{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:WBLTCTO2HAO6Z52RRVV6QL6V7N","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":"dff0156d5012151984453e6670927f9e59511588ef60ce22e0e2ada856550918","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-03-18T00:34:10Z","title_canon_sha256":"2952eeff2c9d02276eef4793bc66257671ff38b32ccb42c8d61a9747e33f8641"},"schema_version":"1.0","source":{"id":"1603.05736","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.05736","created_at":"2026-05-18T00:34:00Z"},{"alias_kind":"arxiv_version","alias_value":"1603.05736v2","created_at":"2026-05-18T00:34:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.05736","created_at":"2026-05-18T00:34:00Z"},{"alias_kind":"pith_short_12","alias_value":"WBLTCTO2HAO6","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"WBLTCTO2HAO6Z52R","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"WBLTCTO2","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:7e98a89f1139c351ec55b135ca70c237a466421dfa3d9f15cee2bb8bfb72580a","target":"graph","created_at":"2026-05-18T00:34:00Z","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":"It is known that polar codes can be efficiently constructed for binary-input channels. At the same time, existing algorithms for general input alphabets are less practical because of high complexity. We address the construction problem for the general case, and analyze an algorithm that is based on successive reduction of the output alphabet size of the subchannels in each recursion step. For this procedure we estimate the approximation error as $O(\\mu^{-1/(q-1)}),$ where $\\mu$ is the \"quantization parameter,\" i.e., the maximum size of the subchannel output alphabet allowed by the algorithm. T","authors_text":"Alexander Barg, Min Ye, Talha Cihad Gulcu","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-03-18T00:34:10Z","title":"Construction of polar codes for arbitrary discrete memoryless channels"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.05736","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:d38f965c3130294d317210f5438fd7823bb3da32fba5af907f1bfebd0247ccbc","target":"record","created_at":"2026-05-18T00:34:00Z","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":"dff0156d5012151984453e6670927f9e59511588ef60ce22e0e2ada856550918","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-03-18T00:34:10Z","title_canon_sha256":"2952eeff2c9d02276eef4793bc66257671ff38b32ccb42c8d61a9747e33f8641"},"schema_version":"1.0","source":{"id":"1603.05736","kind":"arxiv","version":2}},"canonical_sha256":"b057314dda381decf7518d6be82fd5fb7c70e2773d73a6b67edb2b0ee0657ab7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b057314dda381decf7518d6be82fd5fb7c70e2773d73a6b67edb2b0ee0657ab7","first_computed_at":"2026-05-18T00:34:00.065368Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:34:00.065368Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s/1AKnvoQtwFrkywnAJkygUfXfQn59lAlt4kF7TUj98e2c5v0oHHetbdeSOoHFK729tWii4CFFKXUEz1vAInDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:34:00.065972Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.05736","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d38f965c3130294d317210f5438fd7823bb3da32fba5af907f1bfebd0247ccbc","sha256:7e98a89f1139c351ec55b135ca70c237a466421dfa3d9f15cee2bb8bfb72580a"],"state_sha256":"59b52d8d659aa96dcba7aa0ea4df2af0a5a344a81fb969e553dcf71f89bb0925"}