{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:DDR6PEC33BNYCIOZJWC4GGHE6H","short_pith_number":"pith:DDR6PEC3","canonical_record":{"source":{"id":"1006.5166","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-06-26T21:19:41Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"a24d290ea78d0c22a850d443e35687a822366b5c4ec455693c8a5508735ec72e","abstract_canon_sha256":"246e7860a2eab3169537afe589bae4f16e5535b1e8c0db0a317f618992a66d62"},"schema_version":"1.0"},"canonical_sha256":"18e3e7905bd85b8121d94d85c318e4f1f191bdf6e6bf04c850aebdefe93973bf","source":{"kind":"arxiv","id":"1006.5166","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.5166","created_at":"2026-05-18T00:57:57Z"},{"alias_kind":"arxiv_version","alias_value":"1006.5166v2","created_at":"2026-05-18T00:57:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.5166","created_at":"2026-05-18T00:57:57Z"},{"alias_kind":"pith_short_12","alias_value":"DDR6PEC33BNY","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"DDR6PEC33BNYCIOZ","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"DDR6PEC3","created_at":"2026-05-18T12:26:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:DDR6PEC33BNYCIOZJWC4GGHE6H","target":"record","payload":{"canonical_record":{"source":{"id":"1006.5166","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-06-26T21:19:41Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"a24d290ea78d0c22a850d443e35687a822366b5c4ec455693c8a5508735ec72e","abstract_canon_sha256":"246e7860a2eab3169537afe589bae4f16e5535b1e8c0db0a317f618992a66d62"},"schema_version":"1.0"},"canonical_sha256":"18e3e7905bd85b8121d94d85c318e4f1f191bdf6e6bf04c850aebdefe93973bf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:57:57.736904Z","signature_b64":"uS4GhbEiEN0vNWbnnJTg1IhJLj/WXuFxlZUHoALNLzzxwWv/xhsIaann9OFzx5qhrtWWwN6cyyDgEGNDhm2AAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"18e3e7905bd85b8121d94d85c318e4f1f191bdf6e6bf04c850aebdefe93973bf","last_reissued_at":"2026-05-18T00:57:57.736478Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:57:57.736478Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1006.5166","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:57:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iCDufLjE1eV05SFK4i+NJGeC4N0ec5yxHGOrVHcRNJ5LbjUXRgMyIaNikBsQLkI7/s0ut9/WJms6XexZgjmeDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T02:24:04.477047Z"},"content_sha256":"7ad16a6648e136284428cff8edf5edd7a4f28c7d3850c3dd65e04cf6f4bd3a1f","schema_version":"1.0","event_id":"sha256:7ad16a6648e136284428cff8edf5edd7a4f28c7d3850c3dd65e04cf6f4bd3a1f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:DDR6PEC33BNYCIOZJWC4GGHE6H","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Marton's Inner Bound for the General Broadcast Channel","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Abbas El Gamal, Amin Aminzadeh Gohari, Venkat Anantharam","submitted_at":"2010-06-26T21:19:41Z","abstract_excerpt":"We establish several new results on Marton's coding scheme and its corresponding inner bound on the capacity region of the general broadcast channel. We show that unlike the Gaussian case, Marton's coding scheme without superposition coding is not optimal in general even for a degraded broadcast channel with no common message. We then establish properties of Marton's inner bound that help restrict the search space for computing the sum-rate. Next, we show that the inner bound is optimal along certain directions. Finally, we propose a coding scheme that may lead to a larger inner bound."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.5166","kind":"arxiv","version":2},"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":"2026-05-18T00:57:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DXotpIOEt08ws5pGQEqWPcGSjuPwj5f6L1tj8WoMup7kFvzO3yduG8nZerd2tf6XM+YhIN+VyFD2YlhC1HdZBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T02:24:04.477417Z"},"content_sha256":"1c223d5d62d57171892698116c6250cc87a9f787af84ac180054b74a94330578","schema_version":"1.0","event_id":"sha256:1c223d5d62d57171892698116c6250cc87a9f787af84ac180054b74a94330578"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DDR6PEC33BNYCIOZJWC4GGHE6H/bundle.json","state_url