{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:BNGF3Y2IMKCF7GMKCEAPNTXCY2","short_pith_number":"pith:BNGF3Y2I","canonical_record":{"source":{"id":"1411.0103","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-11-01T11:28:33Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"240b4ba9e6b4707554e8787971ebe192d73cd4d397c9ba9bb402eab5c6ad7b9a","abstract_canon_sha256":"87777e3092ece71bd9d65f6dccbe5576840770cb04608e0643ad88e247a6d12e"},"schema_version":"1.0"},"canonical_sha256":"0b4c5de34862845f998a1100f6cee2c6b8de3e63dc0a82c9ec33db6c89b9accd","source":{"kind":"arxiv","id":"1411.0103","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.0103","created_at":"2026-05-18T02:38:52Z"},{"alias_kind":"arxiv_version","alias_value":"1411.0103v1","created_at":"2026-05-18T02:38:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.0103","created_at":"2026-05-18T02:38:52Z"},{"alias_kind":"pith_short_12","alias_value":"BNGF3Y2IMKCF","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"BNGF3Y2IMKCF7GMK","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"BNGF3Y2I","created_at":"2026-05-18T12:28:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:BNGF3Y2IMKCF7GMKCEAPNTXCY2","target":"record","payload":{"canonical_record":{"source":{"id":"1411.0103","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-11-01T11:28:33Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"240b4ba9e6b4707554e8787971ebe192d73cd4d397c9ba9bb402eab5c6ad7b9a","abstract_canon_sha256":"87777e3092ece71bd9d65f6dccbe5576840770cb04608e0643ad88e247a6d12e"},"schema_version":"1.0"},"canonical_sha256":"0b4c5de34862845f998a1100f6cee2c6b8de3e63dc0a82c9ec33db6c89b9accd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:52.536778Z","signature_b64":"ZgcpUBNLpY+Hxpsu7djEsAQmbamLCgNG2h6UBBRGBTsLEh1w+4jyC2D/O0HYHp53PqatA2HERPlfcwG+9h+XBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0b4c5de34862845f998a1100f6cee2c6b8de3e63dc0a82c9ec33db6c89b9accd","last_reissued_at":"2026-05-18T02:38:52.536363Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:52.536363Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.0103","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":"2026-05-18T02:38:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2pe7WIb/Fx5NE6k6e9ccHTdJYLjP6UaXOIrhxLLO+/02NBhDK+pGXENV822smQ1ChdRaPajMJit9t7DqKu2TBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T08:32:17.787886Z"},"content_sha256":"7809345e302a67ba70bdecd8b4f3ad51b65260ddbc330d0905a295cd3de91a5e","schema_version":"1.0","event_id":"sha256:7809345e302a67ba70bdecd8b4f3ad51b65260ddbc330d0905a295cd3de91a5e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:BNGF3Y2IMKCF7GMKCEAPNTXCY2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Optimal Precoding for MIMO Gaussian Wire-Tap Channels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Arash Khabbazibasmenj, Lars K. Rasmussen, Maksym A. Girnyk, Mikko Vehkaper\\\"a, Sergiy A. Vorobyov","submitted_at":"2014-11-01T11:28:33Z","abstract_excerpt":"We consider the problem of finding secrecy rate of a multiple-input multiple-output (MIMO) wire-tap channel. A transmitter, a legitimate receiver, and an eavesdropper are all equipped with multiple antennas. The channel states from the transmitter to the legitimate user and to the eavesdropper are assumed to be known at the transmitter. In this contribution, we address the problem of finding the optimal precoder/transmit covariance matrix maximizing the secrecy rate of the given wiretap channel. The problem formulation is shown to be equivalent to a difference of convex functions programming p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.0103","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":"2026-05-18T02:38:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NMEHba7IJEeehvGSHiXv8Va8Nm186CEh6OvqUhKXBhE/ibQZJ0y7vccw7Z7BwmB5WVY6UqRp9ktNQLmwE6zODg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T08:32:17.788451Z"},"content_sha256":"cc80fcb1102498cda16b9e99a5b70a541449633755a1af1a5f840485ba0162ce","schema_version":"1.0","event_id":"sha256:cc80fcb1102498cda16b9e99a5b70a541449633755a1af1a5f840485ba0162ce"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BNGF3Y2IMKCF7GMKCEAPNTXCY2/bundle.json","state_url