{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:6IAW6UAFYMNL5JA37AUHC6G6BW","short_pith_number":"pith:6IAW6UAF","canonical_record":{"source":{"id":"1404.1856","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2014-04-07T17:36:18Z","cross_cats_sorted":[],"title_canon_sha256":"8e14bfb29183f49ba79f86068a0864e1486eca39fad7e660d8a68ce00ed526b4","abstract_canon_sha256":"dae15f32df3c32b924fe9c699dc052566bab7921165ea58d105fc912d64a2803"},"schema_version":"1.0"},"canonical_sha256":"f2016f5005c31abea41bf8287178de0d912992ef37b863f0c68f56c272869dcd","source":{"kind":"arxiv","id":"1404.1856","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.1856","created_at":"2026-05-18T02:54:40Z"},{"alias_kind":"arxiv_version","alias_value":"1404.1856v1","created_at":"2026-05-18T02:54:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.1856","created_at":"2026-05-18T02:54:40Z"},{"alias_kind":"pith_short_12","alias_value":"6IAW6UAFYMNL","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"6IAW6UAFYMNL5JA3","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"6IAW6UAF","created_at":"2026-05-18T12:28:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:6IAW6UAFYMNL5JA37AUHC6G6BW","target":"record","payload":{"canonical_record":{"source":{"id":"1404.1856","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2014-04-07T17:36:18Z","cross_cats_sorted":[],"title_canon_sha256":"8e14bfb29183f49ba79f86068a0864e1486eca39fad7e660d8a68ce00ed526b4","abstract_canon_sha256":"dae15f32df3c32b924fe9c699dc052566bab7921165ea58d105fc912d64a2803"},"schema_version":"1.0"},"canonical_sha256":"f2016f5005c31abea41bf8287178de0d912992ef37b863f0c68f56c272869dcd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:40.040689Z","signature_b64":"dqDU68tqz6Mt/0XH3FWsCSrclKMc41akmVsh5uFUutHUMYkpR22dqWKH4JBUB3azzQt9po285X9WCc43Wm3XCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f2016f5005c31abea41bf8287178de0d912992ef37b863f0c68f56c272869dcd","last_reissued_at":"2026-05-18T02:54:40.040247Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:40.040247Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.1856","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":"2026-05-18T02:54:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MKTnmiYMp+sa3kID8UBpyblrRTr8t6HQqJ0ajmhcJ1dMFaxPeIN10DmotYWFhXAeWxMPi2Y2d/Zx2H3ivOpBBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T10:24:32.406763Z"},"content_sha256":"2bdf5b98d039c195a134016c4852c116014b0f6d0c626653b1317755da69c7c1","schema_version":"1.0","event_id":"sha256:2bdf5b98d039c195a134016c4852c116014b0f6d0c626653b1317755da69c7c1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:6IAW6UAFYMNL5JA37AUHC6G6BW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sums of Possibly Associated Bernoulli Variables: The Conway-Maxwell-Binomial Distribution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Joseph B. Kadane","submitted_at":"2014-04-07T17:36:18Z","abstract_excerpt":"The study of sums of possibly associated Bernoulli random variables has been hampered by an asymmetry between positive correlation and negative correlation. The Conway-Maxwell Binomial (COMB) distribution and its multivariate extension, the Conway-Maxwell Multinomial (COMM) distribution, gracefully model both positive and negative association. Sufficient statistics and a family of proper conjugate distributions are found. The relationship of this distribution to the exchangeable special case is explored, and two applications are discussed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.1856","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":"2026-05-18T02:54:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7DXU/9/LX12syDYtjjDFJL+ZrwXBCYlZFBZZ5Ql6iGiTDe3sODrB4A6z2mDoFxQ3vU4bi8I7dIQknFqr9N8XCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T10:24:32.407093Z"},"content_sha256":"cc092fb3bfd162ccd535e458abd1012382d7567d62abb71f8a80f59b81a70fa4","schema_version":"1.0","event_id":"sha256:cc092fb3bfd162ccd535e458abd1012382d7567d62abb71f8a80f59b81a70fa4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6IAW6UAFYMNL5JA37AUHC6G6BW/bundle.json","state_url":"https://pith.science