{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:AYPFS3VX72GHUQM32BPFQJ6XES","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":"887f885b7e2aafd4fe91164a9082b07cb7f19a6141d0f553ead570be8ea0045f","cross_cats_sorted":["stat.TH"],"license":"","primary_cat":"math.ST","submitted_at":"2007-07-25T18:06:02Z","title_canon_sha256":"2038b7ed907009a750375a012347510cecf27916290f01fc065063d3ea51b294"},"schema_version":"1.0","source":{"id":"0707.3794","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0707.3794","created_at":"2026-07-04T17:22:44Z"},{"alias_kind":"arxiv_version","alias_value":"0707.3794v1","created_at":"2026-07-04T17:22:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0707.3794","created_at":"2026-07-04T17:22:44Z"},{"alias_kind":"pith_short_12","alias_value":"AYPFS3VX72GH","created_at":"2026-07-04T17:22:44Z"},{"alias_kind":"pith_short_16","alias_value":"AYPFS3VX72GHUQM3","created_at":"2026-07-04T17:22:44Z"},{"alias_kind":"pith_short_8","alias_value":"AYPFS3VX","created_at":"2026-07-04T17:22:44Z"}],"graph_snapshots":[{"event_id":"sha256:862cedefbb19d39cab14406296dba46bdde8762f6c83074b7bc781c709ece5b1","target":"graph","created_at":"2026-07-04T17:22:44Z","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/0707.3794/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Log-linear models are a classical tool for the analysis of contingency tables. In particular, the subclass of graphical log-linear models provides a general framework for modelling conditional independences. However, with the exception of special structures, marginal independence hypotheses cannot be accommodated by these traditional models. Focusing on binary variables, we present a model class that provides a framework for modelling marginal independences in contingency tables. The approach taken is graphical and draws on analogies to multivariate Gaussian models for marginal independence. F","authors_text":"Mathias Drton, Thomas S. Richardson","cross_cats":["stat.TH"],"headline":"","license":"","primary_cat":"math.ST","submitted_at":"2007-07-25T18:06:02Z","title":"Binary Models for Marginal Independence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0707.3794","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":"sha256:75d66a47b9b970197d45455057ae0fd00855cf7be0c435d02d50eda7336da466","target":"record","created_at":"2026-07-04T17:22:44Z","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":"887f885b7e2aafd4fe91164a9082b07cb7f19a6141d0f553ead570be8ea0045f","cross_cats_sorted":["stat.TH"],"license":"","primary_cat":"math.ST","submitted_at":"2007-07-25T18:06:02Z","title_canon_sha256":"2038b7ed907009a750375a012347510cecf27916290f01fc065063d3ea51b294"},"schema_version":"1.0","source":{"id":"0707.3794","kind":"arxiv","version":1}},"canonical_sha256":"061e596eb7fe8c7a419bd05e5827d72488c7931f2e33abfd6628b008c7d895e5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"061e596eb7fe8c7a419bd05e5827d72488c7931f2e33abfd6628b008c7d895e5","first_computed_at":"2026-07-04T17:22:44.932902Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T17:22:44.932902Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OiPbGTSie3fRktwOazwnW01DnmBsmy1XQVlEECsAEZV24tWzcTcAeHGbtfYchN1QccR7y2LFLFTVpSEnzHA2BA==","signature_status":"signed_v1","signed_at":"2026-07-04T17:22:44.933256Z","signed_message":"canonical_sha256_bytes"},"source_id":"0707.3794","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:75d66a47b9b970197d45455057ae0fd00855cf7be0c435d02d50eda7336da466","sha256:862cedefbb19d39cab14406296dba46bdde8762f6c83074b7bc781c709ece5b1"],"state_sha256":"bca46af85a8a5e3dc6707d2334f9f83fca312c67d8278f1b5249d2e3cf60032a"}