{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:X5PYX3GXB22PFBZDWEW6GE45JH","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":"b9496404c48049d6848fd31adbe9db0d227196ee014a056e132e1b120d843105","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-05-02T02:08:41Z","title_canon_sha256":"36d2fce31e037ca39e6137b7124acf9f7d79dd8adfc48fae59868f7d62fcea32"},"schema_version":"1.0","source":{"id":"1505.00303","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.00303","created_at":"2026-05-18T00:58:35Z"},{"alias_kind":"arxiv_version","alias_value":"1505.00303v1","created_at":"2026-05-18T00:58:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.00303","created_at":"2026-05-18T00:58:35Z"},{"alias_kind":"pith_short_12","alias_value":"X5PYX3GXB22P","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"X5PYX3GXB22PFBZD","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"X5PYX3GX","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:3bc83d2605ca4ca615dbbeb95834fe7b4b41b9e24162f4fa9fb8def8eb409bfe","target":"graph","created_at":"2026-05-18T00:58:35Z","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":"Millimeter wave (mmWave) systems will likely employ large antenna arrays at both the transmitters and receivers. A natural application of antenna arrays is simultaneous transmission to multiple users, which requires multi-user precoding at the transmitter. Hardware constraints, however, make it difficult to apply conventional lower frequency MIMO precoding techniques at mmWave. This paper proposes and analyzes a low complexity hybrid analog/digital beamforming algorithm for downlink multi-user mmWave systems. Hybrid precoding involves a combination of analog and digital processing that is moti","authors_text":"Ahmed Alkhateeb, Geert Leus, Robert W. Heath Jr.","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-05-02T02:08:41Z","title":"Achievable Rates of Multi-User Millimeter Wave Systems with Hybrid Precoding"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.00303","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:b13aa592430ea7843b9645ab37b08ab7ba81cc440fd803d7211339b53710da40","target":"record","created_at":"2026-05-18T00:58:35Z","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":"b9496404c48049d6848fd31adbe9db0d227196ee014a056e132e1b120d843105","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-05-02T02:08:41Z","title_canon_sha256":"36d2fce31e037ca39e6137b7124acf9f7d79dd8adfc48fae59868f7d62fcea32"},"schema_version":"1.0","source":{"id":"1505.00303","kind":"arxiv","version":1}},"canonical_sha256":"bf5f8becd70eb4f28723b12de3139d49d66e5724113d8a7040e3b3a8bb4849df","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bf5f8becd70eb4f28723b12de3139d49d66e5724113d8a7040e3b3a8bb4849df","first_computed_at":"2026-05-18T00:58:35.657206Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:58:35.657206Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PCsvkzwU3EPewq3xoaLVi6LoAxQdJzJPb+ST0byrr0/nVNCNdeCriiVFPG+y2WJ5C5xeXYHemqYV0JzKQM70BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:58:35.657917Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.00303","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b13aa592430ea7843b9645ab37b08ab7ba81cc440fd803d7211339b53710da40","sha256:3bc83d2605ca4ca615dbbeb95834fe7b4b41b9e24162f4fa9fb8def8eb409bfe"],"state_sha256":"cbd2b3d6f52a15bdbea18ea1895df7610c3437436ed097e5560573ff95987921"}