{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:KIYVYZUVJUA25QOMEFXCDAMLOU","short_pith_number":"pith:KIYVYZUV","schema_version":"1.0","canonical_sha256":"52315c66954d01aec1cc216e21818b752deb9f343688868a243ae0cdd562954a","source":{"kind":"arxiv","id":"1010.2997","version":1},"attestation_state":"computed","paper":{"title":"Finding Hidden Cliques in Linear Time with High Probability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.PR"],"primary_cat":"math.CO","authors_text":"Ori Gurel-Gurevich, Yael Dekel, Yuval Peres","submitted_at":"2010-10-14T18:08:29Z","abstract_excerpt":"We are given a graph $G$ with $n$ vertices, where a random subset of $k$ vertices has been made into a clique, and the remaining edges are chosen independently with probability $\\tfrac12$. This random graph model is denoted $G(n,\\tfrac12,k)$. The hidden clique problem is to design an algorithm that finds the $k$-clique in polynomial time with high probability. An algorithm due to Alon, Krivelevich and Sudakov uses spectral techniques to find the hidden clique with high probability when $k = c \\sqrt{n}$ for a sufficiently large constant $c > 0$. Recently, an algorithm that solves the same probl"},"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":"1010.2997","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-10-14T18:08:29Z","cross_cats_sorted":["cs.DM","math.PR"],"title_canon_sha256":"7d22b68f571ec6af41539451aa0b2e2fac2af0e4af6c7af1bdf50573143c8b8f","abstract_canon_sha256":"00ced1fe75d609d3cd493b9841a7d967d11004f724163564778daffde8768d4d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:39:18.683673Z","signature_b64":"Xm6uUxrzh3O5nftmgWCTRzQeNIek2qoBoxz0+omGHg9QL7NmICyKrViWD8MOJDDdj+9k98WFsauPN0TUKmPMDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"52315c66954d01aec1cc216e21818b752deb9f343688868a243ae0cdd562954a","last_reissued_at":"2026-05-18T04:39:18.682998Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:39:18.682998Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Finding Hidden Cliques in Linear Time with High Probability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.PR"],"primary_cat":"math.CO","authors_text":"Ori Gurel-Gurevich, Yael Dekel, Yuval Peres","submitted_at":"2010-10-14T18:08:29Z","abstract_excerpt":"We are given a graph $G$ with $n$ vertices, where a random subset of $k$ vertices has been made into a clique, and the remaining edges are chosen independently with probability $\\tfrac12$. This random graph model is denoted $G(n,\\tfrac12,k)$. The hidden clique problem is to design an algorithm that finds the $k$-clique in polynomial time with high probability. An algorithm due to Alon, Krivelevich and Sudakov uses spectral techniques to find the hidden clique with high probability when $k = c \\sqrt{n}$ for a sufficiently large constant $c > 0$. Recently, an algorithm that solves the same probl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.2997","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":""},"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":"1010.2997","created_at":"2026-05-18T04:39:18.683112+00:00"},{"alias_kind":"arxiv_version","alias_value":"1010.2997v1","created_at":"2026-05-18T04:39:18.683112+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.2997","created_at":"2026-05-18T04:39:18.683112+00:00"},{"alias_kind":"pith_short_12","alias_value":"KIYVYZUVJUA2","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_16","alias_value":"KIYVYZUVJUA25QOM","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_8","alias_value":"KIYVYZUV","created_at":"2026-05-18T12:26:09.077623+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/KIYVYZUVJUA25QOMEFXCDAMLOU","json":"https://pith.science/pith/KIYVYZUVJUA25QOMEFXCDAMLOU.json","graph_json":"https://pith.science/api/pith-number/KIYVYZUVJUA25QOMEFXCDAMLOU/graph.json","events_json":"https://pith.science/api/pith-number/KIYVYZUVJUA25QOMEFXCDAMLOU/events.json","paper":"https://pith.science/paper/KIYVYZUV"},"agent_actions":{"view_html":"https://pith.science/pith/KIYVYZUVJUA25QOMEFXCDAMLOU","download_json":"https://pith.science/pith/KIYVYZUVJUA25QOMEFXCDAMLOU.json","view_paper":"https://pith.science/paper/KIYVYZUV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1010.2997&json=true","fetch_graph":"https://pith.science/api/pith-number/KIYVYZUVJUA25QOMEFXCDAMLOU/graph.json","fetch_events":"https://pith.science/api/pith-number/KIYVYZUVJUA25QOMEFXCDAMLOU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KIYVYZUVJUA25QOMEFXCDAMLOU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KIYVYZUVJUA25QOMEFXCDAMLOU/action/storage_attestation","attest_author":"https://pith.science/pith/KIYVYZUVJUA25QOMEFXCDAMLOU/action/author_attestation","sign_citation":"https://pith.science/pith/KIYVYZUVJUA25QOMEFXCDAMLOU/action/citation_signature","submit_replication":"https://pith.science/pith/KIYVYZUVJUA25QOMEFXCDAMLOU/action/replication_record"}},"created_at":"2026-05-18T04:39:18.683112+00:00","updated_at":"2026-05-18T04:39:18.683112+00:00"}