/pith/6IAW6UAFYMNL5JA37AUHC6G6BW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6IAW6UAFYMNL5JA37AUHC6G6BW/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":"2026-06-07T10:24:32Z","links":{"resolver":"https://pith.science/pith/6IAW6UAFYMNL5JA37AUHC6G6BW","bundle":"https://pith.science/pith/6IAW6UAFYMNL5JA37AUHC6G6BW/bundle.json","state":"https://pith.science/pith/6IAW6UAFYMNL5JA37AUHC6G6BW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6IAW6UAFYMNL5JA37AUHC6G6BW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:6IAW6UAFYMNL5JA37AUHC6G6BW","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":"dae15f32df3c32b924fe9c699dc052566bab7921165ea58d105fc912d64a2803","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2014-04-07T17:36:18Z","title_canon_sha256":"8e14bfb29183f49ba79f86068a0864e1486eca39fad7e660d8a68ce00ed526b4"},"schema_version":"1.0","source":{"id":"1404.1856","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.1856","created_at":"2026-05-18T02:54:40Z"},{"alias_kind":"arxiv_version","alias_value":"1404.1856v1","created_at":"2026-05-18T02:54:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.1856","created_at":"2026-05-18T02:54:40Z"},{"alias_kind":"pith_short_12","alias_value":"6IAW6UAFYMNL","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"6IAW6UAFYMNL5JA3","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"6IAW6UAF","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:cc092fb3bfd162ccd535e458abd1012382d7567d62abb71f8a80f59b81a70fa4","target":"graph","created_at":"2026-05-18T02:54:40Z","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":"The study of sums of possibly associated Bernoulli random variables has been hampered by an asymmetry between positive correlation and negative correlation. The Conway-Maxwell Binomial (COMB) distribution and its multivariate extension, the Conway-Maxwell Multinomial (COMM) distribution, gracefully model both positive and negative association. Sufficient statistics and a family of proper conjugate distributions are found. The relationship of this distribution to the exchangeable special case is explored, and two applications are discussed.","authors_text":"Joseph B. Kadane","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2014-04-07T17:36:18Z","title":"Sums of Possibly Associated Bernoulli Variables: The Conway-Maxwell-Binomial Distribution"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.1856","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":"sha256:2bdf5b98d039c195a134016c4852c116014b0f6d0c626653b1317755da69c7c1","target":"record","created_at":"2026-05-18T02:54:40Z","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":"dae15f32df3c32b924fe9c699dc052566bab7921165ea58d105fc912d64a2803","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2014-04-07T17:36:18Z","title_canon_sha256":"8e14bfb29183f49ba79f86068a0864e1486eca39fad7e660d8a68ce00ed526b4"},"schema_version":"1.0","source":{"id":"1404.1856","kind":"arxiv","version":1}},"canonical_sha256":"f2016f5005c31abea41bf8287178de0d912992ef37b863f0c68f56c272869dcd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f2016f5005c31abea41bf8287178de0d912992ef37b863f0c68f56c272869dcd","first_computed_at":"2026-05-18T02:54:40.040247Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:54:40.040247Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dqDU68tqz6Mt/0XH3FWsCSrclKMc41akmVsh5uFUutHUMYkpR22dqWKH4JBUB3azzQt9po285X9WCc43Wm3XCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:54:40.040689Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.1856","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2bdf5b98d039c195a134016c4852c116014b0f6d0c626653b1317755da69c7c1","sha256:cc092fb3bfd162ccd535e458abd1012382d7567d62abb71f8a80f59b81a70fa4"],"state_sha256":"e7e8e7838adf762190887d4ebfff48ce1528949aae991bba0c8cb9cc51ba945f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KqbOYqqVRA/k0F2U3/IdQGfbplqK9GevL20CxVZNasSyji4paRnAVI6ZjbPHWG3TXReLrFPBvepFktMl4u5FDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T10:24:32.409045Z","bundle_sha256":"cc2c3921e0d5c8b851a511f5f8fe32a9126c4c3e87dd40aef2ddc53f534c54d7"}}