{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:MB6SW6MAGXB2ZBZH3PTEQCS5E2","short_pith_number":"pith:MB6SW6MA","canonical_record":{"source":{"id":"1907.00288","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-06-29T22:30:03Z","cross_cats_sorted":["cs.IT","math.IT","stat.ML","stat.TH"],"title_canon_sha256":"0b5d54ea6b36434133d0657858a664df32c7d4aa97f9d7e7e4e9bd70cc1adfcb","abstract_canon_sha256":"936fcdc2fd6be4898d3dafeb2f42a6fae60ae9cd9ba1de7d2737e2059f59701b"},"schema_version":"1.0"},"canonical_sha256":"607d2b798035c3ac8727dbe6480a5d2682df936dd3716e837511bd4de3b3f847","source":{"kind":"arxiv","id":"1907.00288","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.00288","created_at":"2026-07-05T00:16:35Z"},{"alias_kind":"arxiv_version","alias_value":"1907.00288v3","created_at":"2026-07-05T00:16:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.00288","created_at":"2026-07-05T00:16:35Z"},{"alias_kind":"pith_short_12","alias_value":"MB6SW6MAGXB2","created_at":"2026-07-05T00:16:35Z"},{"alias_kind":"pith_short_16","alias_value":"MB6SW6MAGXB2ZBZH","created_at":"2026-07-05T00:16:35Z"},{"alias_kind":"pith_short_8","alias_value":"MB6SW6MA","created_at":"2026-07-05T00:16:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:MB6SW6MAGXB2ZBZH3PTEQCS5E2","target":"record","payload":{"canonical_record":{"source":{"id":"1907.00288","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-06-29T22:30:03Z","cross_cats_sorted":["cs.IT","math.IT","stat.ML","stat.TH"],"title_canon_sha256":"0b5d54ea6b36434133d0657858a664df32c7d4aa97f9d7e7e4e9bd70cc1adfcb","abstract_canon_sha256":"936fcdc2fd6be4898d3dafeb2f42a6fae60ae9cd9ba1de7d2737e2059f59701b"},"schema_version":"1.0"},"canonical_sha256":"607d2b798035c3ac8727dbe6480a5d2682df936dd3716e837511bd4de3b3f847","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:16:35.533567Z","signature_b64":"X+BK/kTWzDnSk69Sc/eJ5+3AptpAtXxOUsZgstMhmGxN1TdhcZ4a099kkeHghGgwnqjIfJKya7riiheVpNdWBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"607d2b798035c3ac8727dbe6480a5d2682df936dd3716e837511bd4de3b3f847","last_reissued_at":"2026-07-05T00:16:35.533073Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:16:35.533073Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1907.00288","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":"2026-07-05T00:16:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6xQoxYYQkodgNdFGrhUmNQLHpMZO3J8X4qYae9tui6iCQ3tYXORSv6pvwF3R1y3KPu0sKFV+pcHCgFb4c/QOCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T09:18:29.050932Z"},"content_sha256":"81f8bdbd890ffd355da0a21106abe28ca86c3d2f278cb2123261a251cbb746e8","schema_version":"1.0","event_id":"sha256:81f8bdbd890ffd355da0a21106abe28ca86c3d2f278cb2123261a251cbb746e8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:MB6SW6MAGXB2ZBZH3PTEQCS5E2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A New Lower Bound for Kullback-Leibler Divergence Based on Hammersley-Chapman-Robbins Bound","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Tomohiro Nishiyama","submitted_at":"2019-06-29T22:30:03Z","abstract_excerpt":"In this paper, we derive a useful lower bound for the Kullback-Leibler divergence (KL-divergence) based on the Hammersley-Chapman-Robbins bound (HCRB). The HCRB states that the variance of an estimator is bounded from below by the Chi-square divergence and the expectation value of the estimator. By using the relation between the KL-divergence and the Chi-square divergence, we show that the lower bound for the KL-divergence which only depends on the expectation value and the variance of a function we choose. This lower bound can also be derived from an information geometric approach. Furthermor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.00288","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1907.00288/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T00:16:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uoWRQ4BF06AIB5AUvApNEeA+MJrmE89NSS8gbiH4EcnnQ2cIvq3yWPGAvXa5areRan5hFTKRVJBqlSvzLlapCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T09:18:29.051484Z"},"content_sha256":"4c5c0026031eb10a866764b127132624d87f1d66d8a6684ffc69961c08e82399","schema_version":"1.0","event_id":"sha256:4c5c0026031eb10a866764b127132624d87f1d66d8a6684ffc69961c08e82399"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MB6SW6MAGXB2ZBZH3PTEQCS5E2/bundle.json","state_url":"https://pith.science/pith/MB6SW6MAGXB2ZBZH3