{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:5SK3YK36LXN7NEVXCU4HOFKLRY","short_pith_number":"pith:5SK3YK36","canonical_record":{"source":{"id":"1812.10741","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-12-27T15:25:52Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"e010eecf2566f73b17f6bf51f9bf03e628f88d31b1a542c24231cc447ea631d3","abstract_canon_sha256":"1c96a786dc23a1209cc020399c7a8bb492ee4b915b4a15148a7c10dcf60ab353"},"schema_version":"1.0"},"canonical_sha256":"ec95bc2b7e5ddbf692b7153877154b8e32ecc7256e0009e0297766e05b1af117","source":{"kind":"arxiv","id":"1812.10741","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.10741","created_at":"2026-05-17T23:57:20Z"},{"alias_kind":"arxiv_version","alias_value":"1812.10741v1","created_at":"2026-05-17T23:57:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.10741","created_at":"2026-05-17T23:57:20Z"},{"alias_kind":"pith_short_12","alias_value":"5SK3YK36LXN7","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"5SK3YK36LXN7NEVX","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"5SK3YK36","created_at":"2026-05-18T12:32:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:5SK3YK36LXN7NEVXCU4HOFKLRY","target":"record","payload":{"canonical_record":{"source":{"id":"1812.10741","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-12-27T15:25:52Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"e010eecf2566f73b17f6bf51f9bf03e628f88d31b1a542c24231cc447ea631d3","abstract_canon_sha256":"1c96a786dc23a1209cc020399c7a8bb492ee4b915b4a15148a7c10dcf60ab353"},"schema_version":"1.0"},"canonical_sha256":"ec95bc2b7e5ddbf692b7153877154b8e32ecc7256e0009e0297766e05b1af117","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:20.134968Z","signature_b64":"IK1CwFmn0mlz03IIBIIIgMRKsaxvFk3933JIU7YQnvTutSN/BnRtz1Tnd6uJYHR8nQc3Uc3ou05fzklIoE9/Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ec95bc2b7e5ddbf692b7153877154b8e32ecc7256e0009e0297766e05b1af117","last_reissued_at":"2026-05-17T23:57:20.134322Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:20.134322Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.10741","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:57:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qHEg74ceWkc5eHS2m3mZG/YsxciIV+CuIASPkLU7YDsahH1fp/iy1StigeE/AIAcoweKEeknAe0GWQiaQWetCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T14:24:08.402250Z"},"content_sha256":"3a0fa4b87da8a27d8e2ce3f895fc93aa86360ba0b7d2d91e0f58fbea66af6eda","schema_version":"1.0","event_id":"sha256:3a0fa4b87da8a27d8e2ce3f895fc93aa86360ba0b7d2d91e0f58fbea66af6eda"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:5SK3YK36LXN7NEVXCU4HOFKLRY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On mutual information estimation for mixed-pair random variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Aleksandr Beknazaryan, Hailin Sang, Xin Dang","submitted_at":"2018-12-27T15:25:52Z","abstract_excerpt":"We study the mutual information estimation for mixed-pair random variables. One random variable is discrete and the other one is continuous. We develop a kernel method to estimate the mutual information between the two random variables. The estimates enjoy a central limit theorem under some regular conditions on the distributions. The theoretical results are demonstrated by simulation study."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.10741","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":""},"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":"2026-05-17T23:57:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tD8AaihKyab3sBdQNbAoDcLBROgzBCqSVVKxDd/e3Cl40gxDoMaubyfh5xht5uw72uo1Zyk0TlHVAk/nEZkaAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T14:24:08.402602Z"},"content_sha256":"11fa3f665b05d1e74efde1b049b329c874698b9d395730b4c32488f0691a66f0","schema_version":"1.0","event_id":"sha256:11fa3f665b05d1e74efde1b049b329c874698b9d395730b4c32488f0691a66f0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5SK3YK36LXN7NEVXCU4HOFKLRY/bundle.json","state_url