{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:AWOPYLJZ3HAXN6ZXTVHVG4CPMS","short_pith_number":"pith:AWOPYLJZ","schema_version":"1.0","canonical_sha256":"059cfc2d39d9c176fb379d4f53704f6499f88d0c8fd0189adc1059e6696b0e4a","source":{"kind":"arxiv","id":"cs/0603097","version":2},"attestation_state":"computed","paper":{"title":"On Pinsker's Type Inequalities and Csiszar's f-divergences. Part I: Second and Fourth-Order Inequalities","license":"","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Gustavo L. Gilardoni","submitted_at":"2006-03-24T11:47:59Z","abstract_excerpt":"We study conditions on $f$ under which an $f$-divergence $D_f$ will satisfy $D_f \\geq c_f V^2$ or $D_f \\geq c_{2,f} V^2 + c_{4,f} V^4$, where $V$ denotes variational distance and the coefficients $c_f$, $c_{2,f}$ and $c_{4,f}$ are {\\em best possible}. As a consequence, we obtain lower bounds in terms of $V$ for many well known distance and divergence measures. For instance, let $D_{(\\alpha)} (P,Q) = [\\alpha (\\alpha-1)]^{-1} [\\int q^{\\alpha} p^{1-\\alpha} d \\mu -1]$ and ${\\cal I}_\\alpha (P,Q) = (\\alpha -1)^{-1} \\log [\\int p^\\alpha q^{1-\\alpha} d \\mu]$ be respectively the {\\em relative informatio"},"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":"cs/0603097","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"cs.IT","submitted_at":"2006-03-24T11:47:59Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"26f1d2ebfb6c475e055eab267a82f1f1709f3b73672443da73b6f2d7622ea0f6","abstract_canon_sha256":"f01c6602786e86984800dc169365254e712af0ac2ce91fdc4251f6e01f1c4c46"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:36:49.598976Z","signature_b64":"Tn+hdSfGTq31+OKp2qD5mC6+H/Ux/hoipwD/Umyj11VCC2v4MXpvLXAS12kJ3XmBEdVpoWSUWvGTSYvpi7HVCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"059cfc2d39d9c176fb379d4f53704f6499f88d0c8fd0189adc1059e6696b0e4a","last_reissued_at":"2026-05-18T04:36:49.598489Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:36:49.598489Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Pinsker's Type Inequalities and Csiszar's f-divergences. Part I: Second and Fourth-Order Inequalities","license":"","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Gustavo L. Gilardoni","submitted_at":"2006-03-24T11:47:59Z","abstract_excerpt":"We study conditions on $f$ under which an $f$-divergence $D_f$ will satisfy $D_f \\geq c_f V^2$ or $D_f \\geq c_{2,f} V^2 + c_{4,f} V^4$, where $V$ denotes variational distance and the coefficients $c_f$, $c_{2,f}$ and $c_{4,f}$ are {\\em best possible}. As a consequence, we obtain lower bounds in terms of $V$ for many well known distance and divergence measures. For instance, let $D_{(\\alpha)} (P,Q) = [\\alpha (\\alpha-1)]^{-1} [\\int q^{\\alpha} p^{1-\\alpha} d \\mu -1]$ and ${\\cal I}_\\alpha (P,Q) = (\\alpha -1)^{-1} \\log [\\int p^\\alpha q^{1-\\alpha} d \\mu]$ be respectively the {\\em relative informatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cs/0603097","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":""},"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":"cs/0603097","created_at":"2026-05-18T04:36:49.598578+00:00"},{"alias_kind":"arxiv_version","alias_value":"cs/0603097v2","created_at":"2026-05-18T04:36:49.598578+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cs/0603097","created_at":"2026-05-18T04:36:49.598578+00:00"},{"alias_kind":"pith_short_12","alias_value":"AWOPYLJZ3HAX","created_at":"2026-05-18T12:25:53.939244+00:00"},{"alias_kind":"pith_short_16","alias_value":"AWOPYLJZ3HAXN6ZX","created_at":"2026-05-18T12:25:53.939244+00:00"},{"alias_kind":"pith_short_8","alias_value":"AWOPYLJZ","created_at":"2026-05-18T12:25:53.939244+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/AWOPYLJZ3HAXN6ZXTVHVG4CPMS","json":"https://pith.science/pith/AWOPYLJZ3HAXN6ZXTVHVG4CPMS.json","graph_json":"https://pith.science/api/pith-number/AWOPYLJZ3HAXN6ZXTVHVG4CPMS/graph.json","events_json":"https://pith.science/api/pith-number/AWOPYLJZ3HAXN6ZXTVHVG4CPMS/events.json","paper":"https://pith.science/paper/AWOPYLJZ"},"agent_actions":{"view_html":"https://pith.science/pith/AWOPYLJZ3HAXN6ZXTVHVG4CPMS","download_json":"https://pith.science/pith/AWOPYLJZ3HAXN6ZXTVHVG4CPMS.json","view_paper":"https://pith.science/paper/AWOPYLJZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=cs/0603097&json=true","fetch_graph":"https://pith.science/api/pith-number/AWOPYLJZ3HAXN6ZXTVHVG4CPMS/graph.json","fetch_events":"https://pith.science/api/pith-number/AWOPYLJZ3HAXN6ZXTVHVG4CPMS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AWOPYLJZ3HAXN6ZXTVHVG4CPMS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AWOPYLJZ3HAXN6ZXTVHVG4CPMS/action/storage_attestation","attest_author":"https://pith.science/pith/AWOPYLJZ3HAXN6ZXTVHVG4CPMS/action/author_attestation","sign_citation":"https://pith.science/pith/AWOPYLJZ3HAXN6ZXTVHVG4CPMS/action/citation_signature","submit_replication":"https://pith.science/pith/AWOPYLJZ3HAXN6ZXTVHVG4CPMS/action/replication_record"}},"created_at":"2026-05-18T04:36:49.598578+00:00","updated_at":"2026-05-18T04:36:49.598578+00:00"}