{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:N7VTGCRWD7UBLRESG7W6SZ7HU4","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":"9e4c2fb7352d8a7f8ee84abaf6d18b43781cfe41e67254a999821ba9a09c1c0a","cross_cats_sorted":["math.FA","math.IT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2024-06-05T16:25:45Z","title_canon_sha256":"610f3b3cb8df7c1820619107f391a8b2c95b7b5b3a1b4947c2d2d509cea275f9"},"schema_version":"1.0","source":{"id":"2406.03427","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.03427","created_at":"2026-07-05T08:27:56Z"},{"alias_kind":"arxiv_version","alias_value":"2406.03427v1","created_at":"2026-07-05T08:27:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.03427","created_at":"2026-07-05T08:27:56Z"},{"alias_kind":"pith_short_12","alias_value":"N7VTGCRWD7UB","created_at":"2026-07-05T08:27:56Z"},{"alias_kind":"pith_short_16","alias_value":"N7VTGCRWD7UBLRES","created_at":"2026-07-05T08:27:56Z"},{"alias_kind":"pith_short_8","alias_value":"N7VTGCRW","created_at":"2026-07-05T08:27:56Z"}],"graph_snapshots":[{"event_id":"sha256:f57d62a9713fd133c6ceafb0a65636eeefa38ef17730be2fcf436eb53b3088af","target":"graph","created_at":"2026-07-05T08:27:56Z","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/2406.03427/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $\\nu$ and $\\mu$ be probability distributions on $\\mathbb{R}^n$, and $\\nu_s,\\mu_s$ be their evolution under the heat flow, that is, the probability distributions resulting from convolving their density with the density of an isotropic Gaussian random vector with variance $s$ in each entry. This paper studies the rate of decay of $s\\mapsto D(\\nu_s\\|\\mu_s)$ for various divergences, including the $\\chi^2$ and Kullback-Leibler (KL) divergences. We prove upper and lower bounds on the strong data-processing inequality (SDPI) coefficients corresponding to the source $\\mu$ and the Gaussian channel.","authors_text":"Bo'az Klartag, Or Ordentlich","cross_cats":["math.FA","math.IT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2024-06-05T16:25:45Z","title":"The strong data processing inequality under the heat flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.03427","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:ab716cf632cdab3d78e3f988162cd6b0736013c5600bf7a747bc536596070126","target":"record","created_at":"2026-07-05T08:27:56Z","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":"9e4c2fb7352d8a7f8ee84abaf6d18b43781cfe41e67254a999821ba9a09c1c0a","cross_cats_sorted":["math.FA","math.IT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2024-06-05T16:25:45Z","title_canon_sha256":"610f3b3cb8df7c1820619107f391a8b2c95b7b5b3a1b4947c2d2d509cea275f9"},"schema_version":"1.0","source":{"id":"2406.03427","kind":"arxiv","version":1}},"canonical_sha256":"6feb330a361fe815c49237ede967e7a719cc858b7d2fc79a97bf5a2c27581d1b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6feb330a361fe815c49237ede967e7a719cc858b7d2fc79a97bf5a2c27581d1b","first_computed_at":"2026-07-05T08:27:56.544825Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:27:56.544825Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4vvDJ79+nqu7aWu6C7jA1lPZZTMT98o9/5MbrTV5kdrcd4Fr24gdAUMP4O0rJ82KwM8mDdwbIGagRlDUiThuBw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:27:56.545258Z","signed_message":"canonical_sha256_bytes"},"source_id":"2406.03427","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ab716cf632cdab3d78e3f988162cd6b0736013c5600bf7a747bc536596070126","sha256:f57d62a9713fd133c6ceafb0a65636eeefa38ef17730be2fcf436eb53b3088af"],"state_sha256":"c357b0c1c4ed1ffdc93cc297213b71d03babe1e67e448e1ec1350933a32aca8d"}