{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:SMWF7T5RXFZCBYBVKN5X7UQEWA","short_pith_number":"pith:SMWF7T5R","schema_version":"1.0","canonical_sha256":"932c5fcfb1b97220e035537b7fd204b01c4abf94c2c9022e5b7684be51e04c2c","source":{"kind":"arxiv","id":"2410.20020","version":1},"attestation_state":"computed","paper":{"title":"List-Decoding Capacity Implies Capacity on the q-ary Symmetric Channel","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Francisco Pernice, Mary Wootters, Oscar Sprumont","submitted_at":"2024-10-26T00:37:47Z","abstract_excerpt":"It is known that the Shannon capacity of the q-ary symmetric channel (qSC) is the same as the list-decoding capacity of an adversarial channel, raising the question of whether there is a formal (and black-box) connection between the two. We show that there is: Any linear code $C\\subseteq \\mathbb{F}_q^n$ that has minimum distance $d_{\\min}=\\omega(q^3)$ and achieves list-decoding capacity also achieves capacity on the qSC."},"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":"2410.20020","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2024-10-26T00:37:47Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"c6f03f9febdd06ec1047c2119fc9abcef28989aa9ecc55e5497e268d82d84096","abstract_canon_sha256":"f63bc895927b2e8bdeace007a10334320bf717191f552e02840f194f31d3023b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:26:37.649150Z","signature_b64":"l5JLd8MD+NvDytLd72sziTvudnZwlRQyhdTyOr8ocAQI8O7EeTYPO0U3ED/Me4jUUa5wDYo2VFwWbYPh+FsWAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"932c5fcfb1b97220e035537b7fd204b01c4abf94c2c9022e5b7684be51e04c2c","last_reissued_at":"2026-07-05T09:26:37.648586Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:26:37.648586Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"List-Decoding Capacity Implies Capacity on the q-ary Symmetric Channel","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Francisco Pernice, Mary Wootters, Oscar Sprumont","submitted_at":"2024-10-26T00:37:47Z","abstract_excerpt":"It is known that the Shannon capacity of the q-ary symmetric channel (qSC) is the same as the list-decoding capacity of an adversarial channel, raising the question of whether there is a formal (and black-box) connection between the two. We show that there is: Any linear code $C\\subseteq \\mathbb{F}_q^n$ that has minimum distance $d_{\\min}=\\omega(q^3)$ and achieves list-decoding capacity also achieves capacity on the qSC."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.20020","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/2410.20020/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":"2410.20020","created_at":"2026-07-05T09:26:37.648655+00:00"},{"alias_kind":"arxiv_version","alias_value":"2410.20020v1","created_at":"2026-07-05T09:26:37.648655+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.20020","created_at":"2026-07-05T09:26:37.648655+00:00"},{"alias_kind":"pith_short_12","alias_value":"SMWF7T5RXFZC","created_at":"2026-07-05T09:26:37.648655+00:00"},{"alias_kind":"pith_short_16","alias_value":"SMWF7T5RXFZCBYBV","created_at":"2026-07-05T09:26:37.648655+00:00"},{"alias_kind":"pith_short_8","alias_value":"SMWF7T5R","created_at":"2026-07-05T09:26:37.648655+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2506.18878","citing_title":"Oblivious Deletion Codes","ref_index":40,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/SMWF7T5RXFZCBYBVKN5X7UQEWA","json":"https://pith.science/pith/SMWF7T5RXFZCBYBVKN5X7UQEWA.json","graph_json":"https://pith.science/api/pith-number/SMWF7T5RXFZCBYBVKN5X7UQEWA/graph.json","events_json":"https://pith.science/api/pith-number/SMWF7T5RXFZCBYBVKN5X7UQEWA/events.json","paper":"https://pith.science/paper/SMWF7T5R"},"agent_actions":{"view_html":"https://pith.science/pith/SMWF7T5RXFZCBYBVKN5X7UQEWA","download_json":"https://pith.science/pith/SMWF7T5RXFZCBYBVKN5X7UQEWA.json","view_paper":"https://pith.science/paper/SMWF7T5R","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2410.20020&json=true","fetch_graph":"https://pith.science/api/pith-number/SMWF7T5RXFZCBYBVKN5X7UQEWA/graph.json","fetch_events":"https://pith.science/api/pith-number/SMWF7T5RXFZCBYBVKN5X7UQEWA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SMWF7T5RXFZCBYBVKN5X7UQEWA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SMWF7T5RXFZCBYBVKN5X7UQEWA/action/storage_attestation","attest_author":"https://pith.science/pith/SMWF7T5RXFZCBYBVKN5X7UQEWA/action/author_attestation","sign_citation":"https://pith.science/pith/SMWF7T5RXFZCBYBVKN5X7UQEWA/action/citation_signature","submit_replication":"https://pith.science/pith/SMWF7T5RXFZCBYBVKN5X7UQEWA/action/replication_record"}},"created_at":"2026-07-05T09:26:37.648655+00:00","updated_at":"2026-07-05T09:26:37.648655+00:00"}