{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:GDJU363TFVW4RW6AHZGJOIPAGK","short_pith_number":"pith:GDJU363T","canonical_record":{"source":{"id":"0811.4162","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2008-11-25T19:20:05Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"1f3b11d9191cc07cdedfa27162f82cb69857ea73f9297fdc44a128b2c8aa69b0","abstract_canon_sha256":"75238295ab6374fa1a51206554c3b7d5ad1501e28b247edc8cfff31b974f3295"},"schema_version":"1.0"},"canonical_sha256":"30d34dfb732d6dc8dbc03e4c9721e032a294364b5d1b0d7496bb0e25c9d59ec3","source":{"kind":"arxiv","id":"0811.4162","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0811.4162","created_at":"2026-05-18T04:10:34Z"},{"alias_kind":"arxiv_version","alias_value":"0811.4162v5","created_at":"2026-05-18T04:10:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0811.4162","created_at":"2026-05-18T04:10:34Z"},{"alias_kind":"pith_short_12","alias_value":"GDJU363TFVW4","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"GDJU363TFVW4RW6A","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"GDJU363T","created_at":"2026-05-18T12:25:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:GDJU363TFVW4RW6AHZGJOIPAGK","target":"record","payload":{"canonical_record":{"source":{"id":"0811.4162","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2008-11-25T19:20:05Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"1f3b11d9191cc07cdedfa27162f82cb69857ea73f9297fdc44a128b2c8aa69b0","abstract_canon_sha256":"75238295ab6374fa1a51206554c3b7d5ad1501e28b247edc8cfff31b974f3295"},"schema_version":"1.0"},"canonical_sha256":"30d34dfb732d6dc8dbc03e4c9721e032a294364b5d1b0d7496bb0e25c9d59ec3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:10:34.719608Z","signature_b64":"7rGDwiNHTu/tIPevmrkbgO12beEmwvqLJQjF8BVKN+FFGNexjE7jXrrl9+JTCf0g3AtgMMJYBVSVYdDnSPEmDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"30d34dfb732d6dc8dbc03e4c9721e032a294364b5d1b0d7496bb0e25c9d59ec3","last_reissued_at":"2026-05-18T04:10:34.718923Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:10:34.718923Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0811.4162","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:10:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y9Fs26k1VjO3KVCrT5b0vSwUoKq8g06rylNf54lxFfXbc+2/PqJSpyB7zDA+zRblQmUSRG9sVwkig0ZYNp1ZCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T08:23:40.770346Z"},"content_sha256":"56db5332d7725bbebb1bee74677d9245ce367883179dc4cfc8148b84afab3f0d","schema_version":"1.0","event_id":"sha256:56db5332d7725bbebb1bee74677d9245ce367883179dc4cfc8148b84afab3f0d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:GDJU363TFVW4RW6AHZGJOIPAGK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal Encoding Schemes for Several Classes of Discrete Degraded Broadcast Channels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Bike Xie, Richard D. Wesel, Thomas Courtade","submitted_at":"2008-11-25T19:20:05Z","abstract_excerpt":"Consider a memoryless degraded broadcast channel (DBC) in which the channel output is a single-letter function of the channel input and the channel noise. As examples, for the Gaussian broadcast channel (BC) this single-letter function is regular Euclidian addition and for the binary-symmetric BC this single-letter function is Galois-Field-two addition. This paper identifies several classes of discrete memoryless DBCs for which a relatively simple encoding scheme, which we call natural encoding, achieves capacity. Natural Encoding (NE) combines symbols from independent codebooks (one for each "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0811.4162","kind":"arxiv","version":5},"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":"2026-05-18T04:10:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SSXJSMVuSuoEvr3t2y5G5oBaJb72TVVK7bKIqSokurXg0h594Ltr1D9w7puPN9X5tEbOj40TmJElWbndKzYPBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T08:23:40.771027Z"},"content_sha256":"1216e3037b6100fad918d2578d42fbc545ef2743fb390910526e0de0eebb8d78","schema_version":"1.0","event_id":"sha256:1216e3037b6100fad918d2578d42fbc545ef2743fb390910526e0de0eebb8d78"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GDJU363TFVW4RW6AHZGJOIPAGK/bundle.json","state_url":"https://pith.science