{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:UQQFRYHGIXZKTLCRCLM4JUOYW2","short_pith_number":"pith:UQQFRYHG","canonical_record":{"source":{"id":"0901.1866","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2009-01-13T19:26:58Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"9ed69a81aab6e911f10e27b26b4f4e2b39ae43ea8be9b0313a4975066de3732b","abstract_canon_sha256":"079b7022d8c62c1fe40e42130684226b84ca348df738c47c6b0836511238dc21"},"schema_version":"1.0"},"canonical_sha256":"a42058e0e645f2a9ac5112d9c4d1d8b69f9f43d12b5876f82fae01359ed0e186","source":{"kind":"arxiv","id":"0901.1866","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0901.1866","created_at":"2026-05-18T04:17:03Z"},{"alias_kind":"arxiv_version","alias_value":"0901.1866v2","created_at":"2026-05-18T04:17:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0901.1866","created_at":"2026-05-18T04:17:03Z"},{"alias_kind":"pith_short_12","alias_value":"UQQFRYHGIXZK","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"UQQFRYHGIXZKTLCR","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"UQQFRYHG","created_at":"2026-05-18T12:26:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:UQQFRYHGIXZKTLCRCLM4JUOYW2","target":"record","payload":{"canonical_record":{"source":{"id":"0901.1866","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2009-01-13T19:26:58Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"9ed69a81aab6e911f10e27b26b4f4e2b39ae43ea8be9b0313a4975066de3732b","abstract_canon_sha256":"079b7022d8c62c1fe40e42130684226b84ca348df738c47c6b0836511238dc21"},"schema_version":"1.0"},"canonical_sha256":"a42058e0e645f2a9ac5112d9c4d1d8b69f9f43d12b5876f82fae01359ed0e186","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:17:03.604359Z","signature_b64":"uJQ1SpIoIkp8gzeyi3CxFEMJLUnbGfCzDkrtrdtbzdtwZMru+Po6kdzrOCcpgYb289IAeJpfz9Qo+n0b/wTdBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a42058e0e645f2a9ac5112d9c4d1d8b69f9f43d12b5876f82fae01359ed0e186","last_reissued_at":"2026-05-18T04:17:03.603812Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:17:03.603812Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0901.1866","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:17:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A2ZKHhgCVzh6c2RFc7XmGC+FChKYFAjz7gHXOGmwVw9uD/FJ+/xNYnPGLIqDlE4aG2STxhP3h8AP4oyDyjHbBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T16:18:03.794083Z"},"content_sha256":"5d9bd401a09cf7b98dd928d28cf1c025afd663c50e41d1656ccb1ff74fb7e3e6","schema_version":"1.0","event_id":"sha256:5d9bd401a09cf7b98dd928d28cf1c025afd663c50e41d1656ccb1ff74fb7e3e6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:UQQFRYHGIXZKTLCRCLM4JUOYW2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Capacity Achieving Codes From Randomness Condensers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Mahdi Cheraghchi","submitted_at":"2009-01-13T19:26:58Z","abstract_excerpt":"We establish a general framework for construction of small ensembles of capacity achieving linear codes for a wide range of (not necessarily memoryless) discrete symmetric channels, and in particular, the binary erasure and symmetric channels. The main tool used in our constructions is the notion of randomness extractors and lossless condensers that are regarded as central tools in theoretical computer science. Same as random codes, the resulting ensembles preserve their capacity achieving properties under any change of basis. Using known explicit constructions of condensers, we obtain specifi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.1866","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:17:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lteAzW/+3D/Q4Qd/jU/p7MmmL96Di14RG8mOjbzR2e5lCI77laeZ86Yilf7YnrFn+4cIEGxI6BS7GHSOGR8rAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T16:18:03.794441Z"},"content_sha256":"7cb918ca5abfe6b95eadbc3ccdd2bf5eed40f29fe5c0ef1204223f23fc5d0eb4","schema_version":"1.0","event_id":"sha256:7cb918ca5abfe6b95eadbc3ccdd2bf5eed40f29fe5c0ef1204223f23fc5d0eb4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UQQFRYHGIXZKTLCRCLM4JUOYW2/bundle.json","state_url":"https://pith.science/pith/UQQFRYHGIXZKTLCRCLM4JUOYW2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UQQFRYHGIXZKTLCRCLM4JUOYW2/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":"2026-06-01T16:18:03Z","links":{"resolver":"https://pith.science/pith/UQQFRYHGIXZKTLCRCLM4JUOYW2","bundle":"https://pith.science/pith/UQQFRYHGIXZKTLCRCLM4JUOYW2/bundle.json","state":"https://pith.science/pith/UQQFRYHGIXZKTLCRCLM4JUOYW2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UQQFRYHGIXZKTLCRCLM4JUOYW2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:UQQFRYHGIXZKTLCRCLM4JUOYW2","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":"079b7022d8c62c1fe40e42130684226b84ca348df738c47c6b0836511238dc21","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2009-01-13T19:26:58Z","title_canon_sha256":"9ed69a81aab6e911f10e27b26b4f4e2b39ae43ea8be9b0313a4975066de3732b"},"schema_version":"1.0","source":{"id":"0901.1866","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0901.1866","created_at":"2026-05-18T04:17:03Z"},{"alias_kind":"arxiv_version","alias_value":"0901.1866v2","created_at":"2026-05-18T04:17:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0901.1866","created_at":"2026-05-18T04:17:03Z"},{"alias_kind":"pith_short_12","alias_value":"UQQFRYHGIXZK","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"UQQFRYHGIXZKTLCR","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"UQQFRYHG","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:7cb918ca5abfe6b95eadbc3ccdd2bf5eed40f29fe5c0ef1204223f23fc5d0eb4","target":"graph","created_at":"2026-05-18T04:17:03Z","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 a general framework for construction of small ensembles of capacity achieving linear codes for a wide range of (not necessarily memoryless) discrete symmetric channels, and in particular, the binary erasure and symmetric channels. The main tool used in our constructions is the notion of randomness extractors and lossless condensers that are regarded as central tools in theoretical computer science. Same as random codes, the resulting ensembles preserve their capacity achieving properties under any change of basis. Using known explicit constructions of condensers, we obtain specifi","authors_text":"Mahdi Cheraghchi","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2009-01-13T19:26:58Z","title":"Capacity Achieving Codes From Randomness Condensers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.1866","kind":"arxiv","version":2},"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":"sha256:5d9bd401a09cf7b98dd928d28cf1c025afd663c50e41d1656ccb1ff74fb7e3e6","target":"record","created_at":"2026-05-18T04:17:03Z","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":"079b7022d8c62c1fe40e42130684226b84ca348df738c47c6b0836511238dc21","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2009-01-13T19:26:58Z","title_canon_sha256":"9ed69a81aab6e911f10e27b26b4f4e2b39ae43ea8be9b0313a4975066de3732b"},"schema_version":"1.0","source":{"id":"0901.1866","kind":"arxiv","version":2}},"canonical_sha256":"a42058e0e645f2a9ac5112d9c4d1d8b69f9f43d12b5876f82fae01359ed0e186","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a42058e0e645f2a9ac5112d9c4d1d8b69f9f43d12b5876f82fae01359ed0e186","first_computed_at":"2026-05-18T04:17:03.603812Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:17:03.603812Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uJQ1SpIoIkp8gzeyi3CxFEMJLUnbGfCzDkrtrdtbzdtwZMru+Po6kdzrOCcpgYb289IAeJpfz9Qo+n0b/wTdBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:17:03.604359Z","signed_message":"canonical_sha256_bytes"},"source_id":"0901.1866","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5d9bd401a09cf7b98dd928d28cf1c025afd663c50e41d1656ccb1ff74fb7e3e6","sha256:7cb918ca5abfe6b95eadbc3ccdd2bf5eed40f29fe5c0ef1204223f23fc5d0eb4"],"state_sha256":"81679dec28713679dd0ecfd636d38a5e5691cd2d82298e19d59b48e9647bb875"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bw3uSYyTizksRkeaF8RkfTkCGlHE5WC6kvtY++MdIjI8IGYJoIkdhE3XrPUnxWzy0HHsMbipo55E/y3MyiDUAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T16:18:03.796388Z","bundle_sha256":"2b72c826267116e2f42d3b561971efcb079a7688a497de404796ce5b8722ca5f"}}