{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:SK7BSJHNFI2I5NFR2E4RBZC3NN","short_pith_number":"pith:SK7BSJHN","canonical_record":{"source":{"id":"1702.04493","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-02-15T07:57:34Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"7932c6ec996a92125d503ffb76be14f0249c6ad0d77f8dcb28b3a72ec11a71ac","abstract_canon_sha256":"26675f26d55dcc86a70cdb121636e9b71552a79ee87478759b245dcc7ef44293"},"schema_version":"1.0"},"canonical_sha256":"92be1924ed2a348eb4b1d13910e45b6b5c5479f3536389ed3933ab0ab9d4b38f","source":{"kind":"arxiv","id":"1702.04493","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.04493","created_at":"2026-05-18T00:46:04Z"},{"alias_kind":"arxiv_version","alias_value":"1702.04493v2","created_at":"2026-05-18T00:46:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.04493","created_at":"2026-05-18T00:46:04Z"},{"alias_kind":"pith_short_12","alias_value":"SK7BSJHNFI2I","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SK7BSJHNFI2I5NFR","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SK7BSJHN","created_at":"2026-05-18T12:31:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:SK7BSJHNFI2I5NFR2E4RBZC3NN","target":"record","payload":{"canonical_record":{"source":{"id":"1702.04493","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-02-15T07:57:34Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"7932c6ec996a92125d503ffb76be14f0249c6ad0d77f8dcb28b3a72ec11a71ac","abstract_canon_sha256":"26675f26d55dcc86a70cdb121636e9b71552a79ee87478759b245dcc7ef44293"},"schema_version":"1.0"},"canonical_sha256":"92be1924ed2a348eb4b1d13910e45b6b5c5479f3536389ed3933ab0ab9d4b38f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:04.023327Z","signature_b64":"vsJBS8bOoXPMm5UiH2Kh2sBnV5QfUsQPFHovLy3fb486Db8HFmSZy8j88lab4DnrS37aQaYg/DuHmZFZ++U4Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"92be1924ed2a348eb4b1d13910e45b6b5c5479f3536389ed3933ab0ab9d4b38f","last_reissued_at":"2026-05-18T00:46:04.022980Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:04.022980Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1702.04493","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:46:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e3NdO6WFXENErVV1pWftbYw86Nvc8D/KoWjpd1iyKHJnwMXb2B5SN103JGYkrLkGwrOyA5rxp2PbunHOTvKyCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T16:13:12.842440Z"},"content_sha256":"967a7212f9fa420ddaaf890b48526cbcd6d9ad02b45de631b05fffa5a115d70c","schema_version":"1.0","event_id":"sha256:967a7212f9fa420ddaaf890b48526cbcd6d9ad02b45de631b05fffa5a115d70c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:SK7BSJHNFI2I5NFR2E4RBZC3NN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Coverage Analysis for Millimeter Wave Networks: The Impact of Directional Antenna Arrays","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Jun Zhang, Khaled B. Letaief, Martin Haenggi, Xianghao Yu","submitted_at":"2017-02-15T07:57:34Z","abstract_excerpt":"Millimeter wave (mm-wave) communications is considered a promising technology for 5G networks. Exploiting beamforming gains with large-scale antenna arrays to combat the increased path loss at mm-wave bands is one of its defining features. However, previous works on mm-wave network analysis usually adopted oversimplified antenna patterns for tractability, which can lead to significant deviation from the performance with actual antenna patterns. In this paper, using tools from stochastic geometry, we carry out a comprehensive investigation on the impact of directional antenna arrays in mm-wave "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.04493","kind":"arxiv","version":2},"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":"2026-05-18T00:46:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rKKT/DsjfVz18xyiKFFJZx89l9P0JEFOePzPav4eZnJtm9I3D502Xg7KlrASKygOiUR1B/J8v+6mcqi8ZRpqAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T16:13:12.843190Z"},"content_sha256":"2799919a3a94bc80925f380b3e29f08291012f100b9b863916f9b61643f9ad2e","schema_version":"1.0","event_id":"sha256:2799919a3a94bc80925f380b3e29f08291012f100b9b863916f9b61643f9ad2e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SK7BSJHNFI2I5NFR2E4RBZC3NN/bundle.json