{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:EKQRVBIV2P5JWJVQKY6MLRIU77","short_pith_number":"pith:EKQRVBIV","canonical_record":{"source":{"id":"1509.06252","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-08-31T00:46:11Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"6b4fc8fce06f391caa64c984bdfaa201918d49bf4cc23dcf782ea140c26a11b0","abstract_canon_sha256":"5bd46bdbd3bd38de06a720adfccbeb5139e4662c13762cacdcb429bde320a32e"},"schema_version":"1.0"},"canonical_sha256":"22a11a8515d3fa9b26b0563cc5c514fff3dddd6f5bc181a5f7ed54367cfd45e7","source":{"kind":"arxiv","id":"1509.06252","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.06252","created_at":"2026-05-18T01:32:35Z"},{"alias_kind":"arxiv_version","alias_value":"1509.06252v1","created_at":"2026-05-18T01:32:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.06252","created_at":"2026-05-18T01:32:35Z"},{"alias_kind":"pith_short_12","alias_value":"EKQRVBIV2P5J","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"EKQRVBIV2P5JWJVQ","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"EKQRVBIV","created_at":"2026-05-18T12:29:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:EKQRVBIV2P5JWJVQKY6MLRIU77","target":"record","payload":{"canonical_record":{"source":{"id":"1509.06252","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-08-31T00:46:11Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"6b4fc8fce06f391caa64c984bdfaa201918d49bf4cc23dcf782ea140c26a11b0","abstract_canon_sha256":"5bd46bdbd3bd38de06a720adfccbeb5139e4662c13762cacdcb429bde320a32e"},"schema_version":"1.0"},"canonical_sha256":"22a11a8515d3fa9b26b0563cc5c514fff3dddd6f5bc181a5f7ed54367cfd45e7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:35.487864Z","signature_b64":"AizlxywSgt7+8cuktJgpMjUPW8LV7jvWJyGE+EvtX72HekVQZ9Ly8dlS0ZAbj6OGZzhsYNDQFcH3wx9aeGacBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"22a11a8515d3fa9b26b0563cc5c514fff3dddd6f5bc181a5f7ed54367cfd45e7","last_reissued_at":"2026-05-18T01:32:35.487458Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:35.487458Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.06252","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:32:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3DMxhc0sup7W8Vhy1a5q7uT/t4EfzgDYqMXGCWCXiRveD1kYzoZ4u6fZ8NvS8Ow/8nvgqciDvUFWGod9mvXwDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T14:09:02.293754Z"},"content_sha256":"3a88de3f83465cba61c89a87501f67d6fa331d8224be4b12efc9d9a4219320f8","schema_version":"1.0","event_id":"sha256:3a88de3f83465cba61c89a87501f67d6fa331d8224be4b12efc9d9a4219320f8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:EKQRVBIV2P5JWJVQKY6MLRIU77","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Algebraic Solution for Beamforming in Two-Way Relay Systems with Analog Network Coding","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Ahsan Aziz, Christopher Thron","submitted_at":"2015-08-31T00:46:11Z","abstract_excerpt":"We reduce the problem of optimal beamforming for two-way relay (TWR) systems with perfect channel state infomation (CSI) that use analog network coding (ANC) to a pair of algebraic equations in two variables that can be solved inexpensively using numerical methods. The solution has greatly reduced complexity compared to previous exact solutions via semidefinite programming (SDP). Together with the linearized robust solution described in (Aziz and Thron, 2014), it provides a high-performance, low-complexity robust beamforming solution for 2-way relays."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06252","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:32:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"doudFgVRysV4tK/VfX7m+4kfltCOhyowsjE5ayq2HxhN42g+wONcAs6CO1ecmnGkVNA4/ht8UMoN6n1vPxt4Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T14:09:02.294100Z"},"content_sha256":"40a736de3fc591e869e4c0125c1e503040567d8b0c55b63721e0b113ac13f2ee","schema_version":"1.0","event_id":"sha256:40a736de3fc591e869e4c0125c1e503040567d8b0c55b63721e0b113ac13f2ee"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EKQRVBIV2P5JWJVQKY6MLRIU77/bundle.json","state_url":"https://pith.science/pith/EKQRVBIV2P5JWJVQKY6MLRIU77/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EKQRVBIV2P5JWJVQKY6MLRIU77/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-30T14:09:02Z","links":{"resolver":"https://pith.science/pith/EKQRVBIV2P5JWJVQKY6MLRIU77","bundle":"https://pith.science/pith/EKQRVBIV2P5JWJVQKY6MLRIU77/bundle.json","state":"https://pith.science/pith/EKQRVBIV2P5JWJVQKY6MLRIU77/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EKQRVBIV2P5JWJVQKY6MLRIU77/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:EKQRVBIV2P5JWJVQKY6MLRIU77","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":"5bd46bdbd3bd38de06a720adfccbeb5139e4662c13762cacdcb429bde320a32e","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-08-31T00:46:11Z","title_canon_sha256":"6b4fc8fce06f391caa64c984bdfaa201918d49bf4cc23dcf782ea140c26a11b0"},"schema_version":"1.0","source":{"id":"1509.06252","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.06252","created_at":"2026-05-18T01:32:35Z"},{"alias_kind":"arxiv_version","alias_value":"1509.06252v1","created_at":"2026-05-18T01:32:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.06252","created_at":"2026-05-18T01:32:35Z"},{"alias_kind":"pith_short_12","alias_value":"EKQRVBIV2P5J","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"EKQRVBIV2P5JWJVQ","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"EKQRVBIV","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:40a736de3fc591e869e4c0125c1e503040567d8b0c55b63721e0b113ac13f2ee","target":"graph","created_at":"2026-05-18T01:32:35Z","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":"We reduce the problem of optimal beamforming for two-way relay (TWR) systems with perfect channel state infomation (CSI) that use analog network coding (ANC) to a pair of algebraic equations in two variables that can be solved inexpensively using numerical methods. The solution has greatly reduced complexity compared to previous exact solutions via semidefinite programming (SDP). Together with the linearized robust solution described in (Aziz and Thron, 2014), it provides a high-performance, low-complexity robust beamforming solution for 2-way relays.","authors_text":"Ahsan Aziz, Christopher Thron","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-08-31T00:46:11Z","title":"Algebraic Solution for Beamforming in Two-Way Relay Systems with Analog Network Coding"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06252","kind":"arxiv","version":1},"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":"sha256:3a88de3f83465cba61c89a87501f67d6fa331d8224be4b12efc9d9a4219320f8","target":"record","created_at":"2026-05-18T01:32:35Z","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":"5bd46bdbd3bd38de06a720adfccbeb5139e4662c13762cacdcb429bde320a32e","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-08-31T00:46:11Z","title_canon_sha256":"6b4fc8fce06f391caa64c984bdfaa201918d49bf4cc23dcf782ea140c26a11b0"},"schema_version":"1.0","source":{"id":"1509.06252","kind":"arxiv","version":1}},"canonical_sha256":"22a11a8515d3fa9b26b0563cc5c514fff3dddd6f5bc181a5f7ed54367cfd45e7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"22a11a8515d3fa9b26b0563cc5c514fff3dddd6f5bc181a5f7ed54367cfd45e7","first_computed_at":"2026-05-18T01:32:35.487458Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:32:35.487458Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AizlxywSgt7+8cuktJgpMjUPW8LV7jvWJyGE+EvtX72HekVQZ9Ly8dlS0ZAbj6OGZzhsYNDQFcH3wx9aeGacBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:32:35.487864Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.06252","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3a88de3f83465cba61c89a87501f67d6fa331d8224be4b12efc9d9a4219320f8","sha256:40a736de3fc591e869e4c0125c1e503040567d8b0c55b63721e0b113ac13f2ee"],"state_sha256":"c7685d18fd6f2764b0a4c22e47dbf85b710278d1504d4ac7cc87480fc8b1e2fd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HIEe5NnkzU+swD5lnnZVT0k+bhJtJuF1foVni9xTxU5T/oJr0xRiPlT8KmGTlIzFFaj2Es7bEu9t2MFcPK5pAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T14:09:02.296950Z","bundle_sha256":"517fc813d58503d99a41c2d5c62ba2db0900ce5f1ed98180766113cb7664e547"}}