":"https://pith.science/pith/5SK3YK36LXN7NEVXCU4HOFKLRY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5SK3YK36LXN7NEVXCU4HOFKLRY/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":"2026-06-02T14:24:08Z","links":{"resolver":"https://pith.science/pith/5SK3YK36LXN7NEVXCU4HOFKLRY","bundle":"https://pith.science/pith/5SK3YK36LXN7NEVXCU4HOFKLRY/bundle.json","state":"https://pith.science/pith/5SK3YK36LXN7NEVXCU4HOFKLRY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5SK3YK36LXN7NEVXCU4HOFKLRY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:5SK3YK36LXN7NEVXCU4HOFKLRY","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":"1c96a786dc23a1209cc020399c7a8bb492ee4b915b4a15148a7c10dcf60ab353","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-12-27T15:25:52Z","title_canon_sha256":"e010eecf2566f73b17f6bf51f9bf03e628f88d31b1a542c24231cc447ea631d3"},"schema_version":"1.0","source":{"id":"1812.10741","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.10741","created_at":"2026-05-17T23:57:20Z"},{"alias_kind":"arxiv_version","alias_value":"1812.10741v1","created_at":"2026-05-17T23:57:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.10741","created_at":"2026-05-17T23:57:20Z"},{"alias_kind":"pith_short_12","alias_value":"5SK3YK36LXN7","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"5SK3YK36LXN7NEVX","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"5SK3YK36","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:11fa3f665b05d1e74efde1b049b329c874698b9d395730b4c32488f0691a66f0","target":"graph","created_at":"2026-05-17T23:57:20Z","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":"We study the mutual information estimation for mixed-pair random variables. One random variable is discrete and the other one is continuous. We develop a kernel method to estimate the mutual information between the two random variables. The estimates enjoy a central limit theorem under some regular conditions on the distributions. The theoretical results are demonstrated by simulation study.","authors_text":"Aleksandr Beknazaryan, Hailin Sang, Xin Dang","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-12-27T15:25:52Z","title":"On mutual information estimation for mixed-pair random variables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.10741","kind":"arxiv","version":1},"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":"sha256:3a0fa4b87da8a27d8e2ce3f895fc93aa86360ba0b7d2d91e0f58fbea66af6eda","target":"record","created_at":"2026-05-17T23:57:20Z","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":"1c96a786dc23a1209cc020399c7a8bb492ee4b915b4a15148a7c10dcf60ab353","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-12-27T15:25:52Z","title_canon_sha256":"e010eecf2566f73b17f6bf51f9bf03e628f88d31b1a542c24231cc447ea631d3"},"schema_version":"1.0","source":{"id":"1812.10741","kind":"arxiv","version":1}},"canonical_sha256":"ec95bc2b7e5ddbf692b7153877154b8e32ecc7256e0009e0297766e05b1af117","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ec95bc2b7e5ddbf692b7153877154b8e32ecc7256e0009e0297766e05b1af117","first_computed_at":"2026-05-17T23:57:20.134322Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:20.134322Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IK1CwFmn0mlz03IIBIIIgMRKsaxvFk3933JIU7YQnvTutSN/BnRtz1Tnd6uJYHR8nQc3Uc3ou05fzklIoE9/Dw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:20.134968Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.10741","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3a0fa4b87da8a27d8e2ce3f895fc93aa86360ba0b7d2d91e0f58fbea66af6eda","sha256:11fa3f665b05d1e74efde1b049b329c874698b9d395730b4c32488f0691a66f0"],"state_sha256":"5ea4794fa81a36079daa828be41032f3b8043658f25ce5b857c7de171ff76463"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UUIX86UKmFFRypgSje22WWMBxnj+E4xo6FtoIUNj7/Wa2Pt2HFNHcq9VYbj5vHL3PuTwHWDZL2KxdP8+CfLLDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T14:24:08.404452Z","bundle_sha256":"f5551a093c1501655cff9db3514b06edddc3942112a9f0a2c36d2f0c9eb7f544"}}