{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:CFWSFN4BUBFJAHH643ETPJWPSH","short_pith_number":"pith:CFWSFN4B","canonical_record":{"source":{"id":"1810.08161","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-10-18T16:57:26Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"44039c29f0f67fe105e2e8ac207c0e2529639f1a0b2da59e439d1f9a78743d08","abstract_canon_sha256":"f5be2ad4f9e98e10228534ba402422059fc5588a70b8362701e11d2d135f5452"},"schema_version":"1.0"},"canonical_sha256":"116d22b781a04a901cfee6c937a6cf91c22a66f402d951d90ed5e34d1027b3e1","source":{"kind":"arxiv","id":"1810.08161","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.08161","created_at":"2026-05-18T00:02:50Z"},{"alias_kind":"arxiv_version","alias_value":"1810.08161v1","created_at":"2026-05-18T00:02:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.08161","created_at":"2026-05-18T00:02:50Z"},{"alias_kind":"pith_short_12","alias_value":"CFWSFN4BUBFJ","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"CFWSFN4BUBFJAHH6","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"CFWSFN4B","created_at":"2026-05-18T12:32:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:CFWSFN4BUBFJAHH643ETPJWPSH","target":"record","payload":{"canonical_record":{"source":{"id":"1810.08161","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-10-18T16:57:26Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"44039c29f0f67fe105e2e8ac207c0e2529639f1a0b2da59e439d1f9a78743d08","abstract_canon_sha256":"f5be2ad4f9e98e10228534ba402422059fc5588a70b8362701e11d2d135f5452"},"schema_version":"1.0"},"canonical_sha256":"116d22b781a04a901cfee6c937a6cf91c22a66f402d951d90ed5e34d1027b3e1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:50.417444Z","signature_b64":"KYZY9LUc6wj9MZDegCBaWP4+8up0OLm7+Mevod1lu4kWyGAPDTs/W2YwfNArLkoDuPjxRtbScLoVTNIRuSlgAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"116d22b781a04a901cfee6c937a6cf91c22a66f402d951d90ed5e34d1027b3e1","last_reissued_at":"2026-05-18T00:02:50.416939Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:50.416939Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.08161","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":"2026-05-18T00:02:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LH/Saxt8x8s97r05I1+z8FmSfP0zBVNSsoHrG5+VdErlqlzvrqnUCyyj6hSIZ3tztyq5e8w4BWxkxmcz+q1GCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T05:37:56.238818Z"},"content_sha256":"c8d28b02f71176ff9bbaa26a544cd63aba8ae89c2a4c7b5d00bca38d95eae32a","schema_version":"1.0","event_id":"sha256:c8d28b02f71176ff9bbaa26a544cd63aba8ae89c2a4c7b5d00bca38d95eae32a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:CFWSFN4BUBFJAHH643ETPJWPSH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Ratio List Decoding","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Anelia Somekh-Baruch","submitted_at":"2018-10-18T16:57:26Z","abstract_excerpt":"We extend the notion of list decoding to {\\em ratio list decoding} which involves a list decoder whose list size is specified as a function of the number of messages $M_n$ and the block length $n$. We present necessary and sufficient conditions on $M_n$ for the existence of code sequences which enable reliable list decoding with respect to the desired list size $L(M_n,n)$. It is shown that the ratio-capacity, defined as the supremum of achievable normalized logarithms of the ratio $r(M_n,n)=M_n/L(M_n,n)$ is equal to the Shannon channel capacity $C$, for both stochastic and deterministic encodi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.08161","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":""},"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":"2026-05-18T00:02:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EfPeyZS9WMcAhP0LiVkw6UTUqRbNBqTCFo8MjE+DuyuqM/zzKEBSS00yNp8sQrtNSwhSKF69AkrQYeUGvBTADg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T05:37:56.239324Z"},"content_sha256":"848a1a78bd6a85c44f2a555e693a0bf2029b40bdd627f6e5430495b66724152d","schema_version":"1.0","event_id":"sha256:848a1a78bd6a85c44f2a555e693a0bf2029b40bdd627f6e5430495b66724152d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CFWSFN4BUBFJAHH643ETPJWPSH/bundle.