{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:3JXTBXWUWDVX4AWCLQEYUIOLA5","short_pith_number":"pith:3JXTBXWU","schema_version":"1.0","canonical_sha256":"da6f30ded4b0eb7e02c25c098a21cb076f4c9495ae5fc6a1566ecf97effaa1a1","source":{"kind":"arxiv","id":"2506.12752","version":1},"attestation_state":"computed","paper":{"title":"Strong Detection Threshold for Correlated Erd\\H{o}s-R\\'enyi Graphs with Constant Average Degree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Chenxu Feng","submitted_at":"2025-06-15T07:19:33Z","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2506.12752","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-06-15T07:19:33Z","cross_cats_sorted":[],"title_canon_sha256":"3526689a771c0664641193ee46783299eb2cc19cae155140bfba03a3e003dabb","abstract_canon_sha256":"ee171f31847d9c67fcf6a90b1b87fbbebb5ff30a6047ec8196e369ea7d725053"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:21:58.903255Z","signature_b64":"gqC1eiVWbRhp0gKGGkIc78aklxSvvFJgPZnKuzgZnpVqTMar99ld54/EE2bUBkleoJENz300WAsHziUPc3UHCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"da6f30ded4b0eb7e02c25c098a21cb076f4c9495ae5fc6a1566ecf97effaa1a1","last_reissued_at":"2026-07-05T11:21:58.902547Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:21:58.902547Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Strong Detection Threshold for Correlated Erd\\H{o}s-R\\'enyi Graphs with Constant Average Degree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Chenxu Feng","submitted_at":"2025-06-15T07:19:33Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.12752","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.12752/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2506.12752","created_at":"2026-07-05T11:21:58.902641+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.12752v1","created_at":"2026-07-05T11:21:58.902641+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.12752","created_at":"2026-07-05T11:21:58.902641+00:00"},{"alias_kind":"pith_short_12","alias_value":"3JXTBXWUWDVX","created_at":"2026-07-05T11:21:58.902641+00:00"},{"alias_kind":"pith_short_16","alias_value":"3JXTBXWUWDVX4AWC","created_at":"2026-07-05T11:21:58.902641+00:00"},{"alias_kind":"pith_short_8","alias_value":"3JXTBXWU","created_at":"2026-07-05T11:21:58.902641+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3JXTBXWUWDVX4AWCLQEYUIOLA5","json":"https://pith.science/pith/3JXTBXWUWDVX4AWCLQEYUIOLA5.json","graph_json":"https://pith.science/api/pith-number/3JXTBXWUWDVX4AWCLQEYUIOLA5/graph.json","events_json":"https://pith.science/api/pith-number/3JXTBXWUWDVX4AWCLQEYUIOLA5/events.json","paper":"https://pith.science/paper/3JXTBXWU"},"agent_actions":{"view_html":"https://pith.science/pith/3JXTBXWUWDVX4AWCLQEYUIOLA5","download_json":"https://pith.science/pith/3JXTBXWUWDVX4AWCLQEYUIOLA5.json","view_paper":"https://pith.science/paper/3JXTBXWU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.12752&json=true","fetch_graph":"https://pith.science/api/pith-number/3JXTBXWUWDVX4AWCLQEYUIOLA5/graph.json","fetch_events":"https://pith.science/api/pith-number/3JXTBXWUWDVX4AWCLQEYUIOLA5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3JXTBXWUWDVX4AWCLQEYUIOLA5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3JXTBXWUWDVX4AWCLQEYUIOLA5/action/storage_attestation","attest_author":"https://pith.science/pith/3JXTBXWUWDVX4AWCLQEYUIOLA5/action/author_attestation","sign_citation":"https://pith.science/pith/3JXTBXWUWDVX4AWCLQEYUIOLA5/action/citation_signature","submit_replication":"https://pith.science/pith/3JXTBXWUWDVX4AWCLQEYUIOLA5/action/replication_record"}},"created_at":"2026-07-05T11:21:58.902641+00:00","updated_at":"2026-07-05T11:21:58.902641+00:00"}