{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:472R7V44ODIZ2RQBICKT2SWC5Q","short_pith_number":"pith:472R7V44","canonical_record":{"source":{"id":"1204.6696","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2012-04-30T16:42:34Z","cross_cats_sorted":[],"title_canon_sha256":"73407c37f3aadf75b752bc8c94025f13dbf868b3d0e60114532df9a7acc4294a","abstract_canon_sha256":"57679a9631c8b7727704c4774f73dfed97d23c0dfa04b1116e165a996e507418"},"schema_version":"1.0"},"canonical_sha256":"e7f51fd79c70d19d460140953d4ac2ec358b2323755c377a4bdc83bb484ab7a1","source":{"kind":"arxiv","id":"1204.6696","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.6696","created_at":"2026-05-18T03:56:44Z"},{"alias_kind":"arxiv_version","alias_value":"1204.6696v1","created_at":"2026-05-18T03:56:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.6696","created_at":"2026-05-18T03:56:44Z"},{"alias_kind":"pith_short_12","alias_value":"472R7V44ODIZ","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"472R7V44ODIZ2RQB","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"472R7V44","created_at":"2026-05-18T12:26:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:472R7V44ODIZ2RQBICKT2SWC5Q","target":"record","payload":{"canonical_record":{"source":{"id":"1204.6696","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2012-04-30T16:42:34Z","cross_cats_sorted":[],"title_canon_sha256":"73407c37f3aadf75b752bc8c94025f13dbf868b3d0e60114532df9a7acc4294a","abstract_canon_sha256":"57679a9631c8b7727704c4774f73dfed97d23c0dfa04b1116e165a996e507418"},"schema_version":"1.0"},"canonical_sha256":"e7f51fd79c70d19d460140953d4ac2ec358b2323755c377a4bdc83bb484ab7a1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:56:44.104024Z","signature_b64":"NvkGOnGsUh63Cwk6C+ogTTDuQ5V5eJt8kAq0EhVxvOp3f2jQsl6DUHT3zZz4b2zT/sOygMLfSm2g3xyMvDllBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e7f51fd79c70d19d460140953d4ac2ec358b2323755c377a4bdc83bb484ab7a1","last_reissued_at":"2026-05-18T03:56:44.103301Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:56:44.103301Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1204.6696","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:56:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FrbJ+pRmIcIKcYvVbfRaXuXzeAj4N7bbP4g2B4itrxjr4tz+6ee+LagvDsctwI+88zDpVXKtTQusXTwqHIR4AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T01:59:35.147663Z"},"content_sha256":"f75991965f5b0a2c8da4e99600b0dad688217fdff402e8cf1f2db3137e511edc","schema_version":"1.0","event_id":"sha256:f75991965f5b0a2c8da4e99600b0dad688217fdff402e8cf1f2db3137e511edc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:472R7V44ODIZ2RQBICKT2SWC5Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nonuniform Kolmogorov extractors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Marius Zimand","submitted_at":"2012-04-30T16:42:34Z","abstract_excerpt":"We establish tight bounds on the amount on nonuniformity that is necessary for extracting a string with randomness rate 1 from a single source of randomness with lower randomness rate. More precisely, as instantiations of more general results, we show that while O(1) amount of advice regarding the source is not enough for extracting a string with randomness rate 1 from a source string with constant subunitary random rate, \\omega(1) amount of advice is."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.6696","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:56:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lwGJZ0wJUIxCUBaLVVOVAyluSpBYDU4WKEONO96p6IKiyU2/OzZBAM9HpvGZy92OJqNAOjK3EsH38wtaSchTDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T01:59:35.148005Z"},"content_sha256":"ceee62e549fcb21e0c415c3580269c8ecba2d0a55fbd4c9be693473be8e3eedd","schema_version":"1.0","event_id":"sha256:ceee62e549fcb21e0c415c3580269c8ecba2d0a55fbd4c9be693473be8e3eedd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/472R7V44ODIZ2RQBICKT2SWC5Q/bundle.json","state_url":"https://pith.science/pith/472