{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:AG7I6D3A7WA3Z4EMV5GRXD2SDO","short_pith_number":"pith:AG7I6D3A","schema_version":"1.0","canonical_sha256":"01be8f0f60fd81bcf08caf4d1b8f521b92af8f3546402e42e78a9bba47124666","source":{"kind":"arxiv","id":"2312.04329","version":1},"attestation_state":"computed","paper":{"title":"Reed-Muller codes have vanishing bit-error probability below capacity: a simple tighter proof via camellia boosting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO","math.IT"],"primary_cat":"cs.IT","authors_text":"Colin Sandon, Emmanuel Abbe","submitted_at":"2023-12-07T14:45:48Z","abstract_excerpt":"This paper shows that a class of codes such as Reed-Muller (RM) codes have vanishing bit-error probability below capacity on symmetric channels. The proof relies on the notion of `camellia codes': a class of symmetric codes decomposable into `camellias', i.e., set systems that differ from sunflowers by allowing for scattered petal overlaps. The proof then follows from a boosting argument on the camellia petals with second moment Fourier analysis. For erasure channels, this gives a self-contained proof of the bit-error result in Kudekar et al.'17, without relying on sharp thresholds for monoton"},"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":"2312.04329","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2023-12-07T14:45:48Z","cross_cats_sorted":["cs.DM","math.CO","math.IT"],"title_canon_sha256":"98e76c93716db56582011b12e200742aa344834b7f60b0b8ef9120fd109ec93c","abstract_canon_sha256":"dc8bb4120e42a575d15a1a58786136d1c9449ae492f65bc7a0d33af2f1544103"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:21:32.681568Z","signature_b64":"0AWkR8lg6bkgMrtcnKQ6gLnb9PsHoUfQ2tx/yz9jLFHyLhm/tjL8/a5VOlSVkpG1BmdXmXl8LBrytbpZL+hjBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"01be8f0f60fd81bcf08caf4d1b8f521b92af8f3546402e42e78a9bba47124666","last_reissued_at":"2026-07-05T07:21:32.680887Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:21:32.680887Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Reed-Muller codes have vanishing bit-error probability below capacity: a simple tighter proof via camellia boosting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO","math.IT"],"primary_cat":"cs.IT","authors_text":"Colin Sandon, Emmanuel Abbe","submitted_at":"2023-12-07T14:45:48Z","abstract_excerpt":"This paper shows that a class of codes such as Reed-Muller (RM) codes have vanishing bit-error probability below capacity on symmetric channels. The proof relies on the notion of `camellia codes': a class of symmetric codes decomposable into `camellias', i.e., set systems that differ from sunflowers by allowing for scattered petal overlaps. The proof then follows from a boosting argument on the camellia petals with second moment Fourier analysis. For erasure channels, this gives a self-contained proof of the bit-error result in Kudekar et al.'17, without relying on sharp thresholds for monoton"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.04329","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2312.04329/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2312.04329","created_at":"2026-07-05T07:21:32.680966+00:00"},{"alias_kind":"arxiv_version","alias_value":"2312.04329v1","created_at":"2026-07-05T07:21:32.680966+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.04329","created_at":"2026-07-05T07:21:32.680966+00:00"},{"alias_kind":"pith_short_12","alias_value":"AG7I6D3A7WA3","created_at":"2026-07-05T07:21:32.680966+00:00"},{"alias_kind":"pith_short_16","alias_value":"AG7I6D3A7WA3Z4EM","created_at":"2026-07-05T07:21:32.680966+00:00"},{"alias_kind":"pith_short_8","alias_value":"AG7I6D3A","created_at":"2026-07-05T07:21:32.680966+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2604.02994","citing_title":"Weight distribution bounds to relate minimum distance, list decoding, and symmetric channel performance","ref_index":3,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/AG7I6D3A7WA3Z4EMV5GRXD2SDO","json":"https://pith.science/pith/AG7I6D3A7WA3Z4EMV5GRXD2SDO.json","graph_json":"https://pith.science/api/pith-number/AG7I6D3A7WA3Z4EMV5GRXD2SDO/graph.json","events_json":"https://pith.science/api/pith-number/AG7I6D3A7WA3Z4EMV5GRXD2SDO/events.json","paper":"https://pith.science/paper/AG7I6D3A"},"agent_actions":{"view_html":"https://pith.science/pith/AG7I6D3A7WA3Z4EMV5GRXD2SDO","download_json":"https://pith.science/pith/AG7I6D3A7WA3Z4EMV5GRXD2SDO.json","view_paper":"https://pith.science/paper/AG7I6D3A","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2312.04329&json=true","fetch_graph":"https://pith.science/api/pith-number/AG7I6D3A7WA3Z4EMV5GRXD2SDO/graph.json","fetch_events":"https://pith.science/api/pith-number/AG7I6D3A7WA3Z4EMV5GRXD2SDO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AG7I6D3A7WA3Z4EMV5GRXD2SDO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AG7I6D3A7WA3Z4EMV5GRXD2SDO/action/storage_attestation","attest_author":"https://pith.science/pith/AG7I6D3A7WA3Z4EMV5GRXD2SDO/action/author_attestation","sign_citation":"https://pith.science/pith/AG7I6D3A7WA3Z4EMV5GRXD2SDO/action/citation_signature","submit_replication":"https://pith.science/pith/AG7I6D3A7WA3Z4EMV5GRXD2SDO/action/replication_record"}},"created_at":"2026-07-05T07:21:32.680966+00:00","updated_at":"2026-07-05T07:21:32.680966+00:00"}