":"https://pith.science/pith/BNGF3Y2IMKCF7GMKCEAPNTXCY2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BNGF3Y2IMKCF7GMKCEAPNTXCY2/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":"2026-05-26T08:32:17Z","links":{"resolver":"https://pith.science/pith/BNGF3Y2IMKCF7GMKCEAPNTXCY2","bundle":"https://pith.science/pith/BNGF3Y2IMKCF7GMKCEAPNTXCY2/bundle.json","state":"https://pith.science/pith/BNGF3Y2IMKCF7GMKCEAPNTXCY2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BNGF3Y2IMKCF7GMKCEAPNTXCY2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:BNGF3Y2IMKCF7GMKCEAPNTXCY2","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":"87777e3092ece71bd9d65f6dccbe5576840770cb04608e0643ad88e247a6d12e","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-11-01T11:28:33Z","title_canon_sha256":"240b4ba9e6b4707554e8787971ebe192d73cd4d397c9ba9bb402eab5c6ad7b9a"},"schema_version":"1.0","source":{"id":"1411.0103","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.0103","created_at":"2026-05-18T02:38:52Z"},{"alias_kind":"arxiv_version","alias_value":"1411.0103v1","created_at":"2026-05-18T02:38:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.0103","created_at":"2026-05-18T02:38:52Z"},{"alias_kind":"pith_short_12","alias_value":"BNGF3Y2IMKCF","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"BNGF3Y2IMKCF7GMK","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"BNGF3Y2I","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:cc80fcb1102498cda16b9e99a5b70a541449633755a1af1a5f840485ba0162ce","target":"graph","created_at":"2026-05-18T02:38:52Z","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 problem of finding secrecy rate of a multiple-input multiple-output (MIMO) wire-tap channel. A transmitter, a legitimate receiver, and an eavesdropper are all equipped with multiple antennas. The channel states from the transmitter to the legitimate user and to the eavesdropper are assumed to be known at the transmitter. In this contribution, we address the problem of finding the optimal precoder/transmit covariance matrix maximizing the secrecy rate of the given wiretap channel. The problem formulation is shown to be equivalent to a difference of convex functions programming p","authors_text":"Arash Khabbazibasmenj, Lars K. Rasmussen, Maksym A. Girnyk, Mikko Vehkaper\\\"a, Sergiy A. Vorobyov","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-11-01T11:28:33Z","title":"On the Optimal Precoding for MIMO Gaussian Wire-Tap Channels"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.0103","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":"sha256:7809345e302a67ba70bdecd8b4f3ad51b65260ddbc330d0905a295cd3de91a5e","target":"record","created_at":"2026-05-18T02:38:52Z","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":"87777e3092ece71bd9d65f6dccbe5576840770cb04608e0643ad88e247a6d12e","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-11-01T11:28:33Z","title_canon_sha256":"240b4ba9e6b4707554e8787971ebe192d73cd4d397c9ba9bb402eab5c6ad7b9a"},"schema_version":"1.0","source":{"id":"1411.0103","kind":"arxiv","version":1}},"canonical_sha256":"0b4c5de34862845f998a1100f6cee2c6b8de3e63dc0a82c9ec33db6c89b9accd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0b4c5de34862845f998a1100f6cee2c6b8de3e63dc0a82c9ec33db6c89b9accd","first_computed_at":"2026-05-18T02:38:52.536363Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:52.536363Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZgcpUBNLpY+Hxpsu7djEsAQmbamLCgNG2h6UBBRGBTsLEh1w+4jyC2D/O0HYHp53PqatA2HERPlfcwG+9h+XBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:52.536778Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.0103","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7809345e302a67ba70bdecd8b4f3ad51b65260ddbc330d0905a295cd3de91a5e","sha256:cc80fcb1102498cda16b9e99a5b70a541449633755a1af1a5f840485ba0162ce"],"state_sha256":"b4ebc5eee5b4f0142ba086694f97805f8df8d710ef60eacf03770bb5764e727e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Gtyx0i/XFKb/Wu43Lhn7jm2hR/Ep5kbFhcF2E74/rpdA5FFeAb73oY049F8Rbkf2HStrA/uE1jJcq11+8ZunAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T08:32:17.791225Z","bundle_sha256":"21bae3dba75bce682046212183b11f32c27cb07043d4b7c8b5c64b48e5d7b4d1"}}