{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:LUWTSJIN4RHC4QS65P5OWDCJDD","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":"5ee3f2cb917319a26c20f168a6303f088884d4ed75299ccdf7578a5e52cd433b","cross_cats_sorted":["cs.CR","math.IT"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"cs.IT","submitted_at":"2011-01-11T02:51:04Z","title_canon_sha256":"a9fc114d3ef12fb1b43ccebf3e3b6c9668f204acdc2f7e61941b282461f59ddb"},"schema_version":"1.0","source":{"id":"1101.2007","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.2007","created_at":"2026-05-18T00:59:10Z"},{"alias_kind":"arxiv_version","alias_value":"1101.2007v1","created_at":"2026-05-18T00:59:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.2007","created_at":"2026-05-18T00:59:10Z"},{"alias_kind":"pith_short_12","alias_value":"LUWTSJIN4RHC","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"LUWTSJIN4RHC4QS6","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"LUWTSJIN","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:ef0e25831a428d91879b66fb47e21bd8d7c3ff8690b87443f96d8b498b4bfa34","target":"graph","created_at":"2026-05-18T00:59:10Z","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":"This paper presents two new results on multiple-input multiple-output (MIMO) Gaussian broadcast channels with confidential messages. First, the problem of the MIMO Gaussian wiretap channel is revisited. A matrix characterization of the capacity-equivocation region is provided, which extends the previous result on the secrecy capacity of the MIMO Gaussian wiretap channel to the general, possibly imperfect secrecy setting. Next, the problem of MIMO Gaussian broadcast channels with two receivers and three independent messages: a common message intended for both receivers, and two confidential mes","authors_text":"H. Vincent Poor, Ruoheng Liu, Shlomo Shamai (Shitz), Tie Liu","cross_cats":["cs.CR","math.IT"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"cs.IT","submitted_at":"2011-01-11T02:51:04Z","title":"New Results on Multiple-Input Multiple-Output Broadcast Channels with Confidential Messages"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.2007","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":"sha256:8ed7c9b25f9a505f2af41fece2337e6d85305452139ed7d5a1363e1b5331a97d","target":"record","created_at":"2026-05-18T00:59:10Z","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":"5ee3f2cb917319a26c20f168a6303f088884d4ed75299ccdf7578a5e52cd433b","cross_cats_sorted":["cs.CR","math.IT"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"cs.IT","submitted_at":"2011-01-11T02:51:04Z","title_canon_sha256":"a9fc114d3ef12fb1b43ccebf3e3b6c9668f204acdc2f7e61941b282461f59ddb"},"schema_version":"1.0","source":{"id":"1101.2007","kind":"arxiv","version":1}},"canonical_sha256":"5d2d39250de44e2e425eebfaeb0c4918f99e680cd21898c0fcf78c5694823239","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5d2d39250de44e2e425eebfaeb0c4918f99e680cd21898c0fcf78c5694823239","first_computed_at":"2026-05-18T00:59:10.541648Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:59:10.541648Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gewfO1zLWNbk8Oyx0rL3W95QSH8WTJ+Dbii4d6k4UYoScuRSmP5K7ksimLRHaqek6RTgA7emFMXRAudexUAVCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:59:10.542251Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.2007","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8ed7c9b25f9a505f2af41fece2337e6d85305452139ed7d5a1363e1b5331a97d","sha256:ef0e25831a428d91879b66fb47e21bd8d7c3ff8690b87443f96d8b498b4bfa34"],"state_sha256":"fc62620426c6a01011ac54905ab107a90ec412082d5ae3d0aa8c8102ef400b97"}