{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:4FJJCDJVOMS57KJYFZ37GH2CIE","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":"b9fbd5f8a5f45dde45e56226624af8a2f49c0f9f30638759386c196cced3fd2a","cross_cats_sorted":["cond-mat.stat-mech","physics.soc-ph","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2013-12-02T21:18:53Z","title_canon_sha256":"3d624c978f0fa402eaf286fe21e349216e29332b625ec72f1042f5c6a282056a"},"schema_version":"1.0","source":{"id":"1312.0631","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.0631","created_at":"2026-05-18T01:45:59Z"},{"alias_kind":"arxiv_version","alias_value":"1312.0631v1","created_at":"2026-05-18T01:45:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.0631","created_at":"2026-05-18T01:45:59Z"},{"alias_kind":"pith_short_12","alias_value":"4FJJCDJVOMS5","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"4FJJCDJVOMS57KJY","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"4FJJCDJV","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:86e044ce0940eb81a756e8aa02006e1ad81cf50e65b6fcb9e5dbcd50fbc984c9","target":"graph","created_at":"2026-05-18T01:45:59Z","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":"Recently, it was shown that there is a phase transition in the community detection problem. This transition was first computed using the cavity method, and has been proved rigorously in the case of $q=2$ groups. However, analytic calculations using the cavity method are challenging since they require us to understand probability distributions of messages. We study analogous transitions in so-called \"zero-temperature inference\" model, where this distribution is supported only on the most-likely messages. Furthermore, whenever several messages are equally likely, we break the tie by choosing amo","authors_text":"Aram Galstyan, Armen E. Allahverdyan, Cristopher Moore, Greg Ver Steeg","cross_cats":["cond-mat.stat-mech","physics.soc-ph","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2013-12-02T21:18:53Z","title":"Phase Transitions in Community Detection: A Solvable Toy Model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.0631","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:b53b8357d766e3e0698e46cdddac0512ec61798d69733f3a6f7072bcb8aeeccb","target":"record","created_at":"2026-05-18T01:45:59Z","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":"b9fbd5f8a5f45dde45e56226624af8a2f49c0f9f30638759386c196cced3fd2a","cross_cats_sorted":["cond-mat.stat-mech","physics.soc-ph","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2013-12-02T21:18:53Z","title_canon_sha256":"3d624c978f0fa402eaf286fe21e349216e29332b625ec72f1042f5c6a282056a"},"schema_version":"1.0","source":{"id":"1312.0631","kind":"arxiv","version":1}},"canonical_sha256":"e152910d357325dfa9382e77f31f42413e1aa01d5b9ed3d9d630f854f67e86f6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e152910d357325dfa9382e77f31f42413e1aa01d5b9ed3d9d630f854f67e86f6","first_computed_at":"2026-05-18T01:45:59.570162Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:45:59.570162Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mCphO8jH/0zqnvnQujh5a+OkvyVBnpPsfmpR1EuxpAtBcqyrAoe+Q2FVSkKmhtzMi1GKP2hhE0zSZFynPslkAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:45:59.570719Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.0631","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b53b8357d766e3e0698e46cdddac0512ec61798d69733f3a6f7072bcb8aeeccb","sha256:86e044ce0940eb81a756e8aa02006e1ad81cf50e65b6fcb9e5dbcd50fbc984c9"],"state_sha256":"05cc91cd5ac2aa0c0e3c8ee662e8e8dba38f88348e37fc46d3e77d90074a2366"}