{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:V2B2MWQ6BPXQEYUQWQRD5F4LB5","short_pith_number":"pith:V2B2MWQ6","canonical_record":{"source":{"id":"2205.01513","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2022-05-03T14:10:11Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"6bcd38da06ac748569c366da6cb8b4a4098ba49a93c25cc4378fdea3e58df90a","abstract_canon_sha256":"271424b42702280dba37c1949ed3d0b68ea7f8de34ea4242cd2b210c0fe9b9ab"},"schema_version":"1.0"},"canonical_sha256":"ae83a65a1e0bef026290b4223e978b0f7e32d3b4eb3a316ebc799a57d62b3d06","source":{"kind":"arxiv","id":"2205.01513","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2205.01513","created_at":"2026-07-05T04:20:05Z"},{"alias_kind":"arxiv_version","alias_value":"2205.01513v1","created_at":"2026-07-05T04:20:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2205.01513","created_at":"2026-07-05T04:20:05Z"},{"alias_kind":"pith_short_12","alias_value":"V2B2MWQ6BPXQ","created_at":"2026-07-05T04:20:05Z"},{"alias_kind":"pith_short_16","alias_value":"V2B2MWQ6BPXQEYUQ","created_at":"2026-07-05T04:20:05Z"},{"alias_kind":"pith_short_8","alias_value":"V2B2MWQ6","created_at":"2026-07-05T04:20:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:V2B2MWQ6BPXQEYUQWQRD5F4LB5","target":"record","payload":{"canonical_record":{"source":{"id":"2205.01513","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2022-05-03T14:10:11Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"6bcd38da06ac748569c366da6cb8b4a4098ba49a93c25cc4378fdea3e58df90a","abstract_canon_sha256":"271424b42702280dba37c1949ed3d0b68ea7f8de34ea4242cd2b210c0fe9b9ab"},"schema_version":"1.0"},"canonical_sha256":"ae83a65a1e0bef026290b4223e978b0f7e32d3b4eb3a316ebc799a57d62b3d06","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:20:05.891140Z","signature_b64":"tFbm3EUtczHEECzrslIbX+qVMlk6BDiKEPJ3uqGN4a7a1rgmtiGybFtg4grYJJRkMnydp2u58Abt6HrmyVkyDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ae83a65a1e0bef026290b4223e978b0f7e32d3b4eb3a316ebc799a57d62b3d06","last_reissued_at":"2026-07-05T04:20:05.890725Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:20:05.890725Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2205.01513","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:20:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Wt7OToZ3YxlnE+fePz5W3y8u6AmIYdDkSC/ydbos9Z1We4SMuk5p67p3GOYrJPownOYzJS+poxqjMC5faFPFAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T08:29:16.665414Z"},"content_sha256":"ae656df0476cb1d2cf64efc6d2386457bc0db58b23d132e064da3771ba6855b7","schema_version":"1.0","event_id":"sha256:ae656df0476cb1d2cf64efc6d2386457bc0db58b23d132e064da3771ba6855b7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:V2B2MWQ6BPXQEYUQWQRD5F4LB5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Threshold Rates of Codes Ensembles: Linear is Best","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Chen Yuan, Nicolas Resch","submitted_at":"2022-05-03T14:10:11Z","abstract_excerpt":"In this work, we prove new results concerning the combinatorial properties of random linear codes.\n  Firstly, we prove a lower bound on the list-size required for random linear codes over $\\mathbb F_q$ $\\varepsilon$-close to capacity to list-recover with error radius $\\rho$ and input lists of size $\\ell$. We show that the list-size $L$ must be at least $\\frac{\\log_q\\binom{q}{\\ell}-R}{\\varepsilon}$, where $R$ is the rate of the random linear code. As a comparison, we also pin down the list size of random codes which is $\\frac{\\log_q\\binom{q}{\\ell}}{\\varepsilon}$. This leaves open the possibilit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2205.01513","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/2205.01513/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:20:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PnJ2o8KyUK1C5HqF4sjXpKr+qXhjsxwQLYVguUIE+Twn+VMyO2ya84G973SGdbHjAGB3xDvg2exBFJd/TWhWAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T08:29:16.666538Z"},"content_sha256":"9d4399eea7d63a81103bef37f8919416b5c9f94ba4b34f5637ddeee36d1d0781","schema_version":"1.0","event_id":"sha256:9d4399eea7d63a81103bef37f8919416b5c9f94ba4b34f5637ddeee36d1d0781"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V2B2MWQ6BPXQEYUQWQRD5F4LB5/bundle.json","state_url":"https://pith.science/pith