{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:53OOW2IXAILF65IEZK7BYCXIDH","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":"8cd17c5727055dc8ef5822c8447d860c60937e637621420857dba72b8be98af9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SP","submitted_at":"2021-05-16T05:45:33Z","title_canon_sha256":"291b38a4c64819519526e8da3f105178f02fd46ef90d3ae207b766aa65963df7"},"schema_version":"1.0","source":{"id":"2105.07359","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2105.07359","created_at":"2026-07-05T03:31:27Z"},{"alias_kind":"arxiv_version","alias_value":"2105.07359v2","created_at":"2026-07-05T03:31:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2105.07359","created_at":"2026-07-05T03:31:27Z"},{"alias_kind":"pith_short_12","alias_value":"53OOW2IXAILF","created_at":"2026-07-05T03:31:27Z"},{"alias_kind":"pith_short_16","alias_value":"53OOW2IXAILF65IE","created_at":"2026-07-05T03:31:27Z"},{"alias_kind":"pith_short_8","alias_value":"53OOW2IX","created_at":"2026-07-05T03:31:27Z"}],"graph_snapshots":[{"event_id":"sha256:813646287a4e436d6714c9c4bcd9cb416a0bc0b54ef5397b2c42c7854e7324e2","target":"graph","created_at":"2026-07-05T03:31:27Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2105.07359/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Three dimensional (3D) resource reuse is an important design requirement for the prospective 6G wireless communication systems. Hence, we propose a cooperative 3D beamformer for use in 3D space. Explicitly, we harness multiple base station antennas for joint zero forcing transmit pre-coding for beaming the transmit signals in specific 3D directions. The technique advocated is judiciously configured for use in both cell-based and cell-free wireless architectures. We evaluated the performance of the proposed scheme using the novel metric of Volumetric Spectral Efficiency (VSE). We also character","authors_text":"Lajos Hanzo, Sarath Gopi, Sheetal Kalyani","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SP","submitted_at":"2021-05-16T05:45:33Z","title":"Cooperative 3D Beamforming for Small-Cell and Cell-Free 6G Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.07359","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:c976fcf50203e4bb4e78dcde715c6872d497a66f436e37173e53ee3cf8994968","target":"record","created_at":"2026-07-05T03:31:27Z","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":"8cd17c5727055dc8ef5822c8447d860c60937e637621420857dba72b8be98af9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SP","submitted_at":"2021-05-16T05:45:33Z","title_canon_sha256":"291b38a4c64819519526e8da3f105178f02fd46ef90d3ae207b766aa65963df7"},"schema_version":"1.0","source":{"id":"2105.07359","kind":"arxiv","version":2}},"canonical_sha256":"eedceb691702165f7504cabe1c0ae819d36c84c7f500ffbb3c15c8cd13da07f0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eedceb691702165f7504cabe1c0ae819d36c84c7f500ffbb3c15c8cd13da07f0","first_computed_at":"2026-07-05T03:31:27.150696Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:31:27.150696Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Rgdt+bJ/Mz/3jycz3cr1uvZunremVfXXZftS2OAfmTaNCjaYNZd5IDnGK2zIrD4VNdJ5MjZ+bTbpExqvi6q7BA==","signature_status":"signed_v1","signed_at":"2026-07-05T03:31:27.151433Z","signed_message":"canonical_sha256_bytes"},"source_id":"2105.07359","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c976fcf50203e4bb4e78dcde715c6872d497a66f436e37173e53ee3cf8994968","sha256:813646287a4e436d6714c9c4bcd9cb416a0bc0b54ef5397b2c42c7854e7324e2"],"state_sha256":"c72422c0513eece08bb664ec0167b4f9e073295691bc40f65ad9f89370137e55"}