R7V44ODIZ2RQBICKT2SWC5Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/472R7V44ODIZ2RQBICKT2SWC5Q/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-22T01:59:35Z","links":{"resolver":"https://pith.science/pith/472R7V44ODIZ2RQBICKT2SWC5Q","bundle":"https://pith.science/pith/472R7V44ODIZ2RQBICKT2SWC5Q/bundle.json","state":"https://pith.science/pith/472R7V44ODIZ2RQBICKT2SWC5Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/472R7V44ODIZ2RQBICKT2SWC5Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:472R7V44ODIZ2RQBICKT2SWC5Q","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":"57679a9631c8b7727704c4774f73dfed97d23c0dfa04b1116e165a996e507418","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2012-04-30T16:42:34Z","title_canon_sha256":"73407c37f3aadf75b752bc8c94025f13dbf868b3d0e60114532df9a7acc4294a"},"schema_version":"1.0","source":{"id":"1204.6696","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.6696","created_at":"2026-05-18T03:56:44Z"},{"alias_kind":"arxiv_version","alias_value":"1204.6696v1","created_at":"2026-05-18T03:56:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.6696","created_at":"2026-05-18T03:56:44Z"},{"alias_kind":"pith_short_12","alias_value":"472R7V44ODIZ","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"472R7V44ODIZ2RQB","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"472R7V44","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:ceee62e549fcb21e0c415c3580269c8ecba2d0a55fbd4c9be693473be8e3eedd","target":"graph","created_at":"2026-05-18T03:56:44Z","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"},"paper":{"abstract_excerpt":"We establish tight bounds on the amount on nonuniformity that is necessary for extracting a string with randomness rate 1 from a single source of randomness with lower randomness rate. More precisely, as instantiations of more general results, we show that while O(1) amount of advice regarding the source is not enough for extracting a string with randomness rate 1 from a source string with constant subunitary random rate, \\omega(1) amount of advice is.","authors_text":"Marius Zimand","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2012-04-30T16:42:34Z","title":"Nonuniform Kolmogorov extractors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.6696","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:f75991965f5b0a2c8da4e99600b0dad688217fdff402e8cf1f2db3137e511edc","target":"record","created_at":"2026-05-18T03:56:44Z","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":"57679a9631c8b7727704c4774f73dfed97d23c0dfa04b1116e165a996e507418","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2012-04-30T16:42:34Z","title_canon_sha256":"73407c37f3aadf75b752bc8c94025f13dbf868b3d0e60114532df9a7acc4294a"},"schema_version":"1.0","source":{"id":"1204.6696","kind":"arxiv","version":1}},"canonical_sha256":"e7f51fd79c70d19d460140953d4ac2ec358b2323755c377a4bdc83bb484ab7a1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e7f51fd79c70d19d460140953d4ac2ec358b2323755c377a4bdc83bb484ab7a1","first_computed_at":"2026-05-18T03:56:44.103301Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:56:44.103301Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NvkGOnGsUh63Cwk6C+ogTTDuQ5V5eJt8kAq0EhVxvOp3f2jQsl6DUHT3zZz4b2zT/sOygMLfSm2g3xyMvDllBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:56:44.104024Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.6696","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f75991965f5b0a2c8da4e99600b0dad688217fdff402e8cf1f2db3137e511edc","sha256:ceee62e549fcb21e0c415c3580269c8ecba2d0a55fbd4c9be693473be8e3eedd"],"state_sha256":"7d0ddfa18d619a33f23dc0495299b22902c10339a1460cfd83c1d3cd5b145ce5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LZjdJIg0NYkeJsFnyu/AC6YIsQWhuTchvMRvcUGIo8EuAJ6xqf6ejm+v1Sg1H5CWuxDmIM0e9W8aPZn6ZzuwAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T01:59:35.149893Z","bundle_sha256":"8ec3969d2d17eab84420aacff72d27e2dd02332eafd5ffad057f8c943c4ae681"}}