/V2B2MWQ6BPXQEYUQWQRD5F4LB5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V2B2MWQ6BPXQEYUQWQRD5F4LB5/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-11T08:29:16Z","links":{"resolver":"https://pith.science/pith/V2B2MWQ6BPXQEYUQWQRD5F4LB5","bundle":"https://pith.science/pith/V2B2MWQ6BPXQEYUQWQRD5F4LB5/bundle.json","state":"https://pith.science/pith/V2B2MWQ6BPXQEYUQWQRD5F4LB5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V2B2MWQ6BPXQEYUQWQRD5F4LB5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:V2B2MWQ6BPXQEYUQWQRD5F4LB5","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":"271424b42702280dba37c1949ed3d0b68ea7f8de34ea4242cd2b210c0fe9b9ab","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2022-05-03T14:10:11Z","title_canon_sha256":"6bcd38da06ac748569c366da6cb8b4a4098ba49a93c25cc4378fdea3e58df90a"},"schema_version":"1.0","source":{"id":"2205.01513","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2205.01513","created_at":"2026-07-05T04:20:05Z"},{"alias_kind":"arxiv_version","alias_value":"2205.01513v1","created_at":"2026-07-05T04:20:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2205.01513","created_at":"2026-07-05T04:20:05Z"},{"alias_kind":"pith_short_12","alias_value":"V2B2MWQ6BPXQ","created_at":"2026-07-05T04:20:05Z"},{"alias_kind":"pith_short_16","alias_value":"V2B2MWQ6BPXQEYUQ","created_at":"2026-07-05T04:20:05Z"},{"alias_kind":"pith_short_8","alias_value":"V2B2MWQ6","created_at":"2026-07-05T04:20:05Z"}],"graph_snapshots":[{"event_id":"sha256:9d4399eea7d63a81103bef37f8919416b5c9f94ba4b34f5637ddeee36d1d0781","target":"graph","created_at":"2026-07-05T04:20:05Z","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/2205.01513/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this work, we prove new results concerning the combinatorial properties of random linear codes.\n  Firstly, we prove a lower bound on the list-size required for random linear codes over $\\mathbb F_q$ $\\varepsilon$-close to capacity to list-recover with error radius $\\rho$ and input lists of size $\\ell$. We show that the list-size $L$ must be at least $\\frac{\\log_q\\binom{q}{\\ell}-R}{\\varepsilon}$, where $R$ is the rate of the random linear code. As a comparison, we also pin down the list size of random codes which is $\\frac{\\log_q\\binom{q}{\\ell}}{\\varepsilon}$. This leaves open the possibilit","authors_text":"Chen Yuan, Nicolas Resch","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2022-05-03T14:10:11Z","title":"Threshold Rates of Codes Ensembles: Linear is Best"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2205.01513","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:ae656df0476cb1d2cf64efc6d2386457bc0db58b23d132e064da3771ba6855b7","target":"record","created_at":"2026-07-05T04:20:05Z","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":"271424b42702280dba37c1949ed3d0b68ea7f8de34ea4242cd2b210c0fe9b9ab","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2022-05-03T14:10:11Z","title_canon_sha256":"6bcd38da06ac748569c366da6cb8b4a4098ba49a93c25cc4378fdea3e58df90a"},"schema_version":"1.0","source":{"id":"2205.01513","kind":"arxiv","version":1}},"canonical_sha256":"ae83a65a1e0bef026290b4223e978b0f7e32d3b4eb3a316ebc799a57d62b3d06","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ae83a65a1e0bef026290b4223e978b0f7e32d3b4eb3a316ebc799a57d62b3d06","first_computed_at":"2026-07-05T04:20:05.890725Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:20:05.890725Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tFbm3EUtczHEECzrslIbX+qVMlk6BDiKEPJ3uqGN4a7a1rgmtiGybFtg4grYJJRkMnydp2u58Abt6HrmyVkyDw==","signature_status":"signed_v1","signed_at":"2026-07-05T04:20:05.891140Z","signed_message":"canonical_sha256_bytes"},"source_id":"2205.01513","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ae656df0476cb1d2cf64efc6d2386457bc0db58b23d132e064da3771ba6855b7","sha256:9d4399eea7d63a81103bef37f8919416b5c9f94ba4b34f5637ddeee36d1d0781"],"state_sha256":"940224d2255dfc0dc35a27dc50e12a5f7215560fead29911950119d48b42d18c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dwmr1LDU5Q39vzAMQxBvd4BbIWCtN+86H/sJLL6wFRNbWtbFHTF+cvaeiYYu6zpwY8XNBTWZ7SF8Wutoy5MBBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T08:29:16.672493Z","bundle_sha256":"a34e189e4ee4a7986d2d88508d2476ed286778f88ae85318e7c79cc75606bf5e"}}