{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:KRKCDE65HQNGQJLKBROFQ4ONAO","short_pith_number":"pith:KRKCDE65","canonical_record":{"source":{"id":"1506.02489","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-08T13:35:28Z","cross_cats_sorted":[],"title_canon_sha256":"67177cfc6e129cab794b51f08a82b983df4254132105ba534c60fb60c68bc80f","abstract_canon_sha256":"beba0c1a574c08f9721b6daf07812ad4cccad14a36d9e08aa9126320d771f1a3"},"schema_version":"1.0"},"canonical_sha256":"54542193dd3c1a68256a0c5c5871cd03ad992d347634e3c326853112219c281d","source":{"kind":"arxiv","id":"1506.02489","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.02489","created_at":"2026-05-18T01:12:49Z"},{"alias_kind":"arxiv_version","alias_value":"1506.02489v3","created_at":"2026-05-18T01:12:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.02489","created_at":"2026-05-18T01:12:49Z"},{"alias_kind":"pith_short_12","alias_value":"KRKCDE65HQNG","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"KRKCDE65HQNGQJLK","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"KRKCDE65","created_at":"2026-05-18T12:29:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:KRKCDE65HQNGQJLKBROFQ4ONAO","target":"record","payload":{"canonical_record":{"source":{"id":"1506.02489","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-08T13:35:28Z","cross_cats_sorted":[],"title_canon_sha256":"67177cfc6e129cab794b51f08a82b983df4254132105ba534c60fb60c68bc80f","abstract_canon_sha256":"beba0c1a574c08f9721b6daf07812ad4cccad14a36d9e08aa9126320d771f1a3"},"schema_version":"1.0"},"canonical_sha256":"54542193dd3c1a68256a0c5c5871cd03ad992d347634e3c326853112219c281d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:49.891289Z","signature_b64":"aMR5byKuQz4REfhsOMuDZuLfsvpXZaz+V8cciByi+RUQBurJ5Hk8+pVEVeuwY44984DlTVq+PXBZPznmNrn9CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"54542193dd3c1a68256a0c5c5871cd03ad992d347634e3c326853112219c281d","last_reissued_at":"2026-05-18T01:12:49.890949Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:49.890949Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.02489","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:12:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ah+3LAz0N/YuRQW1dYfWzP3X0LyrqhA9x20EG9eu+GRY+TOT/i9C3duCHrwSLpoQ7q27phpsELilsi1QtIRiBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T10:16:13.565628Z"},"content_sha256":"30b6e95c47b6eb39217f3cddd24b1a1153f053386af6e38d8e62feaf67294bb3","schema_version":"1.0","event_id":"sha256:30b6e95c47b6eb39217f3cddd24b1a1153f053386af6e38d8e62feaf67294bb3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:KRKCDE65HQNGQJLKBROFQ4ONAO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A new characterization of quadratic transportation-information inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Yuan Liu","submitted_at":"2015-06-08T13:35:28Z","abstract_excerpt":"It is known that a quadratic transportation-information inequality $\\mathrm{W_2I}$ interpolates between the Talagrand's inequality $\\mathrm{W_2H}$ and the log-Sobolev inequality (LSI for short). The aim of the present paper is threefold:\n  (1) To prove the equivalence of $\\mathrm{W_2I}$ and the Lyapunov condition, which gives a new characterization inspired by Cattiaux-Guillin-Wu [8].\n  (2) To prove the stability of $\\mathrm{W_2I}$ under bounded perturbations, which gives a transference principle in the sense of Holley-Stroock.\n  (3) To prove $\\mathrm{W_2H}$ through a restricted $\\mathrm{W_2I}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.02489","kind":"arxiv","version":3},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:12:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U/cw7jE7kao1Gkv9YDr0rYR3XtvdE5K1fYJ4AgeMe4rwvdOmNQMmYG3cvZ0iKmLCmV99WFSVws+wj8Dj66BjCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T10:16:13.566006Z"},"content_sha256":"2171e01aa01fd6ff901bfbd3784385d5dc0fdf55ae8afbb62d80e39030108786","schema_version":"1.0","event_id":"sha256:2171e01aa01fd6ff901bfbd3784385d5dc0fdf55ae8afbb62d80e39030108786"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KRKCDE65HQNGQJLKBROFQ4ONAO/bundle.json","state_url":"https://pith.science/pith/KRKCDE65