value":"34IOBQO7VRFR","created_at":"2026-07-05T02:20:32Z"},{"alias_kind":"pith_short_16","alias_value":"34IOBQO7VRFR5FDM","created_at":"2026-07-05T02:20:32Z"},{"alias_kind":"pith_short_8","alias_value":"34IOBQO7","created_at":"2026-07-05T02:20:32Z"}],"graph_snapshots":[{"event_id":"sha256:4d72d12ec212537215008bb03351c5e56ecd693f17415198707f4cc4300d9553","target":"graph","created_at":"2026-07-05T02:20:32Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2102.11476/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that if ${(P_x)}_{x\\in \\mathscr X}$ is a family of probability measures which satisfy the log-Sobolev inequality and whose pairwise chi-squared divergences are uniformly bounded, and $\\mu$ is any mixing distribution on $\\mathscr X$, then the mixture $\\int P_x \\, \\mathrm{d} \\mu(x)$ satisfies a log-Sobolev inequality. In various settings of interest, the resulting log-Sobolev constant is dimension-free. In particular, our result implies a conjecture of Zimmermann and Bardet et al. that Gaussian convolutions of measures with bounded support enjoy dimension-free log-Sobolev inequalities.","authors_text":"Hong-Bin Chen, Jonathan Niles-Weed, Sinho Chewi","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2021-02-23T03:57:04Z","title":"Dimension-free log-Sobolev inequalities for mixture distributions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.11476","kind":"arxiv","version":2},"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:cc61418f6986050bde48934a3455000dd5446d94aeb3572b3de03669169ef9bb","target":"record","created_at":"2026-07-05T02:20:32Z","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":"136c9176b6169d83cd6475221efd7c3307f8a63be07970bb0b86eecf7863ed5b","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2021-02-23T03:57:04Z","title_canon_sha256":"bfaec15b629a4e99719d2cbdbb344ccc6cc4da7179b2ed1cc43bb8d294d29993"},"schema_version":"1.0","source":{"id":"2102.11476","kind":"arxiv","version":2}},"canonical_sha256":"df10e0c1dfac4b1e946c3b26ac20af200fa66326bbb498343bcc62afa27d2113","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"df10e0c1dfac4b1e946c3b26ac20af200fa66326bbb498343bcc62afa27d2113","first_computed_at":"2026-07-05T02:20:32.399174Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:20:32.399174Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j6qkcZx7xwUHFzYYf7tePam+SRh7F9cz6TwO/OYmmSj38JrWyj0j+6EMagJytOZ7I3ffwv5txxJ+TysH8O/pCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T02:20:32.399557Z","signed_message":"canonical_sha256_bytes"},"source_id":"2102.11476","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cc61418f6986050bde48934a3455000dd5446d94aeb3572b3de03669169ef9bb","sha256:4d72d12ec212537215008bb03351c5e56ecd693f17415198707f4cc4300d9553"],"state_sha256":"c6142a8a702225f39a06bdd7351f3d59506a299afb27c0779a224d28de569cc0"}