{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:SRN27DWBOGXJIPC4A7CC7RLHFU","short_pith_number":"pith:SRN27DWB","schema_version":"1.0","canonical_sha256":"945baf8ec171ae943c5c07c42fc5672d23800ee2322a0853eb966669c660474d","source":{"kind":"arxiv","id":"2507.14982","version":3},"attestation_state":"computed","paper":{"title":"How Many Simultaneous Beamformers are Needed for Integrated Sensing and Communications?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"eess.SP","authors_text":"Kareem M. Attiah, Wei Yu","submitted_at":"2025-07-20T14:37:01Z","abstract_excerpt":"Consider a downlink integrated sensing and communications (ISAC) system in which a base station employs linear beamforming to communicate to $K$ users, while simultaneously uses sensing beams to perform a sensing task of estimating $L$ real parameters. How many beamformers are needed to achieve the best performance for both sensing and communications? This paper establishes bounds on the minimum number of downlink beamformers, in which sensing performance is measured in terms of the Cram\\'{e}r-Rao bound for parameter estimation and communications performance is measured in terms of the signal-"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2507.14982","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SP","submitted_at":"2025-07-20T14:37:01Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"b01dabe137542c20728ac5fc7f5af3e75db23f5fe752b68c08892e8c69e978af","abstract_canon_sha256":"9760af0daf3389d6de6e0824e879b18cad09dfcc8cd41740b6a48a3d2708bf9d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:10:53.626484Z","signature_b64":"5Rq4VUr5nZgTBD56Lu55sS1hx06978l56ZobDLsqH6mMezmw8FQtYFlR/jWouemo9+uNPyEbodiOC2QQhndADA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"945baf8ec171ae943c5c07c42fc5672d23800ee2322a0853eb966669c660474d","last_reissued_at":"2026-06-19T16:10:53.626050Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:10:53.626050Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"How Many Simultaneous Beamformers are Needed for Integrated Sensing and Communications?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"eess.SP","authors_text":"Kareem M. Attiah, Wei Yu","submitted_at":"2025-07-20T14:37:01Z","abstract_excerpt":"Consider a downlink integrated sensing and communications (ISAC) system in which a base station employs linear beamforming to communicate to $K$ users, while simultaneously uses sensing beams to perform a sensing task of estimating $L$ real parameters. How many beamformers are needed to achieve the best performance for both sensing and communications? This paper establishes bounds on the minimum number of downlink beamformers, in which sensing performance is measured in terms of the Cram\\'{e}r-Rao bound for parameter estimation and communications performance is measured in terms of the signal-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.14982","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.14982/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2507.14982","created_at":"2026-06-19T16:10:53.626110+00:00"},{"alias_kind":"arxiv_version","alias_value":"2507.14982v3","created_at":"2026-06-19T16:10:53.626110+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.14982","created_at":"2026-06-19T16:10:53.626110+00:00"},{"alias_kind":"pith_short_12","alias_value":"SRN27DWBOGXJ","created_at":"2026-06-19T16:10:53.626110+00:00"},{"alias_kind":"pith_short_16","alias_value":"SRN27DWBOGXJIPC4","created_at":"2026-06-19T16:10:53.626110+00:00"},{"alias_kind":"pith_short_8","alias_value":"SRN27DWB","created_at":"2026-06-19T16:10:53.626110+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":4,"internal_anchor_count":4,"sample":[{"citing_arxiv_id":"2509.13661","citing_title":"Uplink-Downlink Duality for Beamforming in Integrated Sensing and Communications","ref_index":36,"is_internal_anchor":true},{"citing_arxiv_id":"2604.17582","citing_title":"Active MIMO Sensing With Exploration-Exploitation Tradeoff","ref_index":13,"is_internal_anchor":true},{"citing_arxiv_id":"2604.22392","citing_title":"Multi-User ISAC with Heterogeneous Unknown Parameters: Optimal Beamforming based on Distribution Information","ref_index":17,"is_internal_anchor":true},{"citing_arxiv_id":"2604.21580","citing_title":"Robust Beamforming for MIMO Radar with Imperfect Prior Distribution Information","ref_index":15,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/SRN27DWBOGXJIPC4A7CC7RLHFU","json":"https://pith.science/pith/SRN27DWBOGXJIPC4A7CC7RLHFU.json","graph_json":"https://pith.science/api/pith-number/SRN27DWBOGXJIPC4A7CC7RLHFU/graph.json","events_json":"https://pith.science/api/pith-number/SRN27DWBOGXJIPC4A7CC7RLHFU/events.json","paper":"https://pith.science/paper/SRN27DWB"},"agent_actions":{"view_html":"https://pith.science/pith/SRN27DWBOGXJIPC4A7CC7RLHFU","download_json":"https://pith.science/pith/SRN27DWBOGXJIPC4A7CC7RLHFU.json","view_paper":"https://pith.science/paper/SRN27DWB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2507.14982&json=true","fetch_graph":"https://pith.science/api/pith-number/SRN27DWBOGXJIPC4A7CC7RLHFU/graph.json","fetch_events":"https://pith.science/api/pith-number/SRN27DWBOGXJIPC4A7CC7RLHFU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SRN27DWBOGXJIPC4A7CC7RLHFU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SRN27DWBOGXJIPC4A7CC7RLHFU/action/storage_attestation","attest_author":"https://pith.science/pith/SRN27DWBOGXJIPC4A7CC7RLHFU/action/author_attestation","sign_citation":"https://pith.science/pith/SRN27DWBOGXJIPC4A7CC7RLHFU/action/citation_signature","submit_replication":"https://pith.science/pith/SRN27DWBOGXJIPC4A7CC7RLHFU/action/replication_record"}},"created_at":"2026-06-19T16:10:53.626110+00:00","updated_at":"2026-06-19T16:10:53.626110+00:00"}