{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:XJAFSI3QWF7GAALLQPISN6MIUE","short_pith_number":"pith:XJAFSI3Q","canonical_record":{"source":{"id":"1606.05520","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-06-17T13:35:51Z","cross_cats_sorted":[],"title_canon_sha256":"c20125eb55330a0106dedff52bc5b6521b3bab0adec1b3f31950cf2cc37a8d8e","abstract_canon_sha256":"83fb88c161e066087772842bbdbdfe4ee15abea22d2cca5d045cb16dd79059a4"},"schema_version":"1.0"},"canonical_sha256":"ba40592370b17e60016b83d126f988a13dcec72da8fe7ed438c50c5e893d180f","source":{"kind":"arxiv","id":"1606.05520","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.05520","created_at":"2026-05-18T01:08:32Z"},{"alias_kind":"arxiv_version","alias_value":"1606.05520v2","created_at":"2026-05-18T01:08:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.05520","created_at":"2026-05-18T01:08:32Z"},{"alias_kind":"pith_short_12","alias_value":"XJAFSI3QWF7G","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XJAFSI3QWF7GAALL","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XJAFSI3Q","created_at":"2026-05-18T12:30:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:XJAFSI3QWF7GAALLQPISN6MIUE","target":"record","payload":{"canonical_record":{"source":{"id":"1606.05520","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-06-17T13:35:51Z","cross_cats_sorted":[],"title_canon_sha256":"c20125eb55330a0106dedff52bc5b6521b3bab0adec1b3f31950cf2cc37a8d8e","abstract_canon_sha256":"83fb88c161e066087772842bbdbdfe4ee15abea22d2cca5d045cb16dd79059a4"},"schema_version":"1.0"},"canonical_sha256":"ba40592370b17e60016b83d126f988a13dcec72da8fe7ed438c50c5e893d180f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:32.116010Z","signature_b64":"VV3Sxnb8LDoKha8O22ulGzvZ5U4zRtdQz12y4/V1qcNmfrZE1LhNnu6rExhwSit3lu+l5tYa60uuO6zl6+WeAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ba40592370b17e60016b83d126f988a13dcec72da8fe7ed438c50c5e893d180f","last_reissued_at":"2026-05-18T01:08:32.115456Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:32.115456Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.05520","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:08:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"na0MSjkgXZDm0lIY3iAbHwsjfP2Bqtl7q4z3ZqIyD3eJGcb3yeoBbQkLtIrIlFrJmso2uKXqCzVqa/9a0h3ABA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T07:57:06.367194Z"},"content_sha256":"2f9dbad4fbf9317007e3e6ed45cef4f20c03977d860ed6e97f1fe14ff06a2aa4","schema_version":"1.0","event_id":"sha256:2f9dbad4fbf9317007e3e6ed45cef4f20c03977d860ed6e97f1fe14ff06a2aa4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:XJAFSI3QWF7GAALLQPISN6MIUE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Complete monotonicity of some entropies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Ioan Rasa","submitted_at":"2016-06-17T13:35:51Z","abstract_excerpt":"It is well-known that the Shannon entropies of some parameterized probability distributions are concave functions with respect to the parameter. In this paper we consider a family of such distributions (including the binomial, Poisson, and negative binomial distributions) and investigate the Shannon, R\\'{e}nyi, and Tsallis entropies of them with respect to the complete monotonicity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.05520","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:08:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mZZM4Syn2+xNWwj1ZmPUHd5NjtpdzG2TgWXNYfWEXX4OKnml1xa5NjTIF1L84Oc4cgve4YIkBpYOFoO4Fe7ZBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T07:57:06.367860Z"},"content_sha256":"1eff6a9faa9ac84486e5d1b2438672410e109eb625c2166a5560e89c1c44b55b","schema_version":"1.0","event_id":"sha256:1eff6a9faa9ac84486e5d1b2438672410e109eb625c2166a5560e89c1c44b55b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XJAFSI3QWF7GAALLQPISN6MIUE/bundle.json","state_url":"https://pith.science/pith/XJAFSI3QWF7GAALLQPISN6MIUE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XJAFSI3QWF7GAALLQPISN6MIUE/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":"2026-06-08T07:57:06Z","links":{"resolver":"https://pith.science/pith/XJAFSI3QWF7GAALLQPISN6MIUE","bundle":"https://pith.science/pith/XJAFSI3QWF7GAALLQPISN6MIUE/bundle.json","state":"https://pith.science/pith/XJAFSI3QWF7GAALLQPISN6MIUE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XJAFSI3QWF7GAALLQPISN6MIUE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:XJAFSI3QWF7GAALLQPISN6MIUE","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":"83fb88c161e066087772842bbdbdfe4ee15abea22d2cca5d045cb16dd79059a4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-06-17T13:35:51Z","title_canon_sha256":"c20125eb55330a0106dedff52bc5b6521b3bab0adec1b3f31950cf2cc37a8d8e"},"schema_version":"1.0","source":{"id":"1606.05520","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.05520","created_at":"2026-05-18T01:08:32Z"},{"alias_kind":"arxiv_version","alias_value":"1606.05520v2","created_at":"2026-05-18T01:08:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.05520","created_at":"2026-05-18T01:08:32Z"},{"alias_kind":"pith_short_12","alias_value":"XJAFSI3QWF7G","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XJAFSI3QWF7GAALL","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XJAFSI3Q","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:1eff6a9faa9ac84486e5d1b2438672410e109eb625c2166a5560e89c1c44b55b","target":"graph","created_at":"2026-05-18T01:08:32Z","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 well-known that the Shannon entropies of some parameterized probability distributions are concave functions with respect to the parameter. In this paper we consider a family of such distributions (including the binomial, Poisson, and negative binomial distributions) and investigate the Shannon, R\\'{e}nyi, and Tsallis entropies of them with respect to the complete monotonicity.","authors_text":"Ioan Rasa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-06-17T13:35:51Z","title":"Complete monotonicity of some entropies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.05520","kind":"arxiv","version":2},"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":"sha256:2f9dbad4fbf9317007e3e6ed45cef4f20c03977d860ed6e97f1fe14ff06a2aa4","target":"record","created_at":"2026-05-18T01:08:32Z","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":"83fb88c161e066087772842bbdbdfe4ee15abea22d2cca5d045cb16dd79059a4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-06-17T13:35:51Z","title_canon_sha256":"c20125eb55330a0106dedff52bc5b6521b3bab0adec1b3f31950cf2cc37a8d8e"},"schema_version":"1.0","source":{"id":"1606.05520","kind":"arxiv","version":2}},"canonical_sha256":"ba40592370b17e60016b83d126f988a13dcec72da8fe7ed438c50c5e893d180f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ba40592370b17e60016b83d126f988a13dcec72da8fe7ed438c50c5e893d180f","first_computed_at":"2026-05-18T01:08:32.115456Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:08:32.115456Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VV3Sxnb8LDoKha8O22ulGzvZ5U4zRtdQz12y4/V1qcNmfrZE1LhNnu6rExhwSit3lu+l5tYa60uuO6zl6+WeAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:08:32.116010Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.05520","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2f9dbad4fbf9317007e3e6ed45cef4f20c03977d860ed6e97f1fe14ff06a2aa4","sha256:1eff6a9faa9ac84486e5d1b2438672410e109eb625c2166a5560e89c1c44b55b"],"state_sha256":"302ed8f5135e46dbc2b17f9f07376fc724fe6db731ef97a48627a3942154449f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gdxUPKQB/mlHDQPph1mfRKr3eyV2l+TKFoS78U4MBRO/exQrHT8l0bJKw6C5Yq/LnJbQMCi+xs/2JGyvF4S+Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T07:57:06.371700Z","bundle_sha256":"7b8d21e0a42c980071f9bf1963ad248dcb3f6672f98805b9ebfea9ec7fd95551"}}