{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:JYYJXCACRCZJDTAXYZLSER2SY4","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":"06e42685966d81f389798abc177cd7ae8789fc160fee505f13a7758205acf16e","cross_cats_sorted":["math.IT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2025-05-02T03:30:16Z","title_canon_sha256":"6d1d0e093ff6bb7017b60044a435f7ab84040b7f944d0f2ac0b9a328f0076fb0"},"schema_version":"1.0","source":{"id":"2505.00974","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.00974","created_at":"2026-07-05T10:57:42Z"},{"alias_kind":"arxiv_version","alias_value":"2505.00974v1","created_at":"2026-07-05T10:57:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.00974","created_at":"2026-07-05T10:57:42Z"},{"alias_kind":"pith_short_12","alias_value":"JYYJXCACRCZJ","created_at":"2026-07-05T10:57:42Z"},{"alias_kind":"pith_short_16","alias_value":"JYYJXCACRCZJDTAX","created_at":"2026-07-05T10:57:42Z"},{"alias_kind":"pith_short_8","alias_value":"JYYJXCAC","created_at":"2026-07-05T10:57:42Z"}],"graph_snapshots":[{"event_id":"sha256:368f98f37a309dbf0cee356aa8ad46a8bb2af114bdc68bf363f59818a85903bb","target":"graph","created_at":"2026-07-05T10:57:42Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2505.00974/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Reed--Muller (RM) codes are known to achieve capacity on binary symmetric channels (BSC) under the Maximum a Posteriori (MAP) decoder. However, it remains an open problem to design a capacity achieving polynomial-time RM decoder. Due to a lemma by Liu, Cuff, and Verd\\'u, it can be shown that decoding by sampling from the posterior distribution is also capacity-achieving for RM codes over BSC. The Gibbs decoder is one such Markov Chain Monte Carlo (MCMC) based method, which samples from the posterior distribution by flipping message bits according to the posterior, and can be modified to give o","authors_text":"Lele Wang, Nicholas Kwan, Xuzhe Xia","cross_cats":["math.IT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2025-05-02T03:30:16Z","title":"On the Worst-Case Complexity of Gibbs Decoding for Reed--Muller Codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.00974","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":"sha256:5972c145aa4dce482d0c51d4cfa6fde0d70e43130a9a9e99edffbfe8cc1d11b8","target":"record","created_at":"2026-07-05T10:57:42Z","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":"06e42685966d81f389798abc177cd7ae8789fc160fee505f13a7758205acf16e","cross_cats_sorted":["math.IT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2025-05-02T03:30:16Z","title_canon_sha256":"6d1d0e093ff6bb7017b60044a435f7ab84040b7f944d0f2ac0b9a328f0076fb0"},"schema_version":"1.0","source":{"id":"2505.00974","kind":"arxiv","version":1}},"canonical_sha256":"4e309b880288b291cc17c657224752c709decea3ff5876202db6f76589911a96","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4e309b880288b291cc17c657224752c709decea3ff5876202db6f76589911a96","first_computed_at":"2026-07-05T10:57:42.768650Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:57:42.768650Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nIHHkiMdbNwCIiv037EFRgBXTr6nnDSR1O2G+txf57tGFrm1meMos1eIeMVZB5YOqtuS/s6vpYkgXULCzcR1CA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:57:42.769092Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.00974","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5972c145aa4dce482d0c51d4cfa6fde0d70e43130a9a9e99edffbfe8cc1d11b8","sha256:368f98f37a309dbf0cee356aa8ad46a8bb2af114bdc68bf363f59818a85903bb"],"state_sha256":"772084daf2fb4afb9383d8d51d462998b501a36be4db7a21fafdf33fb9323d2f"}