":"https://pith.science/pith/DDR6PEC33BNYCIOZJWC4GGHE6H/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DDR6PEC33BNYCIOZJWC4GGHE6H/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":"2026-06-03T02:24:04Z","links":{"resolver":"https://pith.science/pith/DDR6PEC33BNYCIOZJWC4GGHE6H","bundle":"https://pith.science/pith/DDR6PEC33BNYCIOZJWC4GGHE6H/bundle.json","state":"https://pith.science/pith/DDR6PEC33BNYCIOZJWC4GGHE6H/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DDR6PEC33BNYCIOZJWC4GGHE6H/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:DDR6PEC33BNYCIOZJWC4GGHE6H","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":"246e7860a2eab3169537afe589bae4f16e5535b1e8c0db0a317f618992a66d62","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-06-26T21:19:41Z","title_canon_sha256":"a24d290ea78d0c22a850d443e35687a822366b5c4ec455693c8a5508735ec72e"},"schema_version":"1.0","source":{"id":"1006.5166","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.5166","created_at":"2026-05-18T00:57:57Z"},{"alias_kind":"arxiv_version","alias_value":"1006.5166v2","created_at":"2026-05-18T00:57:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.5166","created_at":"2026-05-18T00:57:57Z"},{"alias_kind":"pith_short_12","alias_value":"DDR6PEC33BNY","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"DDR6PEC33BNYCIOZ","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"DDR6PEC3","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:1c223d5d62d57171892698116c6250cc87a9f787af84ac180054b74a94330578","target":"graph","created_at":"2026-05-18T00:57:57Z","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 establish several new results on Marton's coding scheme and its corresponding inner bound on the capacity region of the general broadcast channel. We show that unlike the Gaussian case, Marton's coding scheme without superposition coding is not optimal in general even for a degraded broadcast channel with no common message. We then establish properties of Marton's inner bound that help restrict the search space for computing the sum-rate. Next, we show that the inner bound is optimal along certain directions. Finally, we propose a coding scheme that may lead to a larger inner bound.","authors_text":"Abbas El Gamal, Amin Aminzadeh Gohari, Venkat Anantharam","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-06-26T21:19:41Z","title":"On Marton's Inner Bound for the General Broadcast Channel"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.5166","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":"sha256:7ad16a6648e136284428cff8edf5edd7a4f28c7d3850c3dd65e04cf6f4bd3a1f","target":"record","created_at":"2026-05-18T00:57:57Z","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":"246e7860a2eab3169537afe589bae4f16e5535b1e8c0db0a317f618992a66d62","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-06-26T21:19:41Z","title_canon_sha256":"a24d290ea78d0c22a850d443e35687a822366b5c4ec455693c8a5508735ec72e"},"schema_version":"1.0","source":{"id":"1006.5166","kind":"arxiv","version":2}},"canonical_sha256":"18e3e7905bd85b8121d94d85c318e4f1f191bdf6e6bf04c850aebdefe93973bf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"18e3e7905bd85b8121d94d85c318e4f1f191bdf6e6bf04c850aebdefe93973bf","first_computed_at":"2026-05-18T00:57:57.736478Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:57:57.736478Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uS4GhbEiEN0vNWbnnJTg1IhJLj/WXuFxlZUHoALNLzzxwWv/xhsIaann9OFzx5qhrtWWwN6cyyDgEGNDhm2AAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:57:57.736904Z","signed_message":"canonical_sha256_bytes"},"source_id":"1006.5166","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7ad16a6648e136284428cff8edf5edd7a4f28c7d3850c3dd65e04cf6f4bd3a1f","sha256:1c223d5d62d57171892698116c6250cc87a9f787af84ac180054b74a94330578"],"state_sha256":"7b9353ed3179cbc9243306075dd68751b1f0ef7ca5c488b6cfbce84dac79f137"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B7dR8QQ+j9Cy3MO2pmrDk3XX/4Zv2IHk6AYhQZUqkGlwNBs43ALZ+v0m4qoGMAzOVt4bXg7RN7Z/Qn/musMECw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T02:24:04.479392Z","bundle_sha256":"83dc2f4321e473048f6cdc61599d588890b00c034ce5453f606f27ab2304fd93"}}