/pith/GDJU363TFVW4RW6AHZGJOIPAGK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GDJU363TFVW4RW6AHZGJOIPAGK/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":"2026-05-26T08:23:40Z","links":{"resolver":"https://pith.science/pith/GDJU363TFVW4RW6AHZGJOIPAGK","bundle":"https://pith.science/pith/GDJU363TFVW4RW6AHZGJOIPAGK/bundle.json","state":"https://pith.science/pith/GDJU363TFVW4RW6AHZGJOIPAGK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GDJU363TFVW4RW6AHZGJOIPAGK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:GDJU363TFVW4RW6AHZGJOIPAGK","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":"75238295ab6374fa1a51206554c3b7d5ad1501e28b247edc8cfff31b974f3295","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2008-11-25T19:20:05Z","title_canon_sha256":"1f3b11d9191cc07cdedfa27162f82cb69857ea73f9297fdc44a128b2c8aa69b0"},"schema_version":"1.0","source":{"id":"0811.4162","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0811.4162","created_at":"2026-05-18T04:10:34Z"},{"alias_kind":"arxiv_version","alias_value":"0811.4162v5","created_at":"2026-05-18T04:10:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0811.4162","created_at":"2026-05-18T04:10:34Z"},{"alias_kind":"pith_short_12","alias_value":"GDJU363TFVW4","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"GDJU363TFVW4RW6A","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"GDJU363T","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:1216e3037b6100fad918d2578d42fbc545ef2743fb390910526e0de0eebb8d78","target":"graph","created_at":"2026-05-18T04:10:34Z","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":"Consider a memoryless degraded broadcast channel (DBC) in which the channel output is a single-letter function of the channel input and the channel noise. As examples, for the Gaussian broadcast channel (BC) this single-letter function is regular Euclidian addition and for the binary-symmetric BC this single-letter function is Galois-Field-two addition. This paper identifies several classes of discrete memoryless DBCs for which a relatively simple encoding scheme, which we call natural encoding, achieves capacity. Natural Encoding (NE) combines symbols from independent codebooks (one for each ","authors_text":"Bike Xie, Richard D. Wesel, Thomas Courtade","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2008-11-25T19:20:05Z","title":"Optimal Encoding Schemes for Several Classes of Discrete Degraded Broadcast Channels"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0811.4162","kind":"arxiv","version":5},"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":"sha256:56db5332d7725bbebb1bee74677d9245ce367883179dc4cfc8148b84afab3f0d","target":"record","created_at":"2026-05-18T04:10:34Z","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":"75238295ab6374fa1a51206554c3b7d5ad1501e28b247edc8cfff31b974f3295","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2008-11-25T19:20:05Z","title_canon_sha256":"1f3b11d9191cc07cdedfa27162f82cb69857ea73f9297fdc44a128b2c8aa69b0"},"schema_version":"1.0","source":{"id":"0811.4162","kind":"arxiv","version":5}},"canonical_sha256":"30d34dfb732d6dc8dbc03e4c9721e032a294364b5d1b0d7496bb0e25c9d59ec3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"30d34dfb732d6dc8dbc03e4c9721e032a294364b5d1b0d7496bb0e25c9d59ec3","first_computed_at":"2026-05-18T04:10:34.718923Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:10:34.718923Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7rGDwiNHTu/tIPevmrkbgO12beEmwvqLJQjF8BVKN+FFGNexjE7jXrrl9+JTCf0g3AtgMMJYBVSVYdDnSPEmDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:10:34.719608Z","signed_message":"canonical_sha256_bytes"},"source_id":"0811.4162","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:56db5332d7725bbebb1bee74677d9245ce367883179dc4cfc8148b84afab3f0d","sha256:1216e3037b6100fad918d2578d42fbc545ef2743fb390910526e0de0eebb8d78"],"state_sha256":"dbb7ce88d588953f31bc04bd6a0e313342ac9f6ccc077d8c8277882d1a1b46bd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OII0VDwXYzd8r5yrtqBdfguA7a102RXKNce+4TPlvlj+doK4tsC6YnDhCfiyaZnzm5erOvz8261JOvdVtNIvBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T08:23:40.774634Z","bundle_sha256":"60f03b5532450516d82e058b29df06b73779b2569e068b8013e21d52e2234dda"}}