PTEQCS5E2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MB6SW6MAGXB2ZBZH3PTEQCS5E2/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":"2026-08-10T09:18:29Z","links":{"resolver":"https://pith.science/pith/MB6SW6MAGXB2ZBZH3PTEQCS5E2","bundle":"https://pith.science/pith/MB6SW6MAGXB2ZBZH3PTEQCS5E2/bundle.json","state":"https://pith.science/pith/MB6SW6MAGXB2ZBZH3PTEQCS5E2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MB6SW6MAGXB2ZBZH3PTEQCS5E2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:MB6SW6MAGXB2ZBZH3PTEQCS5E2","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":"936fcdc2fd6be4898d3dafeb2f42a6fae60ae9cd9ba1de7d2737e2059f59701b","cross_cats_sorted":["cs.IT","math.IT","stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-06-29T22:30:03Z","title_canon_sha256":"0b5d54ea6b36434133d0657858a664df32c7d4aa97f9d7e7e4e9bd70cc1adfcb"},"schema_version":"1.0","source":{"id":"1907.00288","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.00288","created_at":"2026-07-05T00:16:35Z"},{"alias_kind":"arxiv_version","alias_value":"1907.00288v3","created_at":"2026-07-05T00:16:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.00288","created_at":"2026-07-05T00:16:35Z"},{"alias_kind":"pith_short_12","alias_value":"MB6SW6MAGXB2","created_at":"2026-07-05T00:16:35Z"},{"alias_kind":"pith_short_16","alias_value":"MB6SW6MAGXB2ZBZH","created_at":"2026-07-05T00:16:35Z"},{"alias_kind":"pith_short_8","alias_value":"MB6SW6MA","created_at":"2026-07-05T00:16:35Z"}],"graph_snapshots":[{"event_id":"sha256:4c5c0026031eb10a866764b127132624d87f1d66d8a6684ffc69961c08e82399","target":"graph","created_at":"2026-07-05T00:16:35Z","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/1907.00288/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we derive a useful lower bound for the Kullback-Leibler divergence (KL-divergence) based on the Hammersley-Chapman-Robbins bound (HCRB). The HCRB states that the variance of an estimator is bounded from below by the Chi-square divergence and the expectation value of the estimator. By using the relation between the KL-divergence and the Chi-square divergence, we show that the lower bound for the KL-divergence which only depends on the expectation value and the variance of a function we choose. This lower bound can also be derived from an information geometric approach. Furthermor","authors_text":"Tomohiro Nishiyama","cross_cats":["cs.IT","math.IT","stat.ML","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-06-29T22:30:03Z","title":"A New Lower Bound for Kullback-Leibler Divergence Based on Hammersley-Chapman-Robbins Bound"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.00288","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":"sha256:81f8bdbd890ffd355da0a21106abe28ca86c3d2f278cb2123261a251cbb746e8","target":"record","created_at":"2026-07-05T00:16:35Z","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":"936fcdc2fd6be4898d3dafeb2f42a6fae60ae9cd9ba1de7d2737e2059f59701b","cross_cats_sorted":["cs.IT","math.IT","stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-06-29T22:30:03Z","title_canon_sha256":"0b5d54ea6b36434133d0657858a664df32c7d4aa97f9d7e7e4e9bd70cc1adfcb"},"schema_version":"1.0","source":{"id":"1907.00288","kind":"arxiv","version":3}},"canonical_sha256":"607d2b798035c3ac8727dbe6480a5d2682df936dd3716e837511bd4de3b3f847","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"607d2b798035c3ac8727dbe6480a5d2682df936dd3716e837511bd4de3b3f847","first_computed_at":"2026-07-05T00:16:35.533073Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:16:35.533073Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"X+BK/kTWzDnSk69Sc/eJ5+3AptpAtXxOUsZgstMhmGxN1TdhcZ4a099kkeHghGgwnqjIfJKya7riiheVpNdWBg==","signature_status":"signed_v1","signed_at":"2026-07-05T00:16:35.533567Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.00288","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:81f8bdbd890ffd355da0a21106abe28ca86c3d2f278cb2123261a251cbb746e8","sha256:4c5c0026031eb10a866764b127132624d87f1d66d8a6684ffc69961c08e82399"],"state_sha256":"e6feaa3bc38b5668f5ead25ef14ea0ca7280fb3cfc96880b8f6eb06410c0dda3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uK6SEOfLK1ByMlI6EHzJ+98eDlrF3a3wSNIGYevTmzvsq6MPwiluZQP4BpIAiIvjSLnBOuunV42riPhEM3RgDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T09:18:29.057871Z","bundle_sha256":"b8aa96b512b23965680006ba4c881b0a30577ad70f0bc7658568b95d918fb2b2"}}