{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:6U7Z2AKIZUNC3DSYVUXRPCL7MB","short_pith_number":"pith:6U7Z2AKI","canonical_record":{"source":{"id":"1307.5549","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-07-21T17:45:52Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"1e917af356d634f28f219b8958d47c0d259e0d0b78b400fc5f903ad4f1062705","abstract_canon_sha256":"baeb8a40ea1a35af9f95faf76b70cd55f886305e7fc5ff38fbcef8f3bcae7603"},"schema_version":"1.0"},"canonical_sha256":"f53f9d0148cd1a2d8e58ad2f17897f6042315b0a1e3b524b616bbc1610e54f2d","source":{"kind":"arxiv","id":"1307.5549","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.5549","created_at":"2026-05-18T00:57:56Z"},{"alias_kind":"arxiv_version","alias_value":"1307.5549v1","created_at":"2026-05-18T00:57:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.5549","created_at":"2026-05-18T00:57:56Z"},{"alias_kind":"pith_short_12","alias_value":"6U7Z2AKIZUNC","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6U7Z2AKIZUNC3DSY","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6U7Z2AKI","created_at":"2026-05-18T12:27:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:6U7Z2AKIZUNC3DSYVUXRPCL7MB","target":"record","payload":{"canonical_record":{"source":{"id":"1307.5549","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-07-21T17:45:52Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"1e917af356d634f28f219b8958d47c0d259e0d0b78b400fc5f903ad4f1062705","abstract_canon_sha256":"baeb8a40ea1a35af9f95faf76b70cd55f886305e7fc5ff38fbcef8f3bcae7603"},"schema_version":"1.0"},"canonical_sha256":"f53f9d0148cd1a2d8e58ad2f17897f6042315b0a1e3b524b616bbc1610e54f2d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:57:56.271921Z","signature_b64":"uRpmvxE1RdVt9XtR0lsgcNs7Uci6p5mBJoP8yruSewS9yMY8Qcg4FDplJ1aRtBXw00E09/6gX6jY5L3lA/eUCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f53f9d0148cd1a2d8e58ad2f17897f6042315b0a1e3b524b616bbc1610e54f2d","last_reissued_at":"2026-05-18T00:57:56.271592Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:57:56.271592Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.5549","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":"2026-05-18T00:57:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TPaFFHFGgSkkw3jGsSOw2bXJDhzEoYC7cEiqGxHyp6sj2XYZwy3YhWgSLHiSYsPp72xVdiT4KTX8UdOmEPF8Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T17:41:08.990853Z"},"content_sha256":"b403f58c0fe242881ea43d96bba576b3c1f403d6c22aa7a3569c290c2288d003","schema_version":"1.0","event_id":"sha256:b403f58c0fe242881ea43d96bba576b3c1f403d6c22aa7a3569c290c2288d003"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:6U7Z2AKIZUNC3DSYVUXRPCL7MB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Insufficiency of Linear-Feedback Schemes In Gaussian Broadcast Channels with Common Message","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Mich\\`ele Wigger, Paolo Minero, Youlong Wu","submitted_at":"2013-07-21T17:45:52Z","abstract_excerpt":"We consider the $K\\geq 2$-user memoryless Gaussian broadcast channel (BC) with feedback and common message only. We show that linear-feedback schemes with a message point, in the spirit of Schalkwijk & Kailath's scheme for point-to-point channels or Ozarow & Leung's scheme for BCs with private messages, are strictly suboptimal for this setup. Even with perfect feedback, the largest rate achieved by these schemes is strictly smaller than capacity $C$ (which is the same with and without feedback). In the extreme case where the number of receivers $K\\to \\infty$, the largest rate achieved by linea"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.5549","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":"2026-05-18T00:57:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uYbFhdXo1wyjx+mA1rBQkWaP1kf5qkGZE3fC1M4KfbFL9dbmKG+upqLf7RKZ0kaPkveYO40BTr0i+3BQeVRSCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T17:41:08.991532Z"},"content_sha256":"28b6d325e317003b007920c87de1a2961a921685d9c560ea462b288b5048eeb1","schema_version":"1.0","event_id":"sha256:28b6d325e317003b007920c87de1a2961a921685d9c560ea462b288b5048eeb1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6U7Z2AKIZUNC3DSYVUXRPCL7MB/bundle.json","state