{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:AURKVJBS6SGCQTEMRMMMEKOO74","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":"7fab0a6b7031922eb93e85f947727bbe1615c2fd0ad71b604986997173c257ba","cross_cats_sorted":["stat.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2016-01-11T12:05:01Z","title_canon_sha256":"6b8fd30d8aa0d1077d7f7e1715bca86c9fc56034ae8660c3540cd52a8de2d473"},"schema_version":"1.0","source":{"id":"1601.02410","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.02410","created_at":"2026-05-18T01:23:06Z"},{"alias_kind":"arxiv_version","alias_value":"1601.02410v1","created_at":"2026-05-18T01:23:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.02410","created_at":"2026-05-18T01:23:06Z"},{"alias_kind":"pith_short_12","alias_value":"AURKVJBS6SGC","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"AURKVJBS6SGCQTEM","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"AURKVJBS","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:ba3bca0013ca3b188fc760b792125e156725cf6c6d5bfbc20500f0d32cb658fc","target":"graph","created_at":"2026-05-18T01:23:06Z","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 pseudo likelihood method of Besag(1974), has remained a popular method for estimating Markov random field on a very large lattice, despite various documented deficiencies. This is partly because it remains the only computationally tractable method for large lattices. We introduce a novel method to estimate Markov random fields defined on a regular lattice. The method takes advantage of conditional independence structures and recursively decomposes a large lattice into smaller sublattices. An approximation is made at each decomposition. Doing so completely avoids the need to compute the tro","authors_text":"Wanchuang Zhu, Yanan Fan","cross_cats":["stat.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2016-01-11T12:05:01Z","title":"A novel approach for Markov Random Field with intractable normalising constant on large lattices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.02410","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:ea8c34015e1c42d97ef5e7d1c372d3bd3976ff8caffd8617b4963e989cc07749","target":"record","created_at":"2026-05-18T01:23:06Z","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":"7fab0a6b7031922eb93e85f947727bbe1615c2fd0ad71b604986997173c257ba","cross_cats_sorted":["stat.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2016-01-11T12:05:01Z","title_canon_sha256":"6b8fd30d8aa0d1077d7f7e1715bca86c9fc56034ae8660c3540cd52a8de2d473"},"schema_version":"1.0","source":{"id":"1601.02410","kind":"arxiv","version":1}},"canonical_sha256":"0522aaa432f48c284c8c8b18c229ceff2d63c89224173e24d666968714315261","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0522aaa432f48c284c8c8b18c229ceff2d63c89224173e24d666968714315261","first_computed_at":"2026-05-18T01:23:06.518784Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:06.518784Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hDGTlUbBtEpdae9sw9z7YjcpgKDyuBPlSasgxKEbptCdLxQoe5gG9hl8tN4trSZNVQFJp28TPcFd0xuJlQrSCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:06.519200Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.02410","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ea8c34015e1c42d97ef5e7d1c372d3bd3976ff8caffd8617b4963e989cc07749","sha256:ba3bca0013ca3b188fc760b792125e156725cf6c6d5bfbc20500f0d32cb658fc"],"state_sha256":"67a11bc0ae6382872f8bcde9c663e1eef29bf6d77d5c70e8f1cc7937f9a3143e"}