{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:LZEWWLKASA6DLTTSGQCFNWLMZJ","short_pith_number":"pith:LZEWWLKA","canonical_record":{"source":{"id":"1604.06842","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-04-23T01:17:10Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"5b2f684c7c66e2222c6814d1908ef4baa489e6c2a2f12174f1e8c7e49a8e101e","abstract_canon_sha256":"4bad342cf14acf55f897645b4f5b54d8cbd4996d0cc4a37da5f3f27e68602752"},"schema_version":"1.0"},"canonical_sha256":"5e496b2d40903c35ce72340456d96cca55a443b16c41ba36200ae52f1aad000b","source":{"kind":"arxiv","id":"1604.06842","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.06842","created_at":"2026-05-18T00:58:09Z"},{"alias_kind":"arxiv_version","alias_value":"1604.06842v1","created_at":"2026-05-18T00:58:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.06842","created_at":"2026-05-18T00:58:09Z"},{"alias_kind":"pith_short_12","alias_value":"LZEWWLKASA6D","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LZEWWLKASA6DLTTS","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LZEWWLKA","created_at":"2026-05-18T12:30:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:LZEWWLKASA6DLTTSGQCFNWLMZJ","target":"record","payload":{"canonical_record":{"source":{"id":"1604.06842","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-04-23T01:17:10Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"5b2f684c7c66e2222c6814d1908ef4baa489e6c2a2f12174f1e8c7e49a8e101e","abstract_canon_sha256":"4bad342cf14acf55f897645b4f5b54d8cbd4996d0cc4a37da5f3f27e68602752"},"schema_version":"1.0"},"canonical_sha256":"5e496b2d40903c35ce72340456d96cca55a443b16c41ba36200ae52f1aad000b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:58:09.437200Z","signature_b64":"kDrBUfJHpIL6/s3hVzR0i6ejooVkI04foTHremiM7q7V2eMWG5a79YE1BwjL2eR5RICKf6Zm9KRgkFO6AxqMDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5e496b2d40903c35ce72340456d96cca55a443b16c41ba36200ae52f1aad000b","last_reissued_at":"2026-05-18T00:58:09.436504Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:58:09.436504Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.06842","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":"2026-05-18T00:58:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"08mvOHdfHiZ843XpObaMrc0Uq2xQmxlacTIZKrTblfjQscR/Me0JU7f++oiclqMcwDslykN+pv7c0P/0W8IzBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T16:34:29.751742Z"},"content_sha256":"372108c6b6726094761f9d19cb18217d662ccdd804ba7c2e0f7737a7de799e21","schema_version":"1.0","event_id":"sha256:372108c6b6726094761f9d19cb18217d662ccdd804ba7c2e0f7737a7de799e21"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:LZEWWLKASA6DLTTSGQCFNWLMZJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"How to Diagonalize a MIMO Channel with Arbitrary Transmit Covariance?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Liang Liu, Rui Zhang","submitted_at":"2016-04-23T01:17:10Z","abstract_excerpt":"Multiple-input multiple-output (MIMO) or multi-antenna communication is a key technique to achieve high spectral efficiency in wireless systems. For the point-to-point MIMO channel, it is a well-known result that the channel singular value decomposition (SVD) based linear precoding and decoding achieves the channel capacity, which also diagonalizes the MIMO channel into parallel single-input single-output (SISO) sub-channels for independent encoding and decoding. However, in multi-user MIMO systems, the optimal transmit covariance of each MIMO link is generally not its channel SVD based as a r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.06842","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":"2026-05-18T00:58:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K3h43AlAMWlmTBubcZUx7kiENWfzPeuOFvCVdCouHhvopq3LYbrcSQBfDxoylRqutMUCudHMDvibQFnWve7YAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T16:34:29.752240Z"},"content_sha256":"2072274450966a30d89ab5f268e7985a169ed347c176d78e0849b1f756a1fa03","schema_version":"1.0","event_id":"sha256:2072274450966a30d89ab5f268e7985a169ed347c176d78e0849b1f756a1fa03"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LZEWWLKASA6DLTTSGQCFNWLMZJ/bundle.json","state_url":"