{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:GWR2RZWCHDGYSDWQ2XNFBE3TAO","short_pith_number":"pith:GWR2RZWC","canonical_record":{"source":{"id":"0901.4830","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2009-01-30T06:56:00Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"7f7aebca4823f4985347782a7dd89c44dbaf9f633142ec56a09f364ec2ed1dbb","abstract_canon_sha256":"e5b08c67ea02304e6926be09f49dec5f1c1082f061726074d07d67a5bb1a68c4"},"schema_version":"1.0"},"canonical_sha256":"35a3a8e6c238cd890ed0d5da50937303b6fc9e12beeb479906542224f7155f4b","source":{"kind":"arxiv","id":"0901.4830","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0901.4830","created_at":"2026-07-04T15:37:08Z"},{"alias_kind":"arxiv_version","alias_value":"0901.4830v1","created_at":"2026-07-04T15:37:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0901.4830","created_at":"2026-07-04T15:37:08Z"},{"alias_kind":"pith_short_12","alias_value":"GWR2RZWCHDGY","created_at":"2026-07-04T15:37:08Z"},{"alias_kind":"pith_short_16","alias_value":"GWR2RZWCHDGYSDWQ","created_at":"2026-07-04T15:37:08Z"},{"alias_kind":"pith_short_8","alias_value":"GWR2RZWC","created_at":"2026-07-04T15:37:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:GWR2RZWCHDGYSDWQ2XNFBE3TAO","target":"record","payload":{"canonical_record":{"source":{"id":"0901.4830","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2009-01-30T06:56:00Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"7f7aebca4823f4985347782a7dd89c44dbaf9f633142ec56a09f364ec2ed1dbb","abstract_canon_sha256":"e5b08c67ea02304e6926be09f49dec5f1c1082f061726074d07d67a5bb1a68c4"},"schema_version":"1.0"},"canonical_sha256":"35a3a8e6c238cd890ed0d5da50937303b6fc9e12beeb479906542224f7155f4b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:37:08.281224Z","signature_b64":"Z+RbOVBH2OuS7yCk/HEylvR315AP2TksWNB1R1vJOQGT2gecmMBhFkyWKRGLEZoWq2skgf4O217CF/zWlGZKCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"35a3a8e6c238cd890ed0d5da50937303b6fc9e12beeb479906542224f7155f4b","last_reissued_at":"2026-07-04T15:37:08.280853Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:37:08.280853Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0901.4830","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":"2026-07-04T15:37:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7QLmdtLESp3diyMRfjftJiqN8V1hDvU1mrGQ023+fd/iTasLiYdWd8P9Oqe3ItJn3JgRe3VLk55avx0Lx2V9Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T11:15:10.218405Z"},"content_sha256":"33e2737dbc250cc3fe024d0620d589d03e52b1cc2ef22c1bf3ec8e115a12abb7","schema_version":"1.0","event_id":"sha256:33e2737dbc250cc3fe024d0620d589d03e52b1cc2ef22c1bf3ec8e115a12abb7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:GWR2RZWCHDGYSDWQ2XNFBE3TAO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Relationship Between the Multi-antenna Secrecy Communications and Cognitive Radio Communications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Lan Zhang, Rui Zhang, Shuguang Cui, Yan Xin, Ying-Chang Liang","submitted_at":"2009-01-30T06:56:00Z","abstract_excerpt":"This paper studies the capacity of the multi-antenna or multiple-input multiple-output (MIMO) secrecy channels with multiple eavesdroppers having single/multiple antennas. It is known that the MIMO secrecy capacity is achievable with the optimal transmit covariance matrix that maximizes the minimum difference between the channel mutual information of the secrecy user and those of the eavesdroppers. The MIMO secrecy capacity computation can thus be formulated as a non-convex max-min problem, which cannot be solved efficiently by standard convex optimization techniques. To handle this difficulty"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.4830","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/0901.4830/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T15:37:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y7j5qkdBh9xgD5yA7MuOGgClL0U+o+vHOTWWeDMxAL2kjfpbNWcWvqFLl388WO2l3sCNr1QFGpwMz4cMcQOjDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T11:15:10.218784Z"},"content_sha256":"5770e3e9067e1be767730ce97dde1a40d0425fd0e98e51ac1c9a328bb6c79077","schema_version":"1.0","event_id":"sha256:5770e3e9067e1be767730ce97dde1a40d0425fd0e98e51ac1c9a328bb6c79077"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GWR2RZWCHDGYSDWQ2XNFBE3TAO/bundle.json","state_url":"https://pith.science/pith/GWR2RZWCHDGYSDWQ2XNFBE3TAO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GWR2RZWCHDGYSDWQ2XNFBE3TAO/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":"2026-07-05T11:15:10Z","links":{"resolver":"https://pith.science/pith/GWR2RZWCHDGYSDWQ2XNFBE3TAO","bundle":"https://pith.science/pith/GWR2RZWCHDGYSDWQ2XNFBE3TAO/bundle.json","state":"https://pith.science/pith/GWR2RZWCHDGYSDWQ2XNFBE3TAO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GWR2RZWCHDGYSDWQ2XNFBE3TAO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:GWR2RZWCHDGYSDWQ2XNFBE3TAO","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":"e5b08c67ea02304e6926be09f49dec5f1c1082f061726074d07d67a5bb1a68c4","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2009-01-30T06:56:00Z","title_canon_sha256":"7f7aebca4823f4985347782a7dd89c44dbaf9f633142ec56a09f364ec2ed1dbb"},"schema_version":"1.0","source":{"id":"0901.4830","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0901.4830","created_at":"2026-07-04T15:37:08Z"},{"alias_kind":"arxiv_version","alias_value":"0901.4830v1","created_at":"2026-07-04T15:37:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0901.4830","created_at":"2026-07-04T15:37:08Z"},{"alias_kind":"pith_short_12","alias_value":"GWR2RZWCHDGY","created_at":"2026-07-04T15:37:08Z"},{"alias_kind":"pith_short_16","alias_value":"GWR2RZWCHDGYSDWQ","created_at":"2026-07-04T15:37:08Z"},{"alias_kind":"pith_short_8","alias_value":"GWR2RZWC","created_at":"2026-07-04T15:37:08Z"}],"graph_snapshots":[{"event_id":"sha256:5770e3e9067e1be767730ce97dde1a40d0425fd0e98e51ac1c9a328bb6c79077","target":"graph","created_at":"2026-07-04T15:37:08Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/0901.4830/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper studies the capacity of the multi-antenna or multiple-input multiple-output (MIMO) secrecy channels with multiple eavesdroppers having single/multiple antennas. It is known that the MIMO secrecy capacity is achievable with the optimal transmit covariance matrix that maximizes the minimum difference between the channel mutual information of the secrecy user and those of the eavesdroppers. The MIMO secrecy capacity computation can thus be formulated as a non-convex max-min problem, which cannot be solved efficiently by standard convex optimization techniques. To handle this difficulty","authors_text":"Lan Zhang, Rui Zhang, Shuguang Cui, Yan Xin, Ying-Chang Liang","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2009-01-30T06:56:00Z","title":"On the Relationship Between the Multi-antenna Secrecy Communications and Cognitive Radio Communications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.4830","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":"sha256:33e2737dbc250cc3fe024d0620d589d03e52b1cc2ef22c1bf3ec8e115a12abb7","target":"record","created_at":"2026-07-04T15:37:08Z","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":"e5b08c67ea02304e6926be09f49dec5f1c1082f061726074d07d67a5bb1a68c4","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2009-01-30T06:56:00Z","title_canon_sha256":"7f7aebca4823f4985347782a7dd89c44dbaf9f633142ec56a09f364ec2ed1dbb"},"schema_version":"1.0","source":{"id":"0901.4830","kind":"arxiv","version":1}},"canonical_sha256":"35a3a8e6c238cd890ed0d5da50937303b6fc9e12beeb479906542224f7155f4b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"35a3a8e6c238cd890ed0d5da50937303b6fc9e12beeb479906542224f7155f4b","first_computed_at":"2026-07-04T15:37:08.280853Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:37:08.280853Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Z+RbOVBH2OuS7yCk/HEylvR315AP2TksWNB1R1vJOQGT2gecmMBhFkyWKRGLEZoWq2skgf4O217CF/zWlGZKCA==","signature_status":"signed_v1","signed_at":"2026-07-04T15:37:08.281224Z","signed_message":"canonical_sha256_bytes"},"source_id":"0901.4830","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:33e2737dbc250cc3fe024d0620d589d03e52b1cc2ef22c1bf3ec8e115a12abb7","sha256:5770e3e9067e1be767730ce97dde1a40d0425fd0e98e51ac1c9a328bb6c79077"],"state_sha256":"2ae6c05e9a07d8b5177665314bf40574bda3cdfd1c4d0dcdaa43b59c232b9219"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iUBVHHpEAjn+cuhxJ986sOAs74Y/sFcBqVyxreTGW5PsCq0Pedi0UORVafsC7s1KNaKdJG762jtdhLA9XUYYBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-05T11:15:10.220771Z","bundle_sha256":"c9e48194ca6f269dbb79aa39f631238c89ff8b7de9b4bf84cf8228b5417cf4b2"}}