{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:OMP56HSSVLKUBZ2BZK27742KGW","short_pith_number":"pith:OMP56HSS","canonical_record":{"source":{"id":"1311.3123","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-11-13T13:24:56Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"3f708d09851e2114a41da9c8bd1e5f1301b3ee4e02967e46235f13f7395b412c","abstract_canon_sha256":"978efe605b566cc39de30bea6a4da19701c1c77f2e709eed29fddeba5bdbad78"},"schema_version":"1.0"},"canonical_sha256":"731fdf1e52aad540e741cab5fff34a359249d65c885c88e7b154c0fe669945f6","source":{"kind":"arxiv","id":"1311.3123","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.3123","created_at":"2026-05-18T01:12:25Z"},{"alias_kind":"arxiv_version","alias_value":"1311.3123v1","created_at":"2026-05-18T01:12:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.3123","created_at":"2026-05-18T01:12:25Z"},{"alias_kind":"pith_short_12","alias_value":"OMP56HSSVLKU","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"OMP56HSSVLKUBZ2B","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"OMP56HSS","created_at":"2026-05-18T12:27:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:OMP56HSSVLKUBZ2BZK27742KGW","target":"record","payload":{"canonical_record":{"source":{"id":"1311.3123","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-11-13T13:24:56Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"3f708d09851e2114a41da9c8bd1e5f1301b3ee4e02967e46235f13f7395b412c","abstract_canon_sha256":"978efe605b566cc39de30bea6a4da19701c1c77f2e709eed29fddeba5bdbad78"},"schema_version":"1.0"},"canonical_sha256":"731fdf1e52aad540e741cab5fff34a359249d65c885c88e7b154c0fe669945f6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:25.419156Z","signature_b64":"txRVuQq2HRZ8FxJJSG51XwaRRLyrjgd3NKj1pBpri7gFFM8hYtjIgUD0WDFZPN0KdwfaI40jlPHNFyyxWbKOCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"731fdf1e52aad540e741cab5fff34a359249d65c885c88e7b154c0fe669945f6","last_reissued_at":"2026-05-18T01:12:25.418815Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:25.418815Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1311.3123","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":"2026-05-18T01:12:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hoRY3mwY2KjXJ/Q44PxTmsKXxHZ5uG4Oy0y0odYGb9pVCW7Joi8W1fSIgm2srqcfNJPxSjn0EqH/cpIICUetDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T06:35:03.983663Z"},"content_sha256":"d820a7269e2e05833122eee9dfa9db4490ecb4723da022fcb4022e429befca3f","schema_version":"1.0","event_id":"sha256:d820a7269e2e05833122eee9dfa9db4490ecb4723da022fcb4022e429befca3f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:OMP56HSSVLKUBZ2BZK27742KGW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Polar Codes for Arbitrary DMCs and Arbitrary MACs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Emre Telatar, Rajai Nasser","submitted_at":"2013-11-13T13:24:56Z","abstract_excerpt":"Polar codes are constructed for arbitrary channels by imposing an arbitrary quasigroup structure on the input alphabet. Just as with \"usual\" polar codes, the block error probability under successive cancellation decoding is $o(2^{-N^{1/2-\\epsilon}})$, where $N$ is the block length. Encoding and decoding for these codes can be implemented with a complexity of $O(N\\log N)$. It is shown that the same technique can be used to construct polar codes for arbitrary multiple access channels (MAC) by using an appropriate Abelian group structure. Although the symmetric sum capacity is achieved by this co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.3123","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":"2026-05-18T01:12:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OayxyqszRmVflYQeMTw8NucXIZGUhMCWPhyMdXdcBrDrHKJgMMv+J6vsMSwBX+Ed+ose8pqTfpNabBbd9l7uAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T06:35:03.984052Z"},"content_sha256":"3f2bd25f6f4d9e5c3f1aec3ce42666179bff739c4116a9c409a611d39a98efd1","schema_version":"1.0","event_id":"sha256:3f2bd25f6f4d9e5c3f1aec3ce42666179bff739c4116a9c409a611d39a98efd1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OMP56HSSVLKUBZ2BZK27742KGW/bundle.json","state_url