{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:WG6FWCUIWO7YSFSOBPTUEULAGH","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":"56f62dc46c23bcd2a6cc0aba98d4e961d4b89cc94a464957b3d97c4b76749ef4","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-12-31T01:52:08Z","title_canon_sha256":"3741751be830b32815f4c62af345b7e83e1d54411ed9fbd881a67e97a5728068"},"schema_version":"1.0","source":{"id":"1801.00222","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.00222","created_at":"2026-05-18T00:26:59Z"},{"alias_kind":"arxiv_version","alias_value":"1801.00222v1","created_at":"2026-05-18T00:26:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.00222","created_at":"2026-05-18T00:26:59Z"},{"alias_kind":"pith_short_12","alias_value":"WG6FWCUIWO7Y","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"WG6FWCUIWO7YSFSO","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"WG6FWCUI","created_at":"2026-05-18T12:31:53Z"}],"graph_snapshots":[{"event_id":"sha256:ecd3059164040d19abb4b76b07851c2a15a9e5fd3ac5bfaf94c188f201123b71","target":"graph","created_at":"2026-05-18T00:26:59Z","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":"Benefitting from multi-user gain brought by multi-antenna techniques, space division multiple access (SDMA) is capable of significantly enhancing spatial throughput (ST) in wireless networks. Nevertheless, we show in this letter that, even when SDMA is applied, ST would diminish to be zero in ultra-dense networks (UDN), where small cell base stations (BSs) are fully densified. More importantly, we compare the performance of SDMA, single-user beamforming (SU-BF) (one user is served in each cell) and full SDMA (the number of served users equals the number of equipped antennas). Surprisingly, it ","authors_text":"Jiandong Li, Junyu Liu, Min Sheng","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-12-31T01:52:08Z","title":"Limitation of SDMA in Ultra-Dense Small Cell Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.00222","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:d05d62db436f0f2ac33c87dbe6016736b88a87f61df3c2e2515fce756335cbee","target":"record","created_at":"2026-05-18T00:26:59Z","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":"56f62dc46c23bcd2a6cc0aba98d4e961d4b89cc94a464957b3d97c4b76749ef4","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-12-31T01:52:08Z","title_canon_sha256":"3741751be830b32815f4c62af345b7e83e1d54411ed9fbd881a67e97a5728068"},"schema_version":"1.0","source":{"id":"1801.00222","kind":"arxiv","version":1}},"canonical_sha256":"b1bc5b0a88b3bf89164e0be742516031d9fbef878e82092835d6b57ff59b8de7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b1bc5b0a88b3bf89164e0be742516031d9fbef878e82092835d6b57ff59b8de7","first_computed_at":"2026-05-18T00:26:59.041397Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:59.041397Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4QLpw91G//muOSAd0ajZU/yoS6a+FfSuuAJkAPVoEHNzZNJPvzBD5kqLe9OgnujV75OwC8KFEUTY9brFd2izCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:59.041943Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.00222","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d05d62db436f0f2ac33c87dbe6016736b88a87f61df3c2e2515fce756335cbee","sha256:ecd3059164040d19abb4b76b07851c2a15a9e5fd3ac5bfaf94c188f201123b71"],"state_sha256":"7f0c15f1e455de0cb9a2c7e104e649f321b515f174eff8a7d0da4e8a1f25f0e4"}