{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:N6SQYSHAEWX3EKVHWUDVSCIN7C","short_pith_number":"pith:N6SQYSHA","schema_version":"1.0","canonical_sha256":"6fa50c48e025afb22aa7b50759090df8b020b3baa02389821daddc31f166ccdf","source":{"kind":"arxiv","id":"2202.07198","version":2},"attestation_state":"computed","paper":{"title":"A short note on an inequality between KL and TV","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Cl\\'ement L. Canonne","submitted_at":"2022-02-15T05:12:43Z","abstract_excerpt":"The goal of this short note is to discuss the relation between Kullback--Leibler divergence and total variation distance, starting with the celebrated Pinsker's inequality relating the two, before switching to a simple, yet (arguably) more useful inequality, apparently not as well known, due to Bretagnolle and Huber. We also discuss applications of this bound for minimax testing lower bounds."},"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":"2202.07198","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.PR","submitted_at":"2022-02-15T05:12:43Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"0d7ab3b2b2921ec97726f2129b25787f59f4be0f9084933b90d0edb50a1967dd","abstract_canon_sha256":"eb59525ea26d55e8fd85cd8fa79834c1142e42e1e854d72d2e6cbdcc6b4542e8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:36:51.649896Z","signature_b64":"WrptSwWaqS+2oncKEP5PZ7XbcJ2gxs9PDBA4lyAnaZeoes80goatb+FUJoTVbAh1kLgOonjNPwm2HE8FHf7iBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6fa50c48e025afb22aa7b50759090df8b020b3baa02389821daddc31f166ccdf","last_reissued_at":"2026-07-05T06:36:51.649446Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:36:51.649446Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A short note on an inequality between KL and TV","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Cl\\'ement L. Canonne","submitted_at":"2022-02-15T05:12:43Z","abstract_excerpt":"The goal of this short note is to discuss the relation between Kullback--Leibler divergence and total variation distance, starting with the celebrated Pinsker's inequality relating the two, before switching to a simple, yet (arguably) more useful inequality, apparently not as well known, due to Bretagnolle and Huber. We also discuss applications of this bound for minimax testing lower bounds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2202.07198","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/2202.07198/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":"2202.07198","created_at":"2026-07-05T06:36:51.649516+00:00"},{"alias_kind":"arxiv_version","alias_value":"2202.07198v2","created_at":"2026-07-05T06:36:51.649516+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2202.07198","created_at":"2026-07-05T06:36:51.649516+00:00"},{"alias_kind":"pith_short_12","alias_value":"N6SQYSHAEWX3","created_at":"2026-07-05T06:36:51.649516+00:00"},{"alias_kind":"pith_short_16","alias_value":"N6SQYSHAEWX3EKVH","created_at":"2026-07-05T06:36:51.649516+00:00"},{"alias_kind":"pith_short_8","alias_value":"N6SQYSHA","created_at":"2026-07-05T06:36:51.649516+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":7,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.10446","citing_title":"Proportionality from Sampled Approvals","ref_index":127,"is_internal_anchor":false},{"citing_arxiv_id":"2606.27580","citing_title":"Retroactive Advantage Correction: Closed-Form V-Trace Bias Correction for Delay-Aware RLHF","ref_index":2,"is_internal_anchor":false},{"citing_arxiv_id":"2509.23582","citing_title":"RobuQ: Pushing DiTs to W1.58A2 via Robust Activation Quantization","ref_index":6,"is_internal_anchor":false},{"citing_arxiv_id":"2605.18042","citing_title":"On efficient robust regression with subquadratic samples","ref_index":87,"is_internal_anchor":false},{"citing_arxiv_id":"2601.06688","citing_title":"The Sample Complexity of Lossless Data Compression","ref_index":8,"is_internal_anchor":false},{"citing_arxiv_id":"2605.09291","citing_title":"dFlowGRPO: Rate-Aware Policy Optimization for Discrete Flow Models","ref_index":43,"is_internal_anchor":false},{"citing_arxiv_id":"2604.07639","citing_title":"Exponential quantum advantage in processing massive classical data","ref_index":173,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/N6SQYSHAEWX3EKVHWUDVSCIN7C","json":"https://pith.science/pith/N6SQYSHAEWX3EKVHWUDVSCIN7C.json","graph_json":"https://pith.science/api/pith-number/N6SQYSHAEWX3EKVHWUDVSCIN7C/graph.json","events_json":"https://pith.science/api/pith-number/N6SQYSHAEWX3EKVHWUDVSCIN7C/events.json","paper":"https://pith.science/paper/N6SQYSHA"},"agent_actions":{"view_html":"https://pith.science/pith/N6SQYSHAEWX3EKVHWUDVSCIN7C","download_json":"https://pith.science/pith/N6SQYSHAEWX3EKVHWUDVSCIN7C.json","view_paper":"https://pith.science/paper/N6SQYSHA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2202.07198&json=true","fetch_graph":"https://pith.science/api/pith-number/N6SQYSHAEWX3EKVHWUDVSCIN7C/graph.json","fetch_events":"https://pith.science/api/pith-number/N6SQYSHAEWX3EKVHWUDVSCIN7C/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/N6SQYSHAEWX3EKVHWUDVSCIN7C/action/timestamp_anchor","attest_storage":"https://pith.science/pith/N6SQYSHAEWX3EKVHWUDVSCIN7C/action/storage_attestation","attest_author":"https://pith.science/pith/N6SQYSHAEWX3EKVHWUDVSCIN7C/action/author_attestation","sign_citation":"https://pith.science/pith/N6SQYSHAEWX3EKVHWUDVSCIN7C/action/citation_signature","submit_replication":"https://pith.science/pith/N6SQYSHAEWX3EKVHWUDVSCIN7C/action/replication_record"}},"created_at":"2026-07-05T06:36:51.649516+00:00","updated_at":"2026-07-05T06:36:51.649516+00:00"}