{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:OIWD66YMQ473JXR5RSHSXVZK7X","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":"a8427b9fbae46bb389c4d3330b76f211a49276b8c12aa5dba0836fcf35638b7a","cross_cats_sorted":["math.IT","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2020-04-28T02:29:26Z","title_canon_sha256":"39a0cd962f9423748b74653158932ea778655ebc1f9bc2a8f9eb0001335aad5d"},"schema_version":"1.0","source":{"id":"2004.13247","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2004.13247","created_at":"2026-07-05T08:41:57Z"},{"alias_kind":"arxiv_version","alias_value":"2004.13247v2","created_at":"2026-07-05T08:41:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2004.13247","created_at":"2026-07-05T08:41:57Z"},{"alias_kind":"pith_short_12","alias_value":"OIWD66YMQ473","created_at":"2026-07-05T08:41:57Z"},{"alias_kind":"pith_short_16","alias_value":"OIWD66YMQ473JXR5","created_at":"2026-07-05T08:41:57Z"},{"alias_kind":"pith_short_8","alias_value":"OIWD66YM","created_at":"2026-07-05T08:41:57Z"}],"graph_snapshots":[{"event_id":"sha256:0e84b48de46069d9417c58e34e5bd6d7411216faa226d212ff788a8412580e21","target":"graph","created_at":"2026-07-05T08:41:57Z","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/2004.13247/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A family of error-correcting codes is list-decodable from error fraction $p$ if, for every code in the family, the number of codewords in any Hamming ball of fractional radius $p$ is less than some integer $L$ that is independent of the code length. It is said to be list-recoverable for input list size $\\ell$ if for every sufficiently large subset of codewords (of size $L$ or more), there is a coordinate where the codewords take more than $\\ell$ values. The parameter $L$ is said to be the \"list size\" in either case. The capacity, i.e., the largest possible rate for these notions as the list si","authors_text":"Jonathan Mosheiff, Mary Wootters, Nicolas Resch, Ray Li, Shashwat Silas, Venkatesan Guruswami","cross_cats":["math.IT","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2020-04-28T02:29:26Z","title":"Bounds for list-decoding and list-recovery of random linear codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2004.13247","kind":"arxiv","version":2},"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":"sha256:40d390161d356a47b61bc006b21298ee45a26a112fb082338282154f0840faaa","target":"record","created_at":"2026-07-05T08:41:57Z","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":"a8427b9fbae46bb389c4d3330b76f211a49276b8c12aa5dba0836fcf35638b7a","cross_cats_sorted":["math.IT","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2020-04-28T02:29:26Z","title_canon_sha256":"39a0cd962f9423748b74653158932ea778655ebc1f9bc2a8f9eb0001335aad5d"},"schema_version":"1.0","source":{"id":"2004.13247","kind":"arxiv","version":2}},"canonical_sha256":"722c3f7b0c873fb4de3d8c8f2bd72afde4fab7668a09d77f66379e3cb8587a47","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"722c3f7b0c873fb4de3d8c8f2bd72afde4fab7668a09d77f66379e3cb8587a47","first_computed_at":"2026-07-05T08:41:57.164841Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:41:57.164841Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M0lZgwI0OR1153IVoIFVC7ULtv10MB7snxgTwaTEaDH7Rsn28nljOw9TMu6y92kkByMLmO9mQxWog3LDM3ziCg==","signature_status":"signed_v1","signed_at":"2026-07-05T08:41:57.165248Z","signed_message":"canonical_sha256_bytes"},"source_id":"2004.13247","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:40d390161d356a47b61bc006b21298ee45a26a112fb082338282154f0840faaa","sha256:0e84b48de46069d9417c58e34e5bd6d7411216faa226d212ff788a8412580e21"],"state_sha256":"02e02b72513b9f303bdbcee7f8244f7f1c1b15c5318f9a4e090eb5f7b218c34b"}