{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:46TOCIQ2EK4STXMGFMKRPNKUIT","short_pith_number":"pith:46TOCIQ2","canonical_record":{"source":{"id":"1804.10319","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-04-27T01:35:22Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"675774376945571959444ce31d076299e926afd540449a54f69b662f4e9f522e","abstract_canon_sha256":"60cfa8a29f86af77d6a8bb631035c15c77733a2d793d31ea0db6d4cd7b7d723f"},"schema_version":"1.0"},"canonical_sha256":"e7a6e1221a22b929dd862b1517b55444f5522598bfe9cab4bf6710281cdf9613","source":{"kind":"arxiv","id":"1804.10319","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.10319","created_at":"2026-05-18T00:17:21Z"},{"alias_kind":"arxiv_version","alias_value":"1804.10319v1","created_at":"2026-05-18T00:17:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.10319","created_at":"2026-05-18T00:17:21Z"},{"alias_kind":"pith_short_12","alias_value":"46TOCIQ2EK4S","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"46TOCIQ2EK4STXMG","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"46TOCIQ2","created_at":"2026-05-18T12:32:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:46TOCIQ2EK4STXMGFMKRPNKUIT","target":"record","payload":{"canonical_record":{"source":{"id":"1804.10319","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-04-27T01:35:22Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"675774376945571959444ce31d076299e926afd540449a54f69b662f4e9f522e","abstract_canon_sha256":"60cfa8a29f86af77d6a8bb631035c15c77733a2d793d31ea0db6d4cd7b7d723f"},"schema_version":"1.0"},"canonical_sha256":"e7a6e1221a22b929dd862b1517b55444f5522598bfe9cab4bf6710281cdf9613","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:17:21.131402Z","signature_b64":"51I/GiwcpOnlVb2F4oAsGmFrzDDVEHBitbJVAKjUxnM4YFt2hmcFnVoeGCEXcd47ol3bpU4pJbirk3m8z9KTCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e7a6e1221a22b929dd862b1517b55444f5522598bfe9cab4bf6710281cdf9613","last_reissued_at":"2026-05-18T00:17:21.130791Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:17:21.130791Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.10319","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":"2026-05-18T00:17:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"poavDBIB6JOmvvhu2tU0L8pkQZjLoFLTNbqImCjrRNT5ngPSwIgYPzrLsSd2sNMtoms7Q47g738WDAsu8n2MDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T13:02:36.661301Z"},"content_sha256":"6ccd9554efeef4a8b429bb54d9f3f02e6c8151cad16050d122921a027784acd2","schema_version":"1.0","event_id":"sha256:6ccd9554efeef4a8b429bb54d9f3f02e6c8151cad16050d122921a027784acd2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:46TOCIQ2EK4STXMGFMKRPNKUIT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Decoding Reed-Muller Codes Using Minimum-Weight Parity Checks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Christian H\\\"ager, Elia Santi, Henry D. Pfister","submitted_at":"2018-04-27T01:35:22Z","abstract_excerpt":"Reed-Muller (RM) codes exhibit good performance under maximum-likelihood (ML) decoding due to their highly-symmetric structure. In this paper, we explore the question of whether the code symmetry of RM codes can also be exploited to achieve near-ML performance in practice. The main idea is to apply iterative decoding to a highly-redundant parity-check (PC) matrix that contains only the minimum-weight dual codewords as rows. As examples, we consider the peeling decoder for the binary erasure channel, linear-programming and belief propagation (BP) decoding for the binary-input additive white Gau"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.10319","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":"2026-05-18T00:17:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b6Ke/hjd/AP3toOAWx4I142byqHuGmCQr07/iC5gKOcS8vEqh3FP9QLRfy1o2OEn1y6YLtcvDk2ZdTYQWA1UDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T13:02:36.661977Z"},"content_sha256":"698f7e8f8f1e90562270a8b57d89fa0b9e5c62fed04fb9568425baad9f9c0ac1","schema_version":"1.0","event_id":"sha256:698f7e8f8f1e90562270a8b57d89fa0b9e5c62fed04fb9568425baad9f9c0ac1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/46TOCIQ2EK4STXMGFMKRPNKUIT/bundle.json","state_url":"https://pith.