{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:MX5KPOECGTCLML765MQMJTQREB","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":"cdaba7c62a56fbc7483ae68ed13c0e9bc9948488aedbaebcf0359999e439244a","cross_cats_sorted":["cs.IT","math.IT","stat.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2012-06-22T19:28:39Z","title_canon_sha256":"6bac3890de7fc7b9931a64a72b46b71b67bc3259555bb54f4d18b24322ac9896"},"schema_version":"1.0","source":{"id":"1206.5232","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.5232","created_at":"2026-05-18T03:43:52Z"},{"alias_kind":"arxiv_version","alias_value":"1206.5232v2","created_at":"2026-05-18T03:43:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.5232","created_at":"2026-05-18T03:43:52Z"},{"alias_kind":"pith_short_12","alias_value":"MX5KPOECGTCL","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"MX5KPOECGTCLML76","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"MX5KPOEC","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:1b22a256492c2aaad23644ee6bd2d60c23c1f8eb31c6ca3f318d971e252da684","target":"graph","created_at":"2026-05-18T03:43:52Z","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 partition function of a factor graph can sometimes be accurately estimated by Monte Carlo methods. In this paper, such methods are extended to factor graphs with negative and complex factors.","authors_text":"Hans-Andrea Loeliger, Mehdi Molkaraie","cross_cats":["cs.IT","math.IT","stat.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2012-06-22T19:28:39Z","title":"Extending Monte Carlo Methods to Factor Graphs with Negative and Complex Factors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.5232","kind":"arxiv","version":2},"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":"sha256:3dbebff872bf7bc18f492056d2766f0fd1115af27ba89f228dafdf6c7223a884","target":"record","created_at":"2026-05-18T03:43:52Z","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":"cdaba7c62a56fbc7483ae68ed13c0e9bc9948488aedbaebcf0359999e439244a","cross_cats_sorted":["cs.IT","math.IT","stat.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2012-06-22T19:28:39Z","title_canon_sha256":"6bac3890de7fc7b9931a64a72b46b71b67bc3259555bb54f4d18b24322ac9896"},"schema_version":"1.0","source":{"id":"1206.5232","kind":"arxiv","version":2}},"canonical_sha256":"65faa7b88234c4b62ffeeb20c4ce11207195ed675bd326cc2be5dffbeaf0f3aa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"65faa7b88234c4b62ffeeb20c4ce11207195ed675bd326cc2be5dffbeaf0f3aa","first_computed_at":"2026-05-18T03:43:52.190934Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:43:52.190934Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"y5w7YX2f//Fn7JA1rLtJseCkJH+EeT8YUbMoTp5ROQVtztyh2Rn691X/QY9Alvd+HhgSyBSStzlA21LYg/hfAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:43:52.191747Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.5232","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3dbebff872bf7bc18f492056d2766f0fd1115af27ba89f228dafdf6c7223a884","sha256:1b22a256492c2aaad23644ee6bd2d60c23c1f8eb31c6ca3f318d971e252da684"],"state_sha256":"dfa8df188175b92c6747c8a9321e9e072a514627f125a109d589641e9be95e00"}