{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:JJEYV3GE7IU7JCA3YOVTJF2RO7","short_pith_number":"pith:JJEYV3GE","schema_version":"1.0","canonical_sha256":"4a498aecc4fa29f4881bc3ab34975177fc82cdf368ec4c14e7b1e7ff2e6182a6","source":{"kind":"arxiv","id":"2106.04105","version":2},"attestation_state":"computed","paper":{"title":"Entropic Independence I: Modified Log-Sobolev Inequalities for Fractionally Log-Concave Distributions and High-Temperature Ising Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math-ph","math.MP","math.PR"],"primary_cat":"cs.DS","authors_text":"Frederic Koehler, Huy Tuan Pham, Nima Anari, Thuy-Duong Vuong, Vishesh Jain","submitted_at":"2021-06-08T05:07:24Z","abstract_excerpt":"We introduce a notion called entropic independence that is an entropic analog of spectral notions of high-dimensional expansion. Informally, entropic independence of a background distribution $\\mu$ on $k$-sized subsets of a ground set of elements says that for any (possibly randomly chosen) set $S$, the relative entropy of a single element of $S$ drawn uniformly at random carries at most $O(1/k)$ fraction of the relative entropy of $S$. Entropic independence is the analog of the notion of spectral independence, if one replaces variance by entropy. We use entropic independence to derive tight m"},"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":"2106.04105","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2021-06-08T05:07:24Z","cross_cats_sorted":["cs.DM","math-ph","math.MP","math.PR"],"title_canon_sha256":"525ddf7e0acae544b324ec8ec13c28f02d992f909df82144859d21ff41c9c3dd","abstract_canon_sha256":"27f05c1e1228fc06295a06dfec4870ce567aa702f8be970000fd335d4175bba3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:29:16.800658Z","signature_b64":"QOhwiYdBYgrx/YjV8u+z7lZbkU/rB7+Kj7q8uGcQGSSXF3g1jOE/F7NHQXEQ5q1RSBSKvnFMPTDh8buQEpseAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4a498aecc4fa29f4881bc3ab34975177fc82cdf368ec4c14e7b1e7ff2e6182a6","last_reissued_at":"2026-07-05T03:29:16.799406Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:29:16.799406Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Entropic Independence I: Modified Log-Sobolev Inequalities for Fractionally Log-Concave Distributions and High-Temperature Ising Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math-ph","math.MP","math.PR"],"primary_cat":"cs.DS","authors_text":"Frederic Koehler, Huy Tuan Pham, Nima Anari, Thuy-Duong Vuong, Vishesh Jain","submitted_at":"2021-06-08T05:07:24Z","abstract_excerpt":"We introduce a notion called entropic independence that is an entropic analog of spectral notions of high-dimensional expansion. Informally, entropic independence of a background distribution $\\mu$ on $k$-sized subsets of a ground set of elements says that for any (possibly randomly chosen) set $S$, the relative entropy of a single element of $S$ drawn uniformly at random carries at most $O(1/k)$ fraction of the relative entropy of $S$. Entropic independence is the analog of the notion of spectral independence, if one replaces variance by entropy. We use entropic independence to derive tight m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.04105","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2106.04105/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":"2106.04105","created_at":"2026-07-05T03:29:16.800165+00:00"},{"alias_kind":"arxiv_version","alias_value":"2106.04105v2","created_at":"2026-07-05T03:29:16.800165+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.04105","created_at":"2026-07-05T03:29:16.800165+00:00"},{"alias_kind":"pith_short_12","alias_value":"JJEYV3GE7IU7","created_at":"2026-07-05T03:29:16.800165+00:00"},{"alias_kind":"pith_short_16","alias_value":"JJEYV3GE7IU7JCA3","created_at":"2026-07-05T03:29:16.800165+00:00"},{"alias_kind":"pith_short_8","alias_value":"JJEYV3GE","created_at":"2026-07-05T03:29:16.800165+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":5,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.24845","citing_title":"A Near-Optimal Parallel Algorithm for Finding Matroid Bases","ref_index":137,"is_internal_anchor":false},{"citing_arxiv_id":"2605.14681","citing_title":"Lower bound on the mixing time of $p$-spin glasses","ref_index":2,"is_internal_anchor":false},{"citing_arxiv_id":"2604.10525","citing_title":"Edge-Tilting Field Dynamics: Rapid Mixing at the Uniqueness Threshold and Optimal Mixing for Swendsen-Wang Dynamics","ref_index":1,"is_internal_anchor":false},{"citing_arxiv_id":"2604.10902","citing_title":"Entropic independence via sparse localization","ref_index":1,"is_internal_anchor":false},{"citing_arxiv_id":"2605.02002","citing_title":"Glauber dynamics for random field Ising models on bounded degree graphs and MLSI","ref_index":2,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/JJEYV3GE7IU7JCA3YOVTJF2RO7","json":"https://pith.science/pith/JJEYV3GE7IU7JCA3YOVTJF2RO7.json","graph_json":"https://pith.science/api/pith-number/JJEYV3GE7IU7JCA3YOVTJF2RO7/graph.json","events_json":"https://pith.science/api/pith-number/JJEYV3GE7IU7JCA3YOVTJF2RO7/events.json","paper":"https://pith.science/paper/JJEYV3GE"},"agent_actions":{"view_html":"https://pith.science/pith/JJEYV3GE7IU7JCA3YOVTJF2RO7","download_json":"https://pith.science/pith/JJEYV3GE7IU7JCA3YOVTJF2RO7.json","view_paper":"https://pith.science/paper/JJEYV3GE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2106.04105&json=true","fetch_graph":"https://pith.science/api/pith-number/JJEYV3GE7IU7JCA3YOVTJF2RO7/graph.json","fetch_events":"https://pith.science/api/pith-number/JJEYV3GE7IU7JCA3YOVTJF2RO7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JJEYV3GE7IU7JCA3YOVTJF2RO7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JJEYV3GE7IU7JCA3YOVTJF2RO7/action/storage_attestation","attest_author":"https://pith.science/pith/JJEYV3GE7IU7JCA3YOVTJF2RO7/action/author_attestation","sign_citation":"https://pith.science/pith/JJEYV3GE7IU7JCA3YOVTJF2RO7/action/citation_signature","submit_replication":"https://pith.science/pith/JJEYV3GE7IU7JCA3YOVTJF2RO7/action/replication_record"}},"created_at":"2026-07-05T03:29:16.800165+00:00","updated_at":"2026-07-05T03:29:16.800165+00:00"}