{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:UWM2AZUFGGM4FKQVIJDEIF6TRW","short_pith_number":"pith:UWM2AZUF","schema_version":"1.0","canonical_sha256":"a599a066853199c2aa1542464417d38dbaecaff83ef8f959e36bc2ce69fffeca","source":{"kind":"arxiv","id":"1608.03351","version":2},"attestation_state":"computed","paper":{"title":"Uplink-Downlink Duality for Integer-Forcing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Bobak Nazer, Shlomo Shamai, Wenbo He","submitted_at":"2016-08-11T02:31:51Z","abstract_excerpt":"Consider a Gaussian multiple-input multiple-output (MIMO) multiple-access channel (MAC) with channel matrix $\\mathbf{H}$ and a Gaussian MIMO broadcast channel (BC) with channel matrix $\\mathbf{H}^{\\mathsf{T}}$. For the MIMO MAC, the integer-forcing architecture consists of first decoding integer-linear combinations of the transmitted codewords, which are then solved for the original messages. For the MIMO BC, the integer-forcing architecture consists of pre-inverting the integer-linear combinations at the transmitter so that each receiver can obtain its desired codeword by decoding an integer-"},"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":"1608.03351","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-08-11T02:31:51Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"43fcfcb4017a7facd990d04585c897c92cc1c23f404720f7d3024c677d501cdd","abstract_canon_sha256":"d9eb2ca74e390fa5ec543264c00c0ed9697d5673c8307b172a7d49fb55e47191"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:37.708849Z","signature_b64":"rBRl+orl5rhuEGflcDzbYd+pnEkhpAyhL2IybrW86ZBz8kX+3i/v1cle4fFr7Jp3+A9aPArQYyth50SDcOr3Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a599a066853199c2aa1542464417d38dbaecaff83ef8f959e36bc2ce69fffeca","last_reissued_at":"2026-05-18T00:26:37.708210Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:37.708210Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Uplink-Downlink Duality for Integer-Forcing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Bobak Nazer, Shlomo Shamai, Wenbo He","submitted_at":"2016-08-11T02:31:51Z","abstract_excerpt":"Consider a Gaussian multiple-input multiple-output (MIMO) multiple-access channel (MAC) with channel matrix $\\mathbf{H}$ and a Gaussian MIMO broadcast channel (BC) with channel matrix $\\mathbf{H}^{\\mathsf{T}}$. For the MIMO MAC, the integer-forcing architecture consists of first decoding integer-linear combinations of the transmitted codewords, which are then solved for the original messages. For the MIMO BC, the integer-forcing architecture consists of pre-inverting the integer-linear combinations at the transmitter so that each receiver can obtain its desired codeword by decoding an integer-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.03351","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1608.03351","created_at":"2026-05-18T00:26:37.708310+00:00"},{"alias_kind":"arxiv_version","alias_value":"1608.03351v2","created_at":"2026-05-18T00:26:37.708310+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.03351","created_at":"2026-05-18T00:26:37.708310+00:00"},{"alias_kind":"pith_short_12","alias_value":"UWM2AZUFGGM4","created_at":"2026-05-18T12:30:46.583412+00:00"},{"alias_kind":"pith_short_16","alias_value":"UWM2AZUFGGM4FKQV","created_at":"2026-05-18T12:30:46.583412+00:00"},{"alias_kind":"pith_short_8","alias_value":"UWM2AZUF","created_at":"2026-05-18T12:30:46.583412+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/UWM2AZUFGGM4FKQVIJDEIF6TRW","json":"https://pith.science/pith/UWM2AZUFGGM4FKQVIJDEIF6TRW.json","graph_json":"https://pith.science/api/pith-number/UWM2AZUFGGM4FKQVIJDEIF6TRW/graph.json","events_json":"https://pith.science/api/pith-number/UWM2AZUFGGM4FKQVIJDEIF6TRW/events.json","paper":"https://pith.science/paper/UWM2AZUF"},"agent_actions":{"view_html":"https://pith.science/pith/UWM2AZUFGGM4FKQVIJDEIF6TRW","download_json":"https://pith.science/pith/UWM2AZUFGGM4FKQVIJDEIF6TRW.json","view_paper":"https://pith.science/paper/UWM2AZUF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1608.03351&json=true","fetch_graph":"https://pith.science/api/pith-number/UWM2AZUFGGM4FKQVIJDEIF6TRW/graph.json","fetch_events":"https://pith.science/api/pith-number/UWM2AZUFGGM4FKQVIJDEIF6TRW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UWM2AZUFGGM4FKQVIJDEIF6TRW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UWM2AZUFGGM4FKQVIJDEIF6TRW/action/storage_attestation","attest_author":"https://pith.science/pith/UWM2AZUFGGM4FKQVIJDEIF6TRW/action/author_attestation","sign_citation":"https://pith.science/pith/UWM2AZUFGGM4FKQVIJDEIF6TRW/action/citation_signature","submit_replication":"https://pith.science/pith/UWM2AZUFGGM4FKQVIJDEIF6TRW/action/replication_record"}},"created_at":"2026-05-18T00:26:37.708310+00:00","updated_at":"2026-05-18T00:26:37.708310+00:00"}