{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:7D7YIKMWPLHEZQWMP2DGYEEPEE","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":"1d42f2c2757754230f20a8c375e2a000f0a9e00cce5ecec8b095ae0ec76e412f","cross_cats_sorted":["cs.IT","math.IT","stat.AP","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2025-04-22T21:30:25Z","title_canon_sha256":"578ce8ff1dee9a74a0f2e7093d0b79c7cfd24936497daa4517b460bfb27be11f"},"schema_version":"1.0","source":{"id":"2504.16279","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.16279","created_at":"2026-06-12T01:09:08Z"},{"alias_kind":"arxiv_version","alias_value":"2504.16279v2","created_at":"2026-06-12T01:09:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.16279","created_at":"2026-06-12T01:09:08Z"},{"alias_kind":"pith_short_12","alias_value":"7D7YIKMWPLHE","created_at":"2026-06-12T01:09:08Z"},{"alias_kind":"pith_short_16","alias_value":"7D7YIKMWPLHEZQWM","created_at":"2026-06-12T01:09:08Z"},{"alias_kind":"pith_short_8","alias_value":"7D7YIKMW","created_at":"2026-06-12T01:09:08Z"}],"graph_snapshots":[{"event_id":"sha256:33717ab399fea7a3ce38c4524c3038c19d8849ab69195420f8c495977e862a6f","target":"graph","created_at":"2026-06-12T01:09:08Z","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/2504.16279/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper studies the hypothesis testing problem of deciding whether $m \\geq 2$ complete weighted graphs with Gaussian edge weights are mutually correlated after unknown relabelings of their vertices. Under the null model all edge weights are independent standard Gaussians, whereas under the planted model the graphs share a latent vertex alignment and each pair of corresponding edge weights has correlation $\\rho$. For fixed $m$, we identify the sharp information-theoretic threshold for detection. Above the threshold, a generalized likelihood-ratio test achieves strong detection, whereas even ","authors_text":"Bruce Hajek, Taha Ameen","cross_cats":["cs.IT","math.IT","stat.AP","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2025-04-22T21:30:25Z","title":"Sharp Detection Threshold for Correlation among Multiple Unlabeled Gaussian Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.16279","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:b5ce2151861454cc6765b08a433637bdaec13661440708849619956d8f168a34","target":"record","created_at":"2026-06-12T01:09:08Z","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":"1d42f2c2757754230f20a8c375e2a000f0a9e00cce5ecec8b095ae0ec76e412f","cross_cats_sorted":["cs.IT","math.IT","stat.AP","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2025-04-22T21:30:25Z","title_canon_sha256":"578ce8ff1dee9a74a0f2e7093d0b79c7cfd24936497daa4517b460bfb27be11f"},"schema_version":"1.0","source":{"id":"2504.16279","kind":"arxiv","version":2}},"canonical_sha256":"f8ff8429967ace4cc2cc7e866c108f210eca041ff1ec5a185a549ceb37dfc5cc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f8ff8429967ace4cc2cc7e866c108f210eca041ff1ec5a185a549ceb37dfc5cc","first_computed_at":"2026-06-12T01:09:08.177776Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-12T01:09:08.177776Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ukZwVCO91SQrYVQd09ORVsh+8S3M9YlMd8Sp5JbD6YkdAEHy+3iWs373582+aHSsPPyOB1E0EdvDa+IuT4OuDg==","signature_status":"signed_v1","signed_at":"2026-06-12T01:09:08.178924Z","signed_message":"canonical_sha256_bytes"},"source_id":"2504.16279","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b5ce2151861454cc6765b08a433637bdaec13661440708849619956d8f168a34","sha256:33717ab399fea7a3ce38c4524c3038c19d8849ab69195420f8c495977e862a6f"],"state_sha256":"f873383c5371711971c1e324aa4f5199798fc0ee421d9bc14f3fbe772e036e47"}