{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:2TOGXNPG5B456M7MD5TY5UH6AE","short_pith_number":"pith:2TOGXNPG","schema_version":"1.0","canonical_sha256":"d4dc6bb5e6e879df33ec1f678ed0fe0123894b5c859169f7b8e8e8957bddde3c","source":{"kind":"arxiv","id":"2401.00071","version":1},"attestation_state":"computed","paper":{"title":"Shifted Composition II: Shift Harnack Inequalities and Curvature Upper Bounds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.AP","math.FA","math.IT"],"primary_cat":"math.PR","authors_text":"Jason M. Altschuler, Sinho Chewi","submitted_at":"2023-12-29T20:34:43Z","abstract_excerpt":"We apply the shifted composition rule -- an information-theoretic principle introduced in our earlier work [AC23] -- to establish shift Harnack inequalities for the Langevin diffusion. We obtain sharp constants for these inequalities for the first time, allowing us to investigate their relationship with other properties of the diffusion. Namely, we show that they are equivalent to a sharp \"local gradient-entropy\" bound, and that they imply curvature upper bounds in a compelling reflection of the Bakry-Emery theory of curvature lower bounds. Finally, we show that the local gradient-entropy ineq"},"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":"2401.00071","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2023-12-29T20:34:43Z","cross_cats_sorted":["cs.IT","math.AP","math.FA","math.IT"],"title_canon_sha256":"af3465b204ac452eff416d7f48647ef69c52768b34756a19f2a921a42c6b33cf","abstract_canon_sha256":"4e3efc004784affa9f74eb3f2d8a33fa5134da3d8c91980e86fe41591a28cae5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:29:00.476238Z","signature_b64":"MYFl4SrqrHnWILkH30par1U+uYXvd/Tr3CQnTOLyRRb58GMHsSX946WJ39aNu+bSYklO/MgBVj82UP0sqtfOAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d4dc6bb5e6e879df33ec1f678ed0fe0123894b5c859169f7b8e8e8957bddde3c","last_reissued_at":"2026-07-05T07:29:00.475824Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:29:00.475824Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Shifted Composition II: Shift Harnack Inequalities and Curvature Upper Bounds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.AP","math.FA","math.IT"],"primary_cat":"math.PR","authors_text":"Jason M. Altschuler, Sinho Chewi","submitted_at":"2023-12-29T20:34:43Z","abstract_excerpt":"We apply the shifted composition rule -- an information-theoretic principle introduced in our earlier work [AC23] -- to establish shift Harnack inequalities for the Langevin diffusion. We obtain sharp constants for these inequalities for the first time, allowing us to investigate their relationship with other properties of the diffusion. Namely, we show that they are equivalent to a sharp \"local gradient-entropy\" bound, and that they imply curvature upper bounds in a compelling reflection of the Bakry-Emery theory of curvature lower bounds. Finally, we show that the local gradient-entropy ineq"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.00071","kind":"arxiv","version":1},"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/2401.00071/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":"2401.00071","created_at":"2026-07-05T07:29:00.475882+00:00"},{"alias_kind":"arxiv_version","alias_value":"2401.00071v1","created_at":"2026-07-05T07:29:00.475882+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.00071","created_at":"2026-07-05T07:29:00.475882+00:00"},{"alias_kind":"pith_short_12","alias_value":"2TOGXNPG5B45","created_at":"2026-07-05T07:29:00.475882+00:00"},{"alias_kind":"pith_short_16","alias_value":"2TOGXNPG5B456M7M","created_at":"2026-07-05T07:29:00.475882+00:00"},{"alias_kind":"pith_short_8","alias_value":"2TOGXNPG","created_at":"2026-07-05T07:29:00.475882+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2TOGXNPG5B456M7MD5TY5UH6AE","json":"https://pith.science/pith/2TOGXNPG5B456M7MD5TY5UH6AE.json","graph_json":"https://pith.science/api/pith-number/2TOGXNPG5B456M7MD5TY5UH6AE/graph.json","events_json":"https://pith.science/api/pith-number/2TOGXNPG5B456M7MD5TY5UH6AE/events.json","paper":"https://pith.science/paper/2TOGXNPG"},"agent_actions":{"view_html":"https://pith.science/pith/2TOGXNPG5B456M7MD5TY5UH6AE","download_json":"https://pith.science/pith/2TOGXNPG5B456M7MD5TY5UH6AE.json","view_paper":"https://pith.science/paper/2TOGXNPG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2401.00071&json=true","fetch_graph":"https://pith.science/api/pith-number/2TOGXNPG5B456M7MD5TY5UH6AE/graph.json","fetch_events":"https://pith.science/api/pith-number/2TOGXNPG5B456M7MD5TY5UH6AE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2TOGXNPG5B456M7MD5TY5UH6AE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2TOGXNPG5B456M7MD5TY5UH6AE/action/storage_attestation","attest_author":"https://pith.science/pith/2TOGXNPG5B456M7MD5TY5UH6AE/action/author_attestation","sign_citation":"https://pith.science/pith/2TOGXNPG5B456M7MD5TY5UH6AE/action/citation_signature","submit_replication":"https://pith.science/pith/2TOGXNPG5B456M7MD5TY5UH6AE/action/replication_record"}},"created_at":"2026-07-05T07:29:00.475882+00:00","updated_at":"2026-07-05T07:29:00.475882+00:00"}