{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:7K2PIZDIFDWAIKBCHRIX7ARE7K","short_pith_number":"pith:7K2PIZDI","canonical_record":{"source":{"id":"1005.4461","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-05-25T00:17:36Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"44dc3296498a4be806d6758c5f5de5d6b1586969235d6ea803885fa9e2aa36c5","abstract_canon_sha256":"2d820a35a4c27583c2af65252c6cf85875901c304eca0223fe5c5cd2b3a2dd54"},"schema_version":"1.0"},"canonical_sha256":"fab4f4646828ec0428223c517f8224fa9177e3435a0f84732615b499304ff186","source":{"kind":"arxiv","id":"1005.4461","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.4461","created_at":"2026-05-18T02:23:56Z"},{"alias_kind":"arxiv_version","alias_value":"1005.4461v3","created_at":"2026-05-18T02:23:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.4461","created_at":"2026-05-18T02:23:56Z"},{"alias_kind":"pith_short_12","alias_value":"7K2PIZDIFDWA","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"7K2PIZDIFDWAIKBC","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"7K2PIZDI","created_at":"2026-05-18T12:26:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:7K2PIZDIFDWAIKBCHRIX7ARE7K","target":"record","payload":{"canonical_record":{"source":{"id":"1005.4461","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-05-25T00:17:36Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"44dc3296498a4be806d6758c5f5de5d6b1586969235d6ea803885fa9e2aa36c5","abstract_canon_sha256":"2d820a35a4c27583c2af65252c6cf85875901c304eca0223fe5c5cd2b3a2dd54"},"schema_version":"1.0"},"canonical_sha256":"fab4f4646828ec0428223c517f8224fa9177e3435a0f84732615b499304ff186","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:23:56.147553Z","signature_b64":"VqZv2igpxYolWpCBgQuUdFUfONT+GG02eAQd2sM45UtQAXmrl+wM2+hzJFnRIWhQS5FxKu5Jj4+sHtws4NYRAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fab4f4646828ec0428223c517f8224fa9177e3435a0f84732615b499304ff186","last_reissued_at":"2026-05-18T02:23:56.146579Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:23:56.146579Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1005.4461","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:23:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JZCBudbwhWZEFtdp6nos+Urz4LwT1aIh/y57lF2AB3LvoEDzag49LesjZQ7EUuaobu004ZZqGsTI/RBwQWKFAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T14:39:47.869026Z"},"content_sha256":"69272cd301b2fe64ad537208cdaa27c491fc7235f0db5600059cb7a7f780c167","schema_version":"1.0","event_id":"sha256:69272cd301b2fe64ad537208cdaa27c491fc7235f0db5600059cb7a7f780c167"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:7K2PIZDIFDWAIKBCHRIX7ARE7K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Multiple Decoding Attempts for Reed-Solomon Codes: A Rate-Distortion Approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Henry D. Pfister, Krishna R. Narayanan, Phong S. Nguyen","submitted_at":"2010-05-25T00:17:36Z","abstract_excerpt":"One popular approach to soft-decision decoding of Reed-Solomon (RS) codes is based on using multiple trials of a simple RS decoding algorithm in combination with erasing or flipping a set of symbols or bits in each trial. This paper presents a framework based on rate-distortion (RD) theory to analyze these multiple-decoding algorithms. By defining an appropriate distortion measure between an error pattern and an erasure pattern, the successful decoding condition, for a single errors-and-erasures decoding trial, becomes equivalent to distortion being less than a fixed threshold. Finding the bes"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.4461","kind":"arxiv","version":3},"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":"2026-05-18T02:23:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C6/7JJOE+a+/NnyD047mZBA2JvgQ/A26fbM1fayH+ZEUIlRoH0EPlLTHcgPQQsXb103dyQH6SpzJ1uaLkVAiAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T14:39:47.869748Z"},"content_sha256":"8527e7ed546959fec74e90e4449a753c542e21879bca238464a19bb10c26e982","schema_version":"1.0","event_id":"sha256:8527e7ed546959fec74e90e4449a753c542e21879bca238464a19bb10c26e982"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7K2PIZDIFDWAIKBCHRIX7ARE7K/bundle.json","state_url":"https://pith.science