HQNGQJLKBROFQ4ONAO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KRKCDE65HQNGQJLKBROFQ4ONAO/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-10T10:16:13Z","links":{"resolver":"https://pith.science/pith/KRKCDE65HQNGQJLKBROFQ4ONAO","bundle":"https://pith.science/pith/KRKCDE65HQNGQJLKBROFQ4ONAO/bundle.json","state":"https://pith.science/pith/KRKCDE65HQNGQJLKBROFQ4ONAO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KRKCDE65HQNGQJLKBROFQ4ONAO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:KRKCDE65HQNGQJLKBROFQ4ONAO","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":"beba0c1a574c08f9721b6daf07812ad4cccad14a36d9e08aa9126320d771f1a3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-08T13:35:28Z","title_canon_sha256":"67177cfc6e129cab794b51f08a82b983df4254132105ba534c60fb60c68bc80f"},"schema_version":"1.0","source":{"id":"1506.02489","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.02489","created_at":"2026-05-18T01:12:49Z"},{"alias_kind":"arxiv_version","alias_value":"1506.02489v3","created_at":"2026-05-18T01:12:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.02489","created_at":"2026-05-18T01:12:49Z"},{"alias_kind":"pith_short_12","alias_value":"KRKCDE65HQNG","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"KRKCDE65HQNGQJLK","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"KRKCDE65","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:2171e01aa01fd6ff901bfbd3784385d5dc0fdf55ae8afbb62d80e39030108786","target":"graph","created_at":"2026-05-18T01:12:49Z","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"},"paper":{"abstract_excerpt":"It is known that a quadratic transportation-information inequality $\\mathrm{W_2I}$ interpolates between the Talagrand's inequality $\\mathrm{W_2H}$ and the log-Sobolev inequality (LSI for short). The aim of the present paper is threefold:\n  (1) To prove the equivalence of $\\mathrm{W_2I}$ and the Lyapunov condition, which gives a new characterization inspired by Cattiaux-Guillin-Wu [8].\n  (2) To prove the stability of $\\mathrm{W_2I}$ under bounded perturbations, which gives a transference principle in the sense of Holley-Stroock.\n  (3) To prove $\\mathrm{W_2H}$ through a restricted $\\mathrm{W_2I}","authors_text":"Yuan Liu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-08T13:35:28Z","title":"A new characterization of quadratic transportation-information inequalities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.02489","kind":"arxiv","version":3},"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":"sha256:30b6e95c47b6eb39217f3cddd24b1a1153f053386af6e38d8e62feaf67294bb3","target":"record","created_at":"2026-05-18T01:12:49Z","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":"beba0c1a574c08f9721b6daf07812ad4cccad14a36d9e08aa9126320d771f1a3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-08T13:35:28Z","title_canon_sha256":"67177cfc6e129cab794b51f08a82b983df4254132105ba534c60fb60c68bc80f"},"schema_version":"1.0","source":{"id":"1506.02489","kind":"arxiv","version":3}},"canonical_sha256":"54542193dd3c1a68256a0c5c5871cd03ad992d347634e3c326853112219c281d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"54542193dd3c1a68256a0c5c5871cd03ad992d347634e3c326853112219c281d","first_computed_at":"2026-05-18T01:12:49.890949Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:49.890949Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aMR5byKuQz4REfhsOMuDZuLfsvpXZaz+V8cciByi+RUQBurJ5Hk8+pVEVeuwY44984DlTVq+PXBZPznmNrn9CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:49.891289Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.02489","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:30b6e95c47b6eb39217f3cddd24b1a1153f053386af6e38d8e62feaf67294bb3","sha256:2171e01aa01fd6ff901bfbd3784385d5dc0fdf55ae8afbb62d80e39030108786"],"state_sha256":"a6cfb543bfcbb80a2592af2c0b22371cac70a57dfe0ee5b9b3e455ea98ff26ba"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f95BVhPKusafuwcOEtR5GJufVTILC20bPEM1dVZCjFsYrVHGlueeJWLEJ2QqofVCkzvgF74g8O3iCUnZUOolBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T10:16:13.568058Z","bundle_sha256":"c959d2fb464e6465aa6b9ce92d9c0dc74d81cee26deccc6cb10668bc345b2611"}}