{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:XHYW3GUUC5ZYNXVIFMLA2NLC2M","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":"8df8c8a0c205f9ee56745aa1c1a7bfe01504a526044de031347e1b38fe96f030","cross_cats_sorted":["math.CO","math.FA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-07-18T12:33:58Z","title_canon_sha256":"b94fa86dd73efc1c174ddd327c827ff96a748515f03194b53d14f219f60c5195"},"schema_version":"1.0","source":{"id":"2407.13457","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.13457","created_at":"2026-07-05T08:48:45Z"},{"alias_kind":"arxiv_version","alias_value":"2407.13457v2","created_at":"2026-07-05T08:48:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.13457","created_at":"2026-07-05T08:48:45Z"},{"alias_kind":"pith_short_12","alias_value":"XHYW3GUUC5ZY","created_at":"2026-07-05T08:48:45Z"},{"alias_kind":"pith_short_16","alias_value":"XHYW3GUUC5ZYNXVI","created_at":"2026-07-05T08:48:45Z"},{"alias_kind":"pith_short_8","alias_value":"XHYW3GUU","created_at":"2026-07-05T08:48:45Z"}],"graph_snapshots":[{"event_id":"sha256:6e021f6da1a51696ef17ccc7747bec25e30dbcc33ec645201d891b3a46219ea1","target":"graph","created_at":"2026-07-05T08:48:45Z","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/2407.13457/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We develop a new framework for establishing approximate factorization of entropy on arbitrary probability spaces, using a geometric notion known as non-negative sectional curvature. The resulting estimates are equivalent to entropy subadditivity and generalized Brascamp-Lieb inequalities, and provide a sharp modified log-Sobolev inequality for the Gibbs sampler of several particle systems in both continuous and discrete settings. The method allows us to obtain simple proofs of known results, as well as some new inequalities. We illustrate this through various applications, including discrete G","authors_text":"Justin Salez, Pietro Caputo","cross_cats":["math.CO","math.FA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-07-18T12:33:58Z","title":"Entropy factorization via curvature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.13457","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:aa7ebc9eb9fd859c06daf062c5a8f1c70bf8de42a48b4dfe73a7042d1dfb94e4","target":"record","created_at":"2026-07-05T08:48:45Z","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":"8df8c8a0c205f9ee56745aa1c1a7bfe01504a526044de031347e1b38fe96f030","cross_cats_sorted":["math.CO","math.FA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-07-18T12:33:58Z","title_canon_sha256":"b94fa86dd73efc1c174ddd327c827ff96a748515f03194b53d14f219f60c5195"},"schema_version":"1.0","source":{"id":"2407.13457","kind":"arxiv","version":2}},"canonical_sha256":"b9f16d9a94177386dea82b160d3562d30cbd3181ecdc2162299b947ac35e4b59","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b9f16d9a94177386dea82b160d3562d30cbd3181ecdc2162299b947ac35e4b59","first_computed_at":"2026-07-05T08:48:45.757783Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:48:45.757783Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FbBdvf1tW5ZBi9B0KxtmYXqJiorNHCwFlhqsIB67o/EUXhklw5MYeVOt470C9a1Rj3UkDFnTlcpg5tDbzJAcBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T08:48:45.758308Z","signed_message":"canonical_sha256_bytes"},"source_id":"2407.13457","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aa7ebc9eb9fd859c06daf062c5a8f1c70bf8de42a48b4dfe73a7042d1dfb94e4","sha256:6e021f6da1a51696ef17ccc7747bec25e30dbcc33ec645201d891b3a46219ea1"],"state_sha256":"8ae8f8d755bf751e230bb5cf9062eb0cc1f2180ee7515a2bf084a1044330cf96"}