{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:MU72TNMJBZ5U6KIWPXMRW2ZGGZ","short_pith_number":"pith:MU72TNMJ","schema_version":"1.0","canonical_sha256":"653fa9b5890e7b4f29167dd91b6b2636420973eb234f6b0d41db8cd15459be71","source":{"kind":"arxiv","id":"1207.6260","version":1},"attestation_state":"computed","paper":{"title":"Sparse extractor families for all the entropy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CR"],"primary_cat":"cs.CC","authors_text":"Andrej Bogdanov, Siyao Guo","submitted_at":"2012-07-26T13:00:44Z","abstract_excerpt":"We consider the problem of extracting entropy by sparse transformations, namely functions with a small number of overall input-output dependencies. In contrast to previous works, we seek extractors for essentially all the entropy without any assumption on the underlying distribution beyond a min-entropy requirement. We give two simple constructions of sparse extractor families, which are collections of sparse functions such that for any distribution X on inputs of sufficiently high min-entropy, the output of most functions from the collection on a random input chosen from X is statistically cl"},"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":"1207.6260","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2012-07-26T13:00:44Z","cross_cats_sorted":["cs.CR"],"title_canon_sha256":"dae64f36f31f23426d3799db70a2aa4144ae4ecd938e70dd600fd3bc72357857","abstract_canon_sha256":"9a9c782cd9cd75904c976f48047fe5ee84b0d32cb124d7627d333517007d5d1f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:50:08.324970Z","signature_b64":"8N49sUmOjQAQZYho/RSP8h/JsMD7j1gBBHhn1fo8AssynaEc+SBoupyG3BAksqS3/NF8+drPAaGxVSmHG8oeAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"653fa9b5890e7b4f29167dd91b6b2636420973eb234f6b0d41db8cd15459be71","last_reissued_at":"2026-05-18T03:50:08.324105Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:50:08.324105Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sparse extractor families for all the entropy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CR"],"primary_cat":"cs.CC","authors_text":"Andrej Bogdanov, Siyao Guo","submitted_at":"2012-07-26T13:00:44Z","abstract_excerpt":"We consider the problem of extracting entropy by sparse transformations, namely functions with a small number of overall input-output dependencies. In contrast to previous works, we seek extractors for essentially all the entropy without any assumption on the underlying distribution beyond a min-entropy requirement. We give two simple constructions of sparse extractor families, which are collections of sparse functions such that for any distribution X on inputs of sufficiently high min-entropy, the output of most functions from the collection on a random input chosen from X is statistically cl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.6260","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":"1207.6260","created_at":"2026-05-18T03:50:08.324257+00:00"},{"alias_kind":"arxiv_version","alias_value":"1207.6260v1","created_at":"2026-05-18T03:50:08.324257+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.6260","created_at":"2026-05-18T03:50:08.324257+00:00"},{"alias_kind":"pith_short_12","alias_value":"MU72TNMJBZ5U","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_16","alias_value":"MU72TNMJBZ5U6KIW","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_8","alias_value":"MU72TNMJ","created_at":"2026-05-18T12:27:14.488303+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/MU72TNMJBZ5U6KIWPXMRW2ZGGZ","json":"https://pith.science/pith/MU72TNMJBZ5U6KIWPXMRW2ZGGZ.json","graph_json":"https://pith.science/api/pith-number/MU72TNMJBZ5U6KIWPXMRW2ZGGZ/graph.json","events_json":"https://pith.science/api/pith-number/MU72TNMJBZ5U6KIWPXMRW2ZGGZ/events.json","paper":"https://pith.science/paper/MU72TNMJ"},"agent_actions":{"view_html":"https://pith.science/pith/MU72TNMJBZ5U6KIWPXMRW2ZGGZ","download_json":"https://pith.science/pith/MU72TNMJBZ5U6KIWPXMRW2ZGGZ.json","view_paper":"https://pith.science/paper/MU72TNMJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1207.6260&json=true","fetch_graph":"https://pith.science/api/pith-number/MU72TNMJBZ5U6KIWPXMRW2ZGGZ/graph.json","fetch_events":"https://pith.science/api/pith-number/MU72TNMJBZ5U6KIWPXMRW2ZGGZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MU72TNMJBZ5U6KIWPXMRW2ZGGZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MU72TNMJBZ5U6KIWPXMRW2ZGGZ/action/storage_attestation","attest_author":"https://pith.science/pith/MU72TNMJBZ5U6KIWPXMRW2ZGGZ/action/author_attestation","sign_citation":"https://pith.science/pith/MU72TNMJBZ5U6KIWPXMRW2ZGGZ/action/citation_signature","submit_replication":"https://pith.science/pith/MU72TNMJBZ5U6KIWPXMRW2ZGGZ/action/replication_record"}},"created_at":"2026-05-18T03:50:08.324257+00:00","updated_at":"2026-05-18T03:50:08.324257+00:00"}