","state_url":"https://pith.science/pith/SK7BSJHNFI2I5NFR2E4RBZC3NN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SK7BSJHNFI2I5NFR2E4RBZC3NN/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":"2026-05-31T16:13:12Z","links":{"resolver":"https://pith.science/pith/SK7BSJHNFI2I5NFR2E4RBZC3NN","bundle":"https://pith.science/pith/SK7BSJHNFI2I5NFR2E4RBZC3NN/bundle.json","state":"https://pith.science/pith/SK7BSJHNFI2I5NFR2E4RBZC3NN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SK7BSJHNFI2I5NFR2E4RBZC3NN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:SK7BSJHNFI2I5NFR2E4RBZC3NN","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":"26675f26d55dcc86a70cdb121636e9b71552a79ee87478759b245dcc7ef44293","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-02-15T07:57:34Z","title_canon_sha256":"7932c6ec996a92125d503ffb76be14f0249c6ad0d77f8dcb28b3a72ec11a71ac"},"schema_version":"1.0","source":{"id":"1702.04493","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.04493","created_at":"2026-05-18T00:46:04Z"},{"alias_kind":"arxiv_version","alias_value":"1702.04493v2","created_at":"2026-05-18T00:46:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.04493","created_at":"2026-05-18T00:46:04Z"},{"alias_kind":"pith_short_12","alias_value":"SK7BSJHNFI2I","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SK7BSJHNFI2I5NFR","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SK7BSJHN","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:2799919a3a94bc80925f380b3e29f08291012f100b9b863916f9b61643f9ad2e","target":"graph","created_at":"2026-05-18T00:46:04Z","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 (mm-wave) communications is considered a promising technology for 5G networks. Exploiting beamforming gains with large-scale antenna arrays to combat the increased path loss at mm-wave bands is one of its defining features. However, previous works on mm-wave network analysis usually adopted oversimplified antenna patterns for tractability, which can lead to significant deviation from the performance with actual antenna patterns. In this paper, using tools from stochastic geometry, we carry out a comprehensive investigation on the impact of directional antenna arrays in mm-wave ","authors_text":"Jun Zhang, Khaled B. Letaief, Martin Haenggi, Xianghao Yu","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-02-15T07:57:34Z","title":"Coverage Analysis for Millimeter Wave Networks: The Impact of Directional Antenna Arrays"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.04493","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":"sha256:967a7212f9fa420ddaaf890b48526cbcd6d9ad02b45de631b05fffa5a115d70c","target":"record","created_at":"2026-05-18T00:46:04Z","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":"26675f26d55dcc86a70cdb121636e9b71552a79ee87478759b245dcc7ef44293","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-02-15T07:57:34Z","title_canon_sha256":"7932c6ec996a92125d503ffb76be14f0249c6ad0d77f8dcb28b3a72ec11a71ac"},"schema_version":"1.0","source":{"id":"1702.04493","kind":"arxiv","version":2}},"canonical_sha256":"92be1924ed2a348eb4b1d13910e45b6b5c5479f3536389ed3933ab0ab9d4b38f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"92be1924ed2a348eb4b1d13910e45b6b5c5479f3536389ed3933ab0ab9d4b38f","first_computed_at":"2026-05-18T00:46:04.022980Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:04.022980Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vsJBS8bOoXPMm5UiH2Kh2sBnV5QfUsQPFHovLy3fb486Db8HFmSZy8j88lab4DnrS37aQaYg/DuHmZFZ++U4Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:04.023327Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.04493","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:967a7212f9fa420ddaaf890b48526cbcd6d9ad02b45de631b05fffa5a115d70c","sha256:2799919a3a94bc80925f380b3e29f08291012f100b9b863916f9b61643f9ad2e"],"state_sha256":"de928c447fc1e41284ca856d57d9ea76a931c5a5f144154d9361e5df1ac3450f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bOVk0rjG6god/7FmaPdZ5XpIheaaD6yrY0kmpXgmpYuqUZXI06/EFEN43gZ4MYQE75wpiiGIw1L7gWFCstfDAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T16:13:12.847393Z","bundle_sha256":"de3e2fd7f2096e14832ac7ae8d01d5a4ed21d17a1c70ba118ebe5847d18a9d59"}}