{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:OCV2PJOGK67BSJWBLISOBB5SQU","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":"10e996bc1c207cc25904c635b8d93bed7574c18e8edc672677a2487a3c93d021","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-12-19T17:42:44Z","title_canon_sha256":"ce2caca83602ac04c3a06bbbc3e82cfe085c710e88ddaa9de48cab2fecddc7c7"},"schema_version":"1.0","source":{"id":"1812.08112","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.08112","created_at":"2026-05-17T23:57:54Z"},{"alias_kind":"arxiv_version","alias_value":"1812.08112v1","created_at":"2026-05-17T23:57:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.08112","created_at":"2026-05-17T23:57:54Z"},{"alias_kind":"pith_short_12","alias_value":"OCV2PJOGK67B","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"OCV2PJOGK67BSJWB","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"OCV2PJOG","created_at":"2026-05-18T12:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:057d988d4d82ecf88849853445ec0f21b22bc829c4b46aa61f0611175c8c422f","target":"graph","created_at":"2026-05-17T23:57:54Z","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":"A general framework is proposed that includes polar codes over arbitrary channels with arbitrary kernels. The asymptotic tradeoff among block length $N$, code rate $R$, and error probability $P$ is analyzed.\n  Given a tradeoff between $N,P$ and a tradeoff between $N,R$, we return an interpolating tradeoff among $N,R,P$ (Theorem 5). $\\def\\Capacity{\\text{Capacity}}$Quantitatively, if $P=\\exp(-N^{\\beta^*})$ is possible for some $\\beta^*$ and if $R=\\Capacity-N^{1/\\mu^*}$ is possible for some $1/\\mu^*$, then $(P,R)=(\\exp(-N^{\\beta'}),\\Capacity-N^{-1/\\mu'})$ is possible for some pair $(\\beta',1/\\mu'","authors_text":"Hsin-Po Wang, Iwan Duursma","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-12-19T17:42:44Z","title":"Polar-like Codes and Asymptotic Tradeoff among Block Length, Code Rate, and Error Probability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.08112","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:a0866f1a53c352072bc354c2a47e9ddcb821bd9f923efff9dbb13eaf1e88f2e3","target":"record","created_at":"2026-05-17T23:57:54Z","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":"10e996bc1c207cc25904c635b8d93bed7574c18e8edc672677a2487a3c93d021","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-12-19T17:42:44Z","title_canon_sha256":"ce2caca83602ac04c3a06bbbc3e82cfe085c710e88ddaa9de48cab2fecddc7c7"},"schema_version":"1.0","source":{"id":"1812.08112","kind":"arxiv","version":1}},"canonical_sha256":"70aba7a5c657be1926c15a24e087b28513db626126c71d5d9998309c0603bbfe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"70aba7a5c657be1926c15a24e087b28513db626126c71d5d9998309c0603bbfe","first_computed_at":"2026-05-17T23:57:54.810387Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:54.810387Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nnUc5wztnvy4nhX9lKGDaSBib4repJ2P9afPJU2o2XcnG+XWUWHREmn+ebiLKX96dzgZ9fGmAQefivCGaQf1Ag==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:54.810940Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.08112","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a0866f1a53c352072bc354c2a47e9ddcb821bd9f923efff9dbb13eaf1e88f2e3","sha256:057d988d4d82ecf88849853445ec0f21b22bc829c4b46aa61f0611175c8c422f"],"state_sha256":"4a0c3cf63155e8e68e07321df995aba7d15e1b7745770c48d51c4bd0dda19b0e"}