{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:HXWZ3V65OMQYEGRO24AVBLD3KF","short_pith_number":"pith:HXWZ3V65","schema_version":"1.0","canonical_sha256":"3ded9dd7dd7321821a2ed70150ac7b5162b10e2b93acd14ecaf12502a179d0db","source":{"kind":"arxiv","id":"1007.2315","version":2},"attestation_state":"computed","paper":{"title":"On extracting common random bits from correlated sources","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Andrej Bogdanov, Elchanan Mossel","submitted_at":"2010-07-14T12:46:38Z","abstract_excerpt":"Suppose Alice and Bob receive strings of unbiased independent but noisy bits from some random source. They wish to use their respective strings to extract a common sequence of random bits with high probability but without communicating. How many such bits can they extract? The trivial strategy of outputting the first $k$ bits yields an agreement probability of $(1 - \\eps)^k < 2^{-1.44k\\eps}$, where $\\eps$ is the amount of noise. We show that no strategy can achieve agreement probability better than $2^{-k\\eps/(1 - \\eps)}$.\n  On the other hand, we show that when $k \\geq 10 + 2 (1 - \\eps) / \\eps"},"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":"1007.2315","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-07-14T12:46:38Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"e451339c61ad532c8ba1b7dc75a63a917b6008b950f571647143f4cd3d5908fa","abstract_canon_sha256":"a12664c263655e10938c05fb0f8a4528983dd081ae8bf147de2faff516dbe6b6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:12:32.465956Z","signature_b64":"svOc65RAa+ctUiicOiyR143iLc/8d9ssH83JKbsEPgs7sMfExGBhIGeyPAMdK8eKKOK0wh3E5sd92BBPygOACg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3ded9dd7dd7321821a2ed70150ac7b5162b10e2b93acd14ecaf12502a179d0db","last_reissued_at":"2026-05-18T04:12:32.465424Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:12:32.465424Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On extracting common random bits from correlated sources","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Andrej Bogdanov, Elchanan Mossel","submitted_at":"2010-07-14T12:46:38Z","abstract_excerpt":"Suppose Alice and Bob receive strings of unbiased independent but noisy bits from some random source. They wish to use their respective strings to extract a common sequence of random bits with high probability but without communicating. How many such bits can they extract? The trivial strategy of outputting the first $k$ bits yields an agreement probability of $(1 - \\eps)^k < 2^{-1.44k\\eps}$, where $\\eps$ is the amount of noise. We show that no strategy can achieve agreement probability better than $2^{-k\\eps/(1 - \\eps)}$.\n  On the other hand, we show that when $k \\geq 10 + 2 (1 - \\eps) / \\eps"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.2315","kind":"arxiv","version":2},"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":"1007.2315","created_at":"2026-05-18T04:12:32.465524+00:00"},{"alias_kind":"arxiv_version","alias_value":"1007.2315v2","created_at":"2026-05-18T04:12:32.465524+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.2315","created_at":"2026-05-18T04:12:32.465524+00:00"},{"alias_kind":"pith_short_12","alias_value":"HXWZ3V65OMQY","created_at":"2026-05-18T12:26:07.630475+00:00"},{"alias_kind":"pith_short_16","alias_value":"HXWZ3V65OMQYEGRO","created_at":"2026-05-18T12:26:07.630475+00:00"},{"alias_kind":"pith_short_8","alias_value":"HXWZ3V65","created_at":"2026-05-18T12:26:07.630475+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/HXWZ3V65OMQYEGRO24AVBLD3KF","json":"https://pith.science/pith/HXWZ3V65OMQYEGRO24AVBLD3KF.json","graph_json":"https://pith.science/api/pith-number/HXWZ3V65OMQYEGRO24AVBLD3KF/graph.json","events_json":"https://pith.science/api/pith-number/HXWZ3V65OMQYEGRO24AVBLD3KF/events.json","paper":"https://pith.science/paper/HXWZ3V65"},"agent_actions":{"view_html":"https://pith.science/pith/HXWZ3V65OMQYEGRO24AVBLD3KF","download_json":"https://pith.science/pith/HXWZ3V65OMQYEGRO24AVBLD3KF.json","view_paper":"https://pith.science/paper/HXWZ3V65","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1007.2315&json=true","fetch_graph":"https://pith.science/api/pith-number/HXWZ3V65OMQYEGRO24AVBLD3KF/graph.json","fetch_events":"https://pith.science/api/pith-number/HXWZ3V65OMQYEGRO24AVBLD3KF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HXWZ3V65OMQYEGRO24AVBLD3KF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HXWZ3V65OMQYEGRO24AVBLD3KF/action/storage_attestation","attest_author":"https://pith.science/pith/HXWZ3V65OMQYEGRO24AVBLD3KF/action/author_attestation","sign_citation":"https://pith.science/pith/HXWZ3V65OMQYEGRO24AVBLD3KF/action/citation_signature","submit_replication":"https://pith.science/pith/HXWZ3V65OMQYEGRO24AVBLD3KF/action/replication_record"}},"created_at":"2026-05-18T04:12:32.465524+00:00","updated_at":"2026-05-18T04:12:32.465524+00:00"}