{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:UJAADC5TOWDHB4ZAPPFJ2INXB5","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":"30857d1a547a3171675fdb5a4c018c4e16f71ec456aa7273f586e885bc1f8b86","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-12-20T03:20:55Z","title_canon_sha256":"e83b042447352ddeed62f7f0b270c10800f1f0e1e470a6051474c5871107cb26"},"schema_version":"1.0","source":{"id":"1112.4553","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.4553","created_at":"2026-05-18T00:59:09Z"},{"alias_kind":"arxiv_version","alias_value":"1112.4553v3","created_at":"2026-05-18T00:59:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.4553","created_at":"2026-05-18T00:59:09Z"},{"alias_kind":"pith_short_12","alias_value":"UJAADC5TOWDH","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"UJAADC5TOWDHB4ZA","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"UJAADC5T","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:7d5538df972aea0345145bf22c3992e687675d701b65456ad1b1ab16edbbfe1a","target":"graph","created_at":"2026-05-18T00:59:09Z","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":"Interference alignment is a signaling technique that provides high multiplexing gain in the interference channel. It can be extended to multi-hop interference channels, where relays aid transmission between sources and destinations. In addition to coverage extension and capacity enhancement, relays increase the multiplexing gain in the interference channel. In this paper, three cooperative algorithms are proposed for a multiple-antenna amplify-and-forward (AF) relay interference channel. The algorithms design the transmitters and relays so that interference at the receivers can be aligned and ","authors_text":"Kien T. Truong, Philippe Sartori, Robert W. Heath Jr","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-12-20T03:20:55Z","title":"Cooperative Algorithms for MIMO Amplify-and-Forward Relay Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.4553","kind":"arxiv","version":3},"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:a70fbc41d71111d80d0ee13b48f35783eabc5f6057e06811a168949a52391900","target":"record","created_at":"2026-05-18T00:59:09Z","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":"30857d1a547a3171675fdb5a4c018c4e16f71ec456aa7273f586e885bc1f8b86","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-12-20T03:20:55Z","title_canon_sha256":"e83b042447352ddeed62f7f0b270c10800f1f0e1e470a6051474c5871107cb26"},"schema_version":"1.0","source":{"id":"1112.4553","kind":"arxiv","version":3}},"canonical_sha256":"a240018bb3758670f3207bca9d21b70f4c59cde5c27c48d35c4e6e4de8330688","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a240018bb3758670f3207bca9d21b70f4c59cde5c27c48d35c4e6e4de8330688","first_computed_at":"2026-05-18T00:59:09.978721Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:59:09.978721Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"T5tVRqyJvAxCKa0wGI1fRHe7lrfG0zNb4HI9l0HnB8fIdW8YzPk+mw2u56EXmZlL0PhB9sPcha4/EL8zsCoCCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:59:09.979432Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.4553","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a70fbc41d71111d80d0ee13b48f35783eabc5f6057e06811a168949a52391900","sha256:7d5538df972aea0345145bf22c3992e687675d701b65456ad1b1ab16edbbfe1a"],"state_sha256":"1a62943a88d56f6c91c9da320a3976f844d557fc05807656b41973d52ba4f28b"}