/pith/7K2PIZDIFDWAIKBCHRIX7ARE7K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7K2PIZDIFDWAIKBCHRIX7ARE7K/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":"2026-05-27T14:39:47Z","links":{"resolver":"https://pith.science/pith/7K2PIZDIFDWAIKBCHRIX7ARE7K","bundle":"https://pith.science/pith/7K2PIZDIFDWAIKBCHRIX7ARE7K/bundle.json","state":"https://pith.science/pith/7K2PIZDIFDWAIKBCHRIX7ARE7K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7K2PIZDIFDWAIKBCHRIX7ARE7K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:7K2PIZDIFDWAIKBCHRIX7ARE7K","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":"2d820a35a4c27583c2af65252c6cf85875901c304eca0223fe5c5cd2b3a2dd54","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-05-25T00:17:36Z","title_canon_sha256":"44dc3296498a4be806d6758c5f5de5d6b1586969235d6ea803885fa9e2aa36c5"},"schema_version":"1.0","source":{"id":"1005.4461","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.4461","created_at":"2026-05-18T02:23:56Z"},{"alias_kind":"arxiv_version","alias_value":"1005.4461v3","created_at":"2026-05-18T02:23:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.4461","created_at":"2026-05-18T02:23:56Z"},{"alias_kind":"pith_short_12","alias_value":"7K2PIZDIFDWA","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"7K2PIZDIFDWAIKBC","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"7K2PIZDI","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:8527e7ed546959fec74e90e4449a753c542e21879bca238464a19bb10c26e982","target":"graph","created_at":"2026-05-18T02:23:56Z","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":"One popular approach to soft-decision decoding of Reed-Solomon (RS) codes is based on using multiple trials of a simple RS decoding algorithm in combination with erasing or flipping a set of symbols or bits in each trial. This paper presents a framework based on rate-distortion (RD) theory to analyze these multiple-decoding algorithms. By defining an appropriate distortion measure between an error pattern and an erasure pattern, the successful decoding condition, for a single errors-and-erasures decoding trial, becomes equivalent to distortion being less than a fixed threshold. Finding the bes","authors_text":"Henry D. Pfister, Krishna R. Narayanan, Phong S. Nguyen","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-05-25T00:17:36Z","title":"On Multiple Decoding Attempts for Reed-Solomon Codes: A Rate-Distortion Approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.4461","kind":"arxiv","version":3},"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":"sha256:69272cd301b2fe64ad537208cdaa27c491fc7235f0db5600059cb7a7f780c167","target":"record","created_at":"2026-05-18T02:23:56Z","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":"2d820a35a4c27583c2af65252c6cf85875901c304eca0223fe5c5cd2b3a2dd54","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-05-25T00:17:36Z","title_canon_sha256":"44dc3296498a4be806d6758c5f5de5d6b1586969235d6ea803885fa9e2aa36c5"},"schema_version":"1.0","source":{"id":"1005.4461","kind":"arxiv","version":3}},"canonical_sha256":"fab4f4646828ec0428223c517f8224fa9177e3435a0f84732615b499304ff186","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fab4f4646828ec0428223c517f8224fa9177e3435a0f84732615b499304ff186","first_computed_at":"2026-05-18T02:23:56.146579Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:23:56.146579Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VqZv2igpxYolWpCBgQuUdFUfONT+GG02eAQd2sM45UtQAXmrl+wM2+hzJFnRIWhQS5FxKu5Jj4+sHtws4NYRAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:23:56.147553Z","signed_message":"canonical_sha256_bytes"},"source_id":"1005.4461","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:69272cd301b2fe64ad537208cdaa27c491fc7235f0db5600059cb7a7f780c167","sha256:8527e7ed546959fec74e90e4449a753c542e21879bca238464a19bb10c26e982"],"state_sha256":"f939cb4d41b0ad5d4f6570ceb1e366bb57a3bc6e0ae3789219215d19a874fbee"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6uR56pj24MbBr+9SmYIznsn0irrD3m1veDUloySkEq8JufN70uBck1nLiecLhjFy8pKMFKahNs42bcebDV2GDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T14:39:47.873539Z","bundle_sha256":"3e5ef73f66467506ed640a4cc5ce96d5ff6ec8925302865f8121a402b35dccef"}}