{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:3JXTBXWUWDVX4AWCLQEYUIOLA5","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":"ee171f31847d9c67fcf6a90b1b87fbbebb5ff30a6047ec8196e369ea7d725053","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-06-15T07:19:33Z","title_canon_sha256":"3526689a771c0664641193ee46783299eb2cc19cae155140bfba03a3e003dabb"},"schema_version":"1.0","source":{"id":"2506.12752","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.12752","created_at":"2026-07-05T11:21:58Z"},{"alias_kind":"arxiv_version","alias_value":"2506.12752v1","created_at":"2026-07-05T11:21:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.12752","created_at":"2026-07-05T11:21:58Z"},{"alias_kind":"pith_short_12","alias_value":"3JXTBXWUWDVX","created_at":"2026-07-05T11:21:58Z"},{"alias_kind":"pith_short_16","alias_value":"3JXTBXWUWDVX4AWC","created_at":"2026-07-05T11:21:58Z"},{"alias_kind":"pith_short_8","alias_value":"3JXTBXWU","created_at":"2026-07-05T11:21:58Z"}],"graph_snapshots":[{"event_id":"sha256:2608cf1ad416abb943fb694373b53ebcbc6012b2c05fea492d310e61bf1a1026","target":"graph","created_at":"2026-07-05T11:21:58Z","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/2506.12752/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Consider a pair of correlated Erd\\H{o}s-R\\'enyi graphs $\\mathcal G(n,\\tfrac{\\lambda}{n};s)$ that are subsampled from a common parent Erd\\H{o}s-R\\'enyi graph with average degree $\\lambda$ and subsampling probability $s$. We establish a sharp information-theoretic threshold for the detection problem between this model and two independent Erd\\H{o}s-R\\'enyi graphs $\\mathcal G(n,\\tfrac{\\lambda}{n})$, showing that strong detection is information-theoretically possible if and only if $s>\\min\\{ \\tfrac{1}{\\sqrt{\\lambda}}, \\sqrt{\\alpha} \\}$ where $\\alpha\\approx 0.338$ is the Otter's constant. Our result","authors_text":"Chenxu Feng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-06-15T07:19:33Z","title":"Strong Detection Threshold for Correlated Erd\\H{o}s-R\\'enyi Graphs with Constant Average Degree"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.12752","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:c3f8ea66e63da0727b9d19f914e3cb70cd40f57106fa14bdc0977dcb7eb8ac6b","target":"record","created_at":"2026-07-05T11:21:58Z","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":"ee171f31847d9c67fcf6a90b1b87fbbebb5ff30a6047ec8196e369ea7d725053","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-06-15T07:19:33Z","title_canon_sha256":"3526689a771c0664641193ee46783299eb2cc19cae155140bfba03a3e003dabb"},"schema_version":"1.0","source":{"id":"2506.12752","kind":"arxiv","version":1}},"canonical_sha256":"da6f30ded4b0eb7e02c25c098a21cb076f4c9495ae5fc6a1566ecf97effaa1a1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"da6f30ded4b0eb7e02c25c098a21cb076f4c9495ae5fc6a1566ecf97effaa1a1","first_computed_at":"2026-07-05T11:21:58.902547Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:21:58.902547Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gqC1eiVWbRhp0gKGGkIc78aklxSvvFJgPZnKuzgZnpVqTMar99ld54/EE2bUBkleoJENz300WAsHziUPc3UHCA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:21:58.903255Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.12752","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c3f8ea66e63da0727b9d19f914e3cb70cd40f57106fa14bdc0977dcb7eb8ac6b","sha256:2608cf1ad416abb943fb694373b53ebcbc6012b2c05fea492d310e61bf1a1026"],"state_sha256":"8b35f97d5b11cda68417e347c5635c48e2789c1b50458f745faa9f907c40e6f9"}