{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:A2IC4H5LPLBOFUCY3ATD4HC3XA","short_pith_number":"pith:A2IC4H5L","schema_version":"1.0","canonical_sha256":"06902e1fab7ac2e2d058d8263e1c5bb80a0707272915352937b62516968f71ca","source":{"kind":"arxiv","id":"2308.13424","version":2},"attestation_state":"computed","paper":{"title":"AG codes have no list-decoding friends: Approaching the generalized Singleton bound requires exponential alphabets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO","math.IT"],"primary_cat":"cs.IT","authors_text":"Omar Alrabiah, Ray Li, Venkatesan Guruswami","submitted_at":"2023-08-25T15:09:28Z","abstract_excerpt":"A simple, recently observed generalization of the classical Singleton bound to list-decoding asserts that rate $R$ codes are not list-decodable using list-size $L$ beyond an error fraction $\\frac{L}{L+1} (1-R)$ (the Singleton bound being the case of $L=1$, i.e., unique decoding). We prove that in order to approach this bound for any fixed $L >1$, one needs exponential alphabets. Specifically, for every $L>1$ and $R\\in(0,1)$, if a rate $R$ code can be list-of-$L$ decoded up to error fraction $\\frac{L}{L+1} (1-R -\\varepsilon)$, then its alphabet must have size at least $\\exp(\\Omega_{L,R}(1/\\vare"},"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":"2308.13424","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2023-08-25T15:09:28Z","cross_cats_sorted":["cs.DM","math.CO","math.IT"],"title_canon_sha256":"9c344b8abed3f859e867067d0502e8e0b36a0c7fedd6d03f8948e27db82a7094","abstract_canon_sha256":"ff6436b55b34427176875e588a22e97bffc6ceaec5d1bc7756c5eb1e65015dff"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:50:20.172303Z","signature_b64":"J88QPhF0yUush4avqeN3wt3KoC+3kcuPM8VB0hHURPc3W9UAw2/hFGVGOfk1E30jmqyMZ95/NWOYuulzlYNXDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"06902e1fab7ac2e2d058d8263e1c5bb80a0707272915352937b62516968f71ca","last_reissued_at":"2026-07-05T07:50:20.171898Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:50:20.171898Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"AG codes have no list-decoding friends: Approaching the generalized Singleton bound requires exponential alphabets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO","math.IT"],"primary_cat":"cs.IT","authors_text":"Omar Alrabiah, Ray Li, Venkatesan Guruswami","submitted_at":"2023-08-25T15:09:28Z","abstract_excerpt":"A simple, recently observed generalization of the classical Singleton bound to list-decoding asserts that rate $R$ codes are not list-decodable using list-size $L$ beyond an error fraction $\\frac{L}{L+1} (1-R)$ (the Singleton bound being the case of $L=1$, i.e., unique decoding). We prove that in order to approach this bound for any fixed $L >1$, one needs exponential alphabets. Specifically, for every $L>1$ and $R\\in(0,1)$, if a rate $R$ code can be list-of-$L$ decoded up to error fraction $\\frac{L}{L+1} (1-R -\\varepsilon)$, then its alphabet must have size at least $\\exp(\\Omega_{L,R}(1/\\vare"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.13424","kind":"arxiv","version":2},"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/2308.13424/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":"2308.13424","created_at":"2026-07-05T07:50:20.171954+00:00"},{"alias_kind":"arxiv_version","alias_value":"2308.13424v2","created_at":"2026-07-05T07:50:20.171954+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2308.13424","created_at":"2026-07-05T07:50:20.171954+00:00"},{"alias_kind":"pith_short_12","alias_value":"A2IC4H5LPLBO","created_at":"2026-07-05T07:50:20.171954+00:00"},{"alias_kind":"pith_short_16","alias_value":"A2IC4H5LPLBOFUCY","created_at":"2026-07-05T07:50:20.171954+00:00"},{"alias_kind":"pith_short_8","alias_value":"A2IC4H5L","created_at":"2026-07-05T07:50:20.171954+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/A2IC4H5LPLBOFUCY3ATD4HC3XA","json":"https://pith.science/pith/A2IC4H5LPLBOFUCY3ATD4HC3XA.json","graph_json":"https://pith.science/api/pith-number/A2IC4H5LPLBOFUCY3ATD4HC3XA/graph.json","events_json":"https://pith.science/api/pith-number/A2IC4H5LPLBOFUCY3ATD4HC3XA/events.json","paper":"https://pith.science/paper/A2IC4H5L"},"agent_actions":{"view_html":"https://pith.science/pith/A2IC4H5LPLBOFUCY3ATD4HC3XA","download_json":"https://pith.science/pith/A2IC4H5LPLBOFUCY3ATD4HC3XA.json","view_paper":"https://pith.science/paper/A2IC4H5L","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2308.13424&json=true","fetch_graph":"https://pith.science/api/pith-number/A2IC4H5LPLBOFUCY3ATD4HC3XA/graph.json","fetch_events":"https://pith.science/api/pith-number/A2IC4H5LPLBOFUCY3ATD4HC3XA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/A2IC4H5LPLBOFUCY3ATD4HC3XA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/A2IC4H5LPLBOFUCY3ATD4HC3XA/action/storage_attestation","attest_author":"https://pith.science/pith/A2IC4H5LPLBOFUCY3ATD4HC3XA/action/author_attestation","sign_citation":"https://pith.science/pith/A2IC4H5LPLBOFUCY3ATD4HC3XA/action/citation_signature","submit_replication":"https://pith.science/pith/A2IC4H5LPLBOFUCY3ATD4HC3XA/action/replication_record"}},"created_at":"2026-07-05T07:50:20.171954+00:00","updated_at":"2026-07-05T07:50:20.171954+00:00"}