https://pith.science/pith/LZEWWLKASA6DLTTSGQCFNWLMZJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LZEWWLKASA6DLTTSGQCFNWLMZJ/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":"2026-06-06T16:34:29Z","links":{"resolver":"https://pith.science/pith/LZEWWLKASA6DLTTSGQCFNWLMZJ","bundle":"https://pith.science/pith/LZEWWLKASA6DLTTSGQCFNWLMZJ/bundle.json","state":"https://pith.science/pith/LZEWWLKASA6DLTTSGQCFNWLMZJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LZEWWLKASA6DLTTSGQCFNWLMZJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:LZEWWLKASA6DLTTSGQCFNWLMZJ","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":"4bad342cf14acf55f897645b4f5b54d8cbd4996d0cc4a37da5f3f27e68602752","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-04-23T01:17:10Z","title_canon_sha256":"5b2f684c7c66e2222c6814d1908ef4baa489e6c2a2f12174f1e8c7e49a8e101e"},"schema_version":"1.0","source":{"id":"1604.06842","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.06842","created_at":"2026-05-18T00:58:09Z"},{"alias_kind":"arxiv_version","alias_value":"1604.06842v1","created_at":"2026-05-18T00:58:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.06842","created_at":"2026-05-18T00:58:09Z"},{"alias_kind":"pith_short_12","alias_value":"LZEWWLKASA6D","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LZEWWLKASA6DLTTS","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LZEWWLKA","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:2072274450966a30d89ab5f268e7985a169ed347c176d78e0849b1f756a1fa03","target":"graph","created_at":"2026-05-18T00:58:09Z","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":"Multiple-input multiple-output (MIMO) or multi-antenna communication is a key technique to achieve high spectral efficiency in wireless systems. For the point-to-point MIMO channel, it is a well-known result that the channel singular value decomposition (SVD) based linear precoding and decoding achieves the channel capacity, which also diagonalizes the MIMO channel into parallel single-input single-output (SISO) sub-channels for independent encoding and decoding. However, in multi-user MIMO systems, the optimal transmit covariance of each MIMO link is generally not its channel SVD based as a r","authors_text":"Liang Liu, Rui Zhang","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-04-23T01:17:10Z","title":"How to Diagonalize a MIMO Channel with Arbitrary Transmit Covariance?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.06842","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":"sha256:372108c6b6726094761f9d19cb18217d662ccdd804ba7c2e0f7737a7de799e21","target":"record","created_at":"2026-05-18T00:58:09Z","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":"4bad342cf14acf55f897645b4f5b54d8cbd4996d0cc4a37da5f3f27e68602752","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-04-23T01:17:10Z","title_canon_sha256":"5b2f684c7c66e2222c6814d1908ef4baa489e6c2a2f12174f1e8c7e49a8e101e"},"schema_version":"1.0","source":{"id":"1604.06842","kind":"arxiv","version":1}},"canonical_sha256":"5e496b2d40903c35ce72340456d96cca55a443b16c41ba36200ae52f1aad000b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5e496b2d40903c35ce72340456d96cca55a443b16c41ba36200ae52f1aad000b","first_computed_at":"2026-05-18T00:58:09.436504Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:58:09.436504Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kDrBUfJHpIL6/s3hVzR0i6ejooVkI04foTHremiM7q7V2eMWG5a79YE1BwjL2eR5RICKf6Zm9KRgkFO6AxqMDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:58:09.437200Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.06842","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:372108c6b6726094761f9d19cb18217d662ccdd804ba7c2e0f7737a7de799e21","sha256:2072274450966a30d89ab5f268e7985a169ed347c176d78e0849b1f756a1fa03"],"state_sha256":"00eaab77538b97f9614bb47feb5c7632dd17678e1a95374358d49feef8c556e4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3sJV3091cUhqeNcGEoww7V8gKG1ur6z4RwUKDirAgPqKrNuoFPeLxNphvTfAXPnicv8NOwjyx6vMYyS9HhSvAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T16:34:29.754662Z","bundle_sha256":"8e769c8d8b92171440d49b406c3bcaa9aa349d3e1731f31cd8c29f193ab1f4fd"}}