{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:Y7BC6KRM3DAWAO7DHVCWVMI6IJ","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":"5c5fee61019cf2a27f497afc52636bdf5fd844a98ff95e5a9d6db862d040abc1","cross_cats_sorted":["cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2012-10-27T21:29:23Z","title_canon_sha256":"8bf647375043c00c0ed844c10917d0a95ff077d7045231cc7571893e4a639952"},"schema_version":"1.0","source":{"id":"1210.7375","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.7375","created_at":"2026-05-18T02:49:03Z"},{"alias_kind":"arxiv_version","alias_value":"1210.7375v4","created_at":"2026-05-18T02:49:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.7375","created_at":"2026-05-18T02:49:03Z"},{"alias_kind":"pith_short_12","alias_value":"Y7BC6KRM3DAW","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"Y7BC6KRM3DAWAO7D","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"Y7BC6KRM","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:c5ff6d1eba44c1b230c32e89596d67eca72040c7e82e71f17e01a3a649157f61","target":"graph","created_at":"2026-05-18T02:49:03Z","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":"We define a general class of network formation models, Statistical Exponential Random Graph Models (SERGMs), that nest standard exponential random graph models (ERGMs) as a special case. We provide the first general results on when these models' (including ERGMs) parameters estimated from the observation of a single network are consistent (i.e., become accurate as the number of nodes grows). Next, addressing the problem that standard techniques of estimating ERGMs have been shown to have exponentially slow mixing times for many specifications, we show that by reformulating network formation as","authors_text":"Arun G. Chandrasekhar, Matthew O. Jackson","cross_cats":["cs.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2012-10-27T21:29:23Z","title":"Tractable and Consistent Random Graph Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.7375","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":"sha256:916419c3479ac1473f738f5812166733643f58953eb401a100900de42c2d7999","target":"record","created_at":"2026-05-18T02:49:03Z","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":"5c5fee61019cf2a27f497afc52636bdf5fd844a98ff95e5a9d6db862d040abc1","cross_cats_sorted":["cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2012-10-27T21:29:23Z","title_canon_sha256":"8bf647375043c00c0ed844c10917d0a95ff077d7045231cc7571893e4a639952"},"schema_version":"1.0","source":{"id":"1210.7375","kind":"arxiv","version":4}},"canonical_sha256":"c7c22f2a2cd8c1603be33d456ab11e4251e558291cad9ebd0c125f1ebb6ae5b2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c7c22f2a2cd8c1603be33d456ab11e4251e558291cad9ebd0c125f1ebb6ae5b2","first_computed_at":"2026-05-18T02:49:03.407836Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:49:03.407836Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NFc57A+R8HJGHShJp5LwY2guxd6xMoTdXUOk2CihfIdvAXK5MvXunVU/LQ9/gzqHvpzvTd6ZJE2MbgVhfaeNAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:49:03.408264Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.7375","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:916419c3479ac1473f738f5812166733643f58953eb401a100900de42c2d7999","sha256:c5ff6d1eba44c1b230c32e89596d67eca72040c7e82e71f17e01a3a649157f61"],"state_sha256":"c068b91cb2da8ebc86ee27b93c3ed2e07d6ccbbab02b020440eed7faf25a0dfa"}