{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:VIZ3IQ3IZM3PG3HCZT4K44JWFH","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":"c192951e55efd61600bc22471220efbdc2e885015afaec13a2bc9f2fdbaa04e7","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-11-14T00:00:21Z","title_canon_sha256":"7af4776c560e4e5fde6501f3363b219a6d2e9e30801d4a1a7c027e5f482d2abf"},"schema_version":"1.0","source":{"id":"1611.04212","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.04212","created_at":"2026-05-18T00:44:13Z"},{"alias_kind":"arxiv_version","alias_value":"1611.04212v2","created_at":"2026-05-18T00:44:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.04212","created_at":"2026-05-18T00:44:13Z"},{"alias_kind":"pith_short_12","alias_value":"VIZ3IQ3IZM3P","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"VIZ3IQ3IZM3PG3HC","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"VIZ3IQ3I","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:f765733867d09ce1db7513292bfe69f3a01d4933a7a842c1527388030c19ff44","target":"graph","created_at":"2026-05-18T00:44:13Z","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":"In millimeter wave cellular communication, fast and reliable beam alignment via beam training is crucial to harvest sufficient beamforming gain for the subsequent data transmission. In this paper, we establish fundamental limits in beam-alignment performance under both the exhaustive search and the hierarchical search that adopts multi-resolution beamforming codebooks, accounting for time-domain training overhead. Specifically, we derive lower and upper bounds on the probability of misalignment for an arbitrary level in the hierarchical search, based on a single-path channel model. Using the m","authors_text":"Chunshan Liu, Iain B. Collings, Min Li, Philip Whiting, Stephen V. Hanly","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-11-14T00:00:21Z","title":"Millimeter Wave Beam Alignment: Large Deviations Analysis and Design Insights"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.04212","kind":"arxiv","version":2},"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":"sha256:122b05b7828ee4dd1618cfbfa62a61e2c4c56e7e9c2b1e7e79e3f8547de37736","target":"record","created_at":"2026-05-18T00:44:13Z","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":"c192951e55efd61600bc22471220efbdc2e885015afaec13a2bc9f2fdbaa04e7","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-11-14T00:00:21Z","title_canon_sha256":"7af4776c560e4e5fde6501f3363b219a6d2e9e30801d4a1a7c027e5f482d2abf"},"schema_version":"1.0","source":{"id":"1611.04212","kind":"arxiv","version":2}},"canonical_sha256":"aa33b44368cb36f36ce2ccf8ae713629f1fc765e330a686958112a403912bb49","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aa33b44368cb36f36ce2ccf8ae713629f1fc765e330a686958112a403912bb49","first_computed_at":"2026-05-18T00:44:13.560476Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:13.560476Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WOMD4+V4r5yFrV7zHlmbNE6eHc1TqkI5Wr0gbunE671Q0Sckggc9pivxmvRR8zzFWA5m9p0Iyg8huWNNxHVDDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:13.560876Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.04212","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:122b05b7828ee4dd1618cfbfa62a61e2c4c56e7e9c2b1e7e79e3f8547de37736","sha256:f765733867d09ce1db7513292bfe69f3a01d4933a7a842c1527388030c19ff44"],"state_sha256":"34f1072cc0ead949fa846e6ae38c82ef96e56b22b0b8a9fa0e4ed07f529308e4"}