":"https://pith.science/pith/OMP56HSSVLKUBZ2BZK27742KGW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OMP56HSSVLKUBZ2BZK27742KGW/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":"2026-05-25T06:35:03Z","links":{"resolver":"https://pith.science/pith/OMP56HSSVLKUBZ2BZK27742KGW","bundle":"https://pith.science/pith/OMP56HSSVLKUBZ2BZK27742KGW/bundle.json","state":"https://pith.science/pith/OMP56HSSVLKUBZ2BZK27742KGW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OMP56HSSVLKUBZ2BZK27742KGW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:OMP56HSSVLKUBZ2BZK27742KGW","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":"978efe605b566cc39de30bea6a4da19701c1c77f2e709eed29fddeba5bdbad78","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-11-13T13:24:56Z","title_canon_sha256":"3f708d09851e2114a41da9c8bd1e5f1301b3ee4e02967e46235f13f7395b412c"},"schema_version":"1.0","source":{"id":"1311.3123","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.3123","created_at":"2026-05-18T01:12:25Z"},{"alias_kind":"arxiv_version","alias_value":"1311.3123v1","created_at":"2026-05-18T01:12:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.3123","created_at":"2026-05-18T01:12:25Z"},{"alias_kind":"pith_short_12","alias_value":"OMP56HSSVLKU","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"OMP56HSSVLKUBZ2B","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"OMP56HSS","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:3f2bd25f6f4d9e5c3f1aec3ce42666179bff739c4116a9c409a611d39a98efd1","target":"graph","created_at":"2026-05-18T01:12:25Z","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":"Polar codes are constructed for arbitrary channels by imposing an arbitrary quasigroup structure on the input alphabet. Just as with \"usual\" polar codes, the block error probability under successive cancellation decoding is $o(2^{-N^{1/2-\\epsilon}})$, where $N$ is the block length. Encoding and decoding for these codes can be implemented with a complexity of $O(N\\log N)$. It is shown that the same technique can be used to construct polar codes for arbitrary multiple access channels (MAC) by using an appropriate Abelian group structure. Although the symmetric sum capacity is achieved by this co","authors_text":"Emre Telatar, Rajai Nasser","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-11-13T13:24:56Z","title":"Polar Codes for Arbitrary DMCs and Arbitrary MACs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.3123","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:d820a7269e2e05833122eee9dfa9db4490ecb4723da022fcb4022e429befca3f","target":"record","created_at":"2026-05-18T01:12:25Z","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":"978efe605b566cc39de30bea6a4da19701c1c77f2e709eed29fddeba5bdbad78","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-11-13T13:24:56Z","title_canon_sha256":"3f708d09851e2114a41da9c8bd1e5f1301b3ee4e02967e46235f13f7395b412c"},"schema_version":"1.0","source":{"id":"1311.3123","kind":"arxiv","version":1}},"canonical_sha256":"731fdf1e52aad540e741cab5fff34a359249d65c885c88e7b154c0fe669945f6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"731fdf1e52aad540e741cab5fff34a359249d65c885c88e7b154c0fe669945f6","first_computed_at":"2026-05-18T01:12:25.418815Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:25.418815Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"txRVuQq2HRZ8FxJJSG51XwaRRLyrjgd3NKj1pBpri7gFFM8hYtjIgUD0WDFZPN0KdwfaI40jlPHNFyyxWbKOCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:25.419156Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.3123","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d820a7269e2e05833122eee9dfa9db4490ecb4723da022fcb4022e429befca3f","sha256:3f2bd25f6f4d9e5c3f1aec3ce42666179bff739c4116a9c409a611d39a98efd1"],"state_sha256":"e2c4e35db7ccd5ff9b0fc4eb1fda5e5407c87c30b25d1bb3ba9aa27a77c403eb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bZWdI/SnRWFavwoQtvlPC9GKODeIQGXU4aQHkJGBChiucBRbn4Z1QYfvZOetvROq+7u+SEt5J2U7E+mXcq5wAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T06:35:03.986626Z","bundle_sha256":"be402a50ea6a4333a992d41117613e370c619afd471f06dab0d7f4d7e0a0c975"}}