_url":"https://pith.science/pith/6U7Z2AKIZUNC3DSYVUXRPCL7MB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6U7Z2AKIZUNC3DSYVUXRPCL7MB/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":"2026-05-26T17:41:08Z","links":{"resolver":"https://pith.science/pith/6U7Z2AKIZUNC3DSYVUXRPCL7MB","bundle":"https://pith.science/pith/6U7Z2AKIZUNC3DSYVUXRPCL7MB/bundle.json","state":"https://pith.science/pith/6U7Z2AKIZUNC3DSYVUXRPCL7MB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6U7Z2AKIZUNC3DSYVUXRPCL7MB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:6U7Z2AKIZUNC3DSYVUXRPCL7MB","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":"baeb8a40ea1a35af9f95faf76b70cd55f886305e7fc5ff38fbcef8f3bcae7603","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-07-21T17:45:52Z","title_canon_sha256":"1e917af356d634f28f219b8958d47c0d259e0d0b78b400fc5f903ad4f1062705"},"schema_version":"1.0","source":{"id":"1307.5549","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.5549","created_at":"2026-05-18T00:57:56Z"},{"alias_kind":"arxiv_version","alias_value":"1307.5549v1","created_at":"2026-05-18T00:57:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.5549","created_at":"2026-05-18T00:57:56Z"},{"alias_kind":"pith_short_12","alias_value":"6U7Z2AKIZUNC","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6U7Z2AKIZUNC3DSY","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6U7Z2AKI","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:28b6d325e317003b007920c87de1a2961a921685d9c560ea462b288b5048eeb1","target":"graph","created_at":"2026-05-18T00:57:56Z","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 consider the $K\\geq 2$-user memoryless Gaussian broadcast channel (BC) with feedback and common message only. We show that linear-feedback schemes with a message point, in the spirit of Schalkwijk & Kailath's scheme for point-to-point channels or Ozarow & Leung's scheme for BCs with private messages, are strictly suboptimal for this setup. Even with perfect feedback, the largest rate achieved by these schemes is strictly smaller than capacity $C$ (which is the same with and without feedback). In the extreme case where the number of receivers $K\\to \\infty$, the largest rate achieved by linea","authors_text":"Mich\\`ele Wigger, Paolo Minero, Youlong Wu","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-07-21T17:45:52Z","title":"Insufficiency of Linear-Feedback Schemes In Gaussian Broadcast Channels with Common Message"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.5549","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:b403f58c0fe242881ea43d96bba576b3c1f403d6c22aa7a3569c290c2288d003","target":"record","created_at":"2026-05-18T00:57:56Z","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":"baeb8a40ea1a35af9f95faf76b70cd55f886305e7fc5ff38fbcef8f3bcae7603","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-07-21T17:45:52Z","title_canon_sha256":"1e917af356d634f28f219b8958d47c0d259e0d0b78b400fc5f903ad4f1062705"},"schema_version":"1.0","source":{"id":"1307.5549","kind":"arxiv","version":1}},"canonical_sha256":"f53f9d0148cd1a2d8e58ad2f17897f6042315b0a1e3b524b616bbc1610e54f2d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f53f9d0148cd1a2d8e58ad2f17897f6042315b0a1e3b524b616bbc1610e54f2d","first_computed_at":"2026-05-18T00:57:56.271592Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:57:56.271592Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uRpmvxE1RdVt9XtR0lsgcNs7Uci6p5mBJoP8yruSewS9yMY8Qcg4FDplJ1aRtBXw00E09/6gX6jY5L3lA/eUCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:57:56.271921Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.5549","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b403f58c0fe242881ea43d96bba576b3c1f403d6c22aa7a3569c290c2288d003","sha256:28b6d325e317003b007920c87de1a2961a921685d9c560ea462b288b5048eeb1"],"state_sha256":"5d4517fc78b623761cdbf98a50d3dd26f19ccf7bb3e783f4bc363afb4f03619f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C8JAGgG6441V04MzxK5b3xdAl/Uu9yBTByvdTWDmbEamh1i8XIzx9eR7guplQM1WD/3O1uLcErWXk5qCOnBiAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T17:41:08.994824Z","bundle_sha256":"1a8ac035a6fa515bfcf931d64f381037e1a21b3fbe86a725002080e24d5bf549"}}