science/pith/46TOCIQ2EK4STXMGFMKRPNKUIT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/46TOCIQ2EK4STXMGFMKRPNKUIT/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":"2026-05-27T13:02:36Z","links":{"resolver":"https://pith.science/pith/46TOCIQ2EK4STXMGFMKRPNKUIT","bundle":"https://pith.science/pith/46TOCIQ2EK4STXMGFMKRPNKUIT/bundle.json","state":"https://pith.science/pith/46TOCIQ2EK4STXMGFMKRPNKUIT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/46TOCIQ2EK4STXMGFMKRPNKUIT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:46TOCIQ2EK4STXMGFMKRPNKUIT","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":"60cfa8a29f86af77d6a8bb631035c15c77733a2d793d31ea0db6d4cd7b7d723f","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-04-27T01:35:22Z","title_canon_sha256":"675774376945571959444ce31d076299e926afd540449a54f69b662f4e9f522e"},"schema_version":"1.0","source":{"id":"1804.10319","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.10319","created_at":"2026-05-18T00:17:21Z"},{"alias_kind":"arxiv_version","alias_value":"1804.10319v1","created_at":"2026-05-18T00:17:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.10319","created_at":"2026-05-18T00:17:21Z"},{"alias_kind":"pith_short_12","alias_value":"46TOCIQ2EK4S","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"46TOCIQ2EK4STXMG","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"46TOCIQ2","created_at":"2026-05-18T12:32:05Z"}],"graph_snapshots":[{"event_id":"sha256:698f7e8f8f1e90562270a8b57d89fa0b9e5c62fed04fb9568425baad9f9c0ac1","target":"graph","created_at":"2026-05-18T00:17:21Z","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":"Reed-Muller (RM) codes exhibit good performance under maximum-likelihood (ML) decoding due to their highly-symmetric structure. In this paper, we explore the question of whether the code symmetry of RM codes can also be exploited to achieve near-ML performance in practice. The main idea is to apply iterative decoding to a highly-redundant parity-check (PC) matrix that contains only the minimum-weight dual codewords as rows. As examples, we consider the peeling decoder for the binary erasure channel, linear-programming and belief propagation (BP) decoding for the binary-input additive white Gau","authors_text":"Christian H\\\"ager, Elia Santi, Henry D. Pfister","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-04-27T01:35:22Z","title":"Decoding Reed-Muller Codes Using Minimum-Weight Parity Checks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.10319","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":"sha256:6ccd9554efeef4a8b429bb54d9f3f02e6c8151cad16050d122921a027784acd2","target":"record","created_at":"2026-05-18T00:17:21Z","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":"60cfa8a29f86af77d6a8bb631035c15c77733a2d793d31ea0db6d4cd7b7d723f","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-04-27T01:35:22Z","title_canon_sha256":"675774376945571959444ce31d076299e926afd540449a54f69b662f4e9f522e"},"schema_version":"1.0","source":{"id":"1804.10319","kind":"arxiv","version":1}},"canonical_sha256":"e7a6e1221a22b929dd862b1517b55444f5522598bfe9cab4bf6710281cdf9613","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e7a6e1221a22b929dd862b1517b55444f5522598bfe9cab4bf6710281cdf9613","first_computed_at":"2026-05-18T00:17:21.130791Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:17:21.130791Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"51I/GiwcpOnlVb2F4oAsGmFrzDDVEHBitbJVAKjUxnM4YFt2hmcFnVoeGCEXcd47ol3bpU4pJbirk3m8z9KTCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:17:21.131402Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.10319","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6ccd9554efeef4a8b429bb54d9f3f02e6c8151cad16050d122921a027784acd2","sha256:698f7e8f8f1e90562270a8b57d89fa0b9e5c62fed04fb9568425baad9f9c0ac1"],"state_sha256":"91789b1a7628a2683a315a41716a2dfad3b688b6349be4d3dfc82edf1dc69337"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BYx6ObTkEt8f4EEjit/wv/5uYJMXwmg7FVMRiviAkHDp2W+Mu1e1z2m4uJ9v5UPGsnL/zcodhdU8fcfJgeuXBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T13:02:36.665086Z","bundle_sha256":"6d55beba9b9c4f80db01b713452699d17073c0296eebf2bedeb16aa1f46051d3"}}