{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:BZHR6MHT6KLICDJWTMZ74B6E45","short_pith_number":"pith:BZHR6MHT","schema_version":"1.0","canonical_sha256":"0e4f1f30f3f296810d369b33fe07c4e75c6eb42cc8980214daa08ad7c98edd13","source":{"kind":"arxiv","id":"0904.4526","version":1},"attestation_state":"computed","paper":{"title":"Feasibility Conditions for Interference Alignment","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AR","math.IT"],"primary_cat":"cs.IT","authors_text":"Ahmet H. Kayran, Cenk M. Yetis, Syed A. Jafar","submitted_at":"2009-04-29T03:11:52Z","abstract_excerpt":"The degrees of freedom of MIMO interference networks with constant channel coefficients are not known in general. Determining the feasibility of a linear interference alignment solution is a key step toward solving this open problem. Our approach in this paper is to view the alignment problem as a system of bilinear equations and determine its solvability by comparing the number of equations and the number of variables. To this end, we divide interference alignment problems into two classes - proper and improper. An interference alignment problem is called proper if the number of equations doe"},"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":"0904.4526","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2009-04-29T03:11:52Z","cross_cats_sorted":["cs.AR","math.IT"],"title_canon_sha256":"ea309e1e9ac50c9951d8ccb69525140f5e126d3e6ba489d66f1ebf4bc1d8ba66","abstract_canon_sha256":"e435cf16db12cbe2c1f72a8f0cebd1ef20fe24075adbacef6f5e34f5da815433"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:13:49.342185Z","signature_b64":"KR5lzn+q1LDhFbspRpZsbbAvJkqLhzLArRz7PNwm33PJ9BIOjTpQfycKrBxHl9AUz8QAg5IMQW5kanJfBOBFDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0e4f1f30f3f296810d369b33fe07c4e75c6eb42cc8980214daa08ad7c98edd13","last_reissued_at":"2026-05-18T02:13:49.341449Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:13:49.341449Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Feasibility Conditions for Interference Alignment","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AR","math.IT"],"primary_cat":"cs.IT","authors_text":"Ahmet H. Kayran, Cenk M. Yetis, Syed A. Jafar","submitted_at":"2009-04-29T03:11:52Z","abstract_excerpt":"The degrees of freedom of MIMO interference networks with constant channel coefficients are not known in general. Determining the feasibility of a linear interference alignment solution is a key step toward solving this open problem. Our approach in this paper is to view the alignment problem as a system of bilinear equations and determine its solvability by comparing the number of equations and the number of variables. To this end, we divide interference alignment problems into two classes - proper and improper. An interference alignment problem is called proper if the number of equations doe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.4526","kind":"arxiv","version":1},"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":"0904.4526","created_at":"2026-05-18T02:13:49.341571+00:00"},{"alias_kind":"arxiv_version","alias_value":"0904.4526v1","created_at":"2026-05-18T02:13:49.341571+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0904.4526","created_at":"2026-05-18T02:13:49.341571+00:00"},{"alias_kind":"pith_short_12","alias_value":"BZHR6MHT6KLI","created_at":"2026-05-18T12:25:58.837520+00:00"},{"alias_kind":"pith_short_16","alias_value":"BZHR6MHT6KLICDJW","created_at":"2026-05-18T12:25:58.837520+00:00"},{"alias_kind":"pith_short_8","alias_value":"BZHR6MHT","created_at":"2026-05-18T12:25:58.837520+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/BZHR6MHT6KLICDJWTMZ74B6E45","json":"https://pith.science/pith/BZHR6MHT6KLICDJWTMZ74B6E45.json","graph_json":"https://pith.science/api/pith-number/BZHR6MHT6KLICDJWTMZ74B6E45/graph.json","events_json":"https://pith.science/api/pith-number/BZHR6MHT6KLICDJWTMZ74B6E45/events.json","paper":"https://pith.science/paper/BZHR6MHT"},"agent_actions":{"view_html":"https://pith.science/pith/BZHR6MHT6KLICDJWTMZ74B6E45","download_json":"https://pith.science/pith/BZHR6MHT6KLICDJWTMZ74B6E45.json","view_paper":"https://pith.science/paper/BZHR6MHT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0904.4526&json=true","fetch_graph":"https://pith.science/api/pith-number/BZHR6MHT6KLICDJWTMZ74B6E45/graph.json","fetch_events":"https://pith.science/api/pith-number/BZHR6MHT6KLICDJWTMZ74B6E45/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BZHR6MHT6KLICDJWTMZ74B6E45/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BZHR6MHT6KLICDJWTMZ74B6E45/action/storage_attestation","attest_author":"https://pith.science/pith/BZHR6MHT6KLICDJWTMZ74B6E45/action/author_attestation","sign_citation":"https://pith.science/pith/BZHR6MHT6KLICDJWTMZ74B6E45/action/citation_signature","submit_replication":"https://pith.science/pith/BZHR6MHT6KLICDJWTMZ74B6E45/action/replication_record"}},"created_at":"2026-05-18T02:13:49.341571+00:00","updated_at":"2026-05-18T02:13:49.341571+00:00"}