{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:3LYQB3SJMOOI5PP4IUWR4XKHPG","short_pith_number":"pith:3LYQB3SJ","canonical_record":{"source":{"id":"1704.06762","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-04-22T08:01:17Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"3052f7c9fd990647bba89138e17b1b6cb3150105147a664ddf0b01f6c8752fd7","abstract_canon_sha256":"c58ebbccf89f05d34f4ae25ec894eed1f5297a7b279e62ef7341570c2cf0f468"},"schema_version":"1.0"},"canonical_sha256":"daf100ee49639c8ebdfc452d1e5d4779bddb03459452d5321b6197030a610df5","source":{"kind":"arxiv","id":"1704.06762","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.06762","created_at":"2026-05-18T00:18:31Z"},{"alias_kind":"arxiv_version","alias_value":"1704.06762v4","created_at":"2026-05-18T00:18:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.06762","created_at":"2026-05-18T00:18:31Z"},{"alias_kind":"pith_short_12","alias_value":"3LYQB3SJMOOI","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3LYQB3SJMOOI5PP4","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3LYQB3SJ","created_at":"2026-05-18T12:30:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:3LYQB3SJMOOI5PP4IUWR4XKHPG","target":"record","payload":{"canonical_record":{"source":{"id":"1704.06762","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-04-22T08:01:17Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"3052f7c9fd990647bba89138e17b1b6cb3150105147a664ddf0b01f6c8752fd7","abstract_canon_sha256":"c58ebbccf89f05d34f4ae25ec894eed1f5297a7b279e62ef7341570c2cf0f468"},"schema_version":"1.0"},"canonical_sha256":"daf100ee49639c8ebdfc452d1e5d4779bddb03459452d5321b6197030a610df5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:31.882290Z","signature_b64":"8ZB2M7434JRkFBJvOsA4MEPylnbpG2Zl7pjyditXgnMgMbTeP95tmbRP8q+IWsisEMyNio9+RYK660ulLQbNAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"daf100ee49639c8ebdfc452d1e5d4779bddb03459452d5321b6197030a610df5","last_reissued_at":"2026-05-18T00:18:31.881869Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:31.881869Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.06762","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:18:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lrDBeC0Zh+eZQCGcHQMIOru/bqi8UOG9+4+r0VtIezIuxjT0A9K7eKCY2EcRdW2OFRbnZ049iTq3bWrtadxGDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T19:41:15.863126Z"},"content_sha256":"5bb439b7b73fb1462404bd71995e0c40c5f648aad91b9a63c6de49f529327f54","schema_version":"1.0","event_id":"sha256:5bb439b7b73fb1462404bd71995e0c40c5f648aad91b9a63c6de49f529327f54"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:3LYQB3SJMOOI5PP4IUWR4XKHPG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multiplicative models for frequency data, estimation and testing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Antonio Forcina","submitted_at":"2017-04-22T08:01:17Z","abstract_excerpt":"This paper is about models for a vector of probabilities whose elements must have a multiplicative structure and sum to 1 at the same time; in certain applications, as basket analysis, these models may be seen as a constrained version of quasi-independence. After reviewing the basic properties of these models, their geometric features as a curved exponential family are investigated. A new algorithm for computing maximum likelihood estimates is presented and new insights are provided on the underlying geometry. The asymptotic distribution of three statistics for hypothesis testing are derived a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.06762","kind":"arxiv","version":4},"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":"2026-05-18T00:18:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GyJUfH8A2QgeCPxAK7aQ42LM1ewZZ4UZxDITIBPpfCIBbZ35A31nifJ3M/nRRKFcR1xCQEuI5+xH/0vSrByyCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T19:41:15.863540Z"},"content_sha256":"3203f7251a0f068e50a183a2ec6efb1423a45720385c9bd2ac4cab93c4f3d87d","schema_version":"1.0","event_id":"sha256:3203f7251a0f068e50a183a2ec6efb1423a45720385c9bd2ac4cab93c4f3d87d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3LYQB3SJMOOI5PP4IUWR4XKHPG/bundle.json","state_url":"https://pith