json","state_url":"https://pith.science/pith/CFWSFN4BUBFJAHH643ETPJWPSH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CFWSFN4BUBFJAHH643ETPJWPSH/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":"2026-05-31T05:37:56Z","links":{"resolver":"https://pith.science/pith/CFWSFN4BUBFJAHH643ETPJWPSH","bundle":"https://pith.science/pith/CFWSFN4BUBFJAHH643ETPJWPSH/bundle.json","state":"https://pith.science/pith/CFWSFN4BUBFJAHH643ETPJWPSH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CFWSFN4BUBFJAHH643ETPJWPSH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:CFWSFN4BUBFJAHH643ETPJWPSH","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":"f5be2ad4f9e98e10228534ba402422059fc5588a70b8362701e11d2d135f5452","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-10-18T16:57:26Z","title_canon_sha256":"44039c29f0f67fe105e2e8ac207c0e2529639f1a0b2da59e439d1f9a78743d08"},"schema_version":"1.0","source":{"id":"1810.08161","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.08161","created_at":"2026-05-18T00:02:50Z"},{"alias_kind":"arxiv_version","alias_value":"1810.08161v1","created_at":"2026-05-18T00:02:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.08161","created_at":"2026-05-18T00:02:50Z"},{"alias_kind":"pith_short_12","alias_value":"CFWSFN4BUBFJ","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"CFWSFN4BUBFJAHH6","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"CFWSFN4B","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:848a1a78bd6a85c44f2a555e693a0bf2029b40bdd627f6e5430495b66724152d","target":"graph","created_at":"2026-05-18T00:02:50Z","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"},"paper":{"abstract_excerpt":"We extend the notion of list decoding to {\\em ratio list decoding} which involves a list decoder whose list size is specified as a function of the number of messages $M_n$ and the block length $n$. We present necessary and sufficient conditions on $M_n$ for the existence of code sequences which enable reliable list decoding with respect to the desired list size $L(M_n,n)$. It is shown that the ratio-capacity, defined as the supremum of achievable normalized logarithms of the ratio $r(M_n,n)=M_n/L(M_n,n)$ is equal to the Shannon channel capacity $C$, for both stochastic and deterministic encodi","authors_text":"Anelia Somekh-Baruch","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-10-18T16:57:26Z","title":"Ratio List Decoding"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.08161","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:c8d28b02f71176ff9bbaa26a544cd63aba8ae89c2a4c7b5d00bca38d95eae32a","target":"record","created_at":"2026-05-18T00:02:50Z","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":"f5be2ad4f9e98e10228534ba402422059fc5588a70b8362701e11d2d135f5452","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-10-18T16:57:26Z","title_canon_sha256":"44039c29f0f67fe105e2e8ac207c0e2529639f1a0b2da59e439d1f9a78743d08"},"schema_version":"1.0","source":{"id":"1810.08161","kind":"arxiv","version":1}},"canonical_sha256":"116d22b781a04a901cfee6c937a6cf91c22a66f402d951d90ed5e34d1027b3e1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"116d22b781a04a901cfee6c937a6cf91c22a66f402d951d90ed5e34d1027b3e1","first_computed_at":"2026-05-18T00:02:50.416939Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:50.416939Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KYZY9LUc6wj9MZDegCBaWP4+8up0OLm7+Mevod1lu4kWyGAPDTs/W2YwfNArLkoDuPjxRtbScLoVTNIRuSlgAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:50.417444Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.08161","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c8d28b02f71176ff9bbaa26a544cd63aba8ae89c2a4c7b5d00bca38d95eae32a","sha256:848a1a78bd6a85c44f2a555e693a0bf2029b40bdd627f6e5430495b66724152d"],"state_sha256":"441dabf6df7c075c0e928b1da05876a061bdc3458cf2d7f879dee74fb7c08512"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3IWMbyggeg+0gOa/y1DD/DeGpQEqyFrF+Mqxj6RnPpFJss96wsS6O5R4OvNNiA3dJFpvhZkUswPJajK2ZartAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T05:37:56.242898Z","bundle_sha256":"8f2018557eb50643f1e1f3cd94e6a133fab6f9cbf7a72778650599c28278570f"}}