.science/pith/3LYQB3SJMOOI5PP4IUWR4XKHPG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3LYQB3SJMOOI5PP4IUWR4XKHPG/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":"2026-06-09T19:41:15Z","links":{"resolver":"https://pith.science/pith/3LYQB3SJMOOI5PP4IUWR4XKHPG","bundle":"https://pith.science/pith/3LYQB3SJMOOI5PP4IUWR4XKHPG/bundle.json","state":"https://pith.science/pith/3LYQB3SJMOOI5PP4IUWR4XKHPG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3LYQB3SJMOOI5PP4IUWR4XKHPG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:3LYQB3SJMOOI5PP4IUWR4XKHPG","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":"c58ebbccf89f05d34f4ae25ec894eed1f5297a7b279e62ef7341570c2cf0f468","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-04-22T08:01:17Z","title_canon_sha256":"3052f7c9fd990647bba89138e17b1b6cb3150105147a664ddf0b01f6c8752fd7"},"schema_version":"1.0","source":{"id":"1704.06762","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.06762","created_at":"2026-05-18T00:18:31Z"},{"alias_kind":"arxiv_version","alias_value":"1704.06762v4","created_at":"2026-05-18T00:18:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.06762","created_at":"2026-05-18T00:18:31Z"},{"alias_kind":"pith_short_12","alias_value":"3LYQB3SJMOOI","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3LYQB3SJMOOI5PP4","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3LYQB3SJ","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:3203f7251a0f068e50a183a2ec6efb1423a45720385c9bd2ac4cab93c4f3d87d","target":"graph","created_at":"2026-05-18T00:18:31Z","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":"This paper is about models for a vector of probabilities whose elements must have a multiplicative structure and sum to 1 at the same time; in certain applications, as basket analysis, these models may be seen as a constrained version of quasi-independence. After reviewing the basic properties of these models, their geometric features as a curved exponential family are investigated. A new algorithm for computing maximum likelihood estimates is presented and new insights are provided on the underlying geometry. The asymptotic distribution of three statistics for hypothesis testing are derived a","authors_text":"Antonio Forcina","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-04-22T08:01:17Z","title":"Multiplicative models for frequency data, estimation and testing"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.06762","kind":"arxiv","version":4},"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":"sha256:5bb439b7b73fb1462404bd71995e0c40c5f648aad91b9a63c6de49f529327f54","target":"record","created_at":"2026-05-18T00:18:31Z","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":"c58ebbccf89f05d34f4ae25ec894eed1f5297a7b279e62ef7341570c2cf0f468","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-04-22T08:01:17Z","title_canon_sha256":"3052f7c9fd990647bba89138e17b1b6cb3150105147a664ddf0b01f6c8752fd7"},"schema_version":"1.0","source":{"id":"1704.06762","kind":"arxiv","version":4}},"canonical_sha256":"daf100ee49639c8ebdfc452d1e5d4779bddb03459452d5321b6197030a610df5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"daf100ee49639c8ebdfc452d1e5d4779bddb03459452d5321b6197030a610df5","first_computed_at":"2026-05-18T00:18:31.881869Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:31.881869Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8ZB2M7434JRkFBJvOsA4MEPylnbpG2Zl7pjyditXgnMgMbTeP95tmbRP8q+IWsisEMyNio9+RYK660ulLQbNAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:31.882290Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.06762","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5bb439b7b73fb1462404bd71995e0c40c5f648aad91b9a63c6de49f529327f54","sha256:3203f7251a0f068e50a183a2ec6efb1423a45720385c9bd2ac4cab93c4f3d87d"],"state_sha256":"89602a7abdf808e999b993433a00fc9cf309b46a8b1f4928b3fdf71ae53122fd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ENBZC36wpGWblEgIeFDkv/I/A9cV1aqxOOeNyPxBv30ziXKwlAmHWI41jjbpzij3MceqEHq/483KvnQDl1gACA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T19:41:15.865813Z","bundle_sha256":"30a6bddf62c87780eed22133da78d9fc883c6fecc3e5bb4245afe0daa103381e"}}