{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:DQJDUB3QM4MYIDADQLP4WI3REL","short_pith_number":"pith:DQJDUB3Q","canonical_record":{"source":{"id":"1307.5240","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-07-19T14:44:46Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"021615edb83fa3c3635ff46870959bffb48d912168e734c1928494d1ed452d7e","abstract_canon_sha256":"93e8c9928f53f5eed3fc3e91b4645a3ec38e510d6787cbd6babc352da7b8ea0d"},"schema_version":"1.0"},"canonical_sha256":"1c123a07706719840c0382dfcb237122f5f337988988d61f91b66478840804da","source":{"kind":"arxiv","id":"1307.5240","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.5240","created_at":"2026-05-18T03:18:05Z"},{"alias_kind":"arxiv_version","alias_value":"1307.5240v1","created_at":"2026-05-18T03:18:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.5240","created_at":"2026-05-18T03:18:05Z"},{"alias_kind":"pith_short_12","alias_value":"DQJDUB3QM4MY","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"DQJDUB3QM4MYIDAD","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"DQJDUB3Q","created_at":"2026-05-18T12:27:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:DQJDUB3QM4MYIDADQLP4WI3REL","target":"record","payload":{"canonical_record":{"source":{"id":"1307.5240","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-07-19T14:44:46Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"021615edb83fa3c3635ff46870959bffb48d912168e734c1928494d1ed452d7e","abstract_canon_sha256":"93e8c9928f53f5eed3fc3e91b4645a3ec38e510d6787cbd6babc352da7b8ea0d"},"schema_version":"1.0"},"canonical_sha256":"1c123a07706719840c0382dfcb237122f5f337988988d61f91b66478840804da","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:18:05.360695Z","signature_b64":"4EC//M1UqMgMYle0SfNF05GYsC+x/IdDKiakvNjrcIXqBY1bNL8XaXAcMdw4PQXWHZY0uQS5EqWU+DyqmRSCDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1c123a07706719840c0382dfcb237122f5f337988988d61f91b66478840804da","last_reissued_at":"2026-05-18T03:18:05.359995Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:18:05.359995Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.5240","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":"2026-05-18T03:18:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Yx/Ty2cB6MflhlYp4hr3ZSR0NyThHosi/xUfzXDyo6LjVA5q9PDO9dQoJ0VeqBCzBTsfZ76I1xHxdBhgr+HxAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T11:17:24.626949Z"},"content_sha256":"a235e11e0926de8549780827569392361af6dee4ab7ae458aabaaba01437b435","schema_version":"1.0","event_id":"sha256:a235e11e0926de8549780827569392361af6dee4ab7ae458aabaaba01437b435"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:DQJDUB3QM4MYIDADQLP4WI3REL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Performance Analysis of Optimum Zero-Forcing Beamforming with Greedy User Selection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Murat Torlak, Serdar Ozyurt","submitted_at":"2013-07-19T14:44:46Z","abstract_excerpt":"In this letter, an exact performance analysis is presented on the sum rate of zero-forcing beamforming with a greedy user scheduling algorithm in a downlink system. Adopting water-filling power allocation, we derive a compact form for the joint probability density function of the scheduled users' squared subchannel gains when a transmitter with multiple antennas sends information to at most two scheduled users with each having a single antenna. The analysis is verified by numerical results."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.5240","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":"2026-05-18T03:18:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+FOma0uTdJkiFesXT0/iX2FKMjTODvLvyyzl92w1SBXe6G2RwFLzGtCHs01GXG8mfw9ZTjs7BNAV3pdQNdmMDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T11:17:24.627288Z"},"content_sha256":"9a4d1c76b8daf7c4335fd7c0a917f9f3672e1293e03897e42f7cae64474b7295","schema_version":"1.0","event_id":"sha256:9a4d1c76b8daf7c4335fd7c0a917f9f3672e1293e03897e42f7cae64474b7295"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DQJDUB3QM4MYIDADQLP4WI3REL/bundle.json","state_url":"https://pith.science/pith/DQJDUB3QM4MYIDADQLP4WI3REL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DQJDUB3QM4MYIDADQLP4WI3REL/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":"2026-06-20T11:17:24Z","links":{"resolver":"https://pith.science/pith/DQJDUB3QM4MYIDADQLP4WI3REL","bundle":"https://pith.science/pith/DQJDUB3QM4MYIDADQLP4WI3REL/bundle.json","state":"https://pith.science/pith/DQJDUB3QM4MYIDADQLP4WI3REL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DQJDUB3QM4MYIDADQLP4WI3REL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:DQJDUB3QM4MYIDADQLP4WI3REL","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":"93e8c9928f53f5eed3fc3e91b4645a3ec38e510d6787cbd6babc352da7b8ea0d","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-07-19T14:44:46Z","title_canon_sha256":"021615edb83fa3c3635ff46870959bffb48d912168e734c1928494d1ed452d7e"},"schema_version":"1.0","source":{"id":"1307.5240","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.5240","created_at":"2026-05-18T03:18:05Z"},{"alias_kind":"arxiv_version","alias_value":"1307.5240v1","created_at":"2026-05-18T03:18:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.5240","created_at":"2026-05-18T03:18:05Z"},{"alias_kind":"pith_short_12","alias_value":"DQJDUB3QM4MY","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"DQJDUB3QM4MYIDAD","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"DQJDUB3Q","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:9a4d1c76b8daf7c4335fd7c0a917f9f3672e1293e03897e42f7cae64474b7295","target":"graph","created_at":"2026-05-18T03:18:05Z","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":"In this letter, an exact performance analysis is presented on the sum rate of zero-forcing beamforming with a greedy user scheduling algorithm in a downlink system. Adopting water-filling power allocation, we derive a compact form for the joint probability density function of the scheduled users' squared subchannel gains when a transmitter with multiple antennas sends information to at most two scheduled users with each having a single antenna. The analysis is verified by numerical results.","authors_text":"Murat Torlak, Serdar Ozyurt","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-07-19T14:44:46Z","title":"Performance Analysis of Optimum Zero-Forcing Beamforming with Greedy User Selection"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.5240","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:a235e11e0926de8549780827569392361af6dee4ab7ae458aabaaba01437b435","target":"record","created_at":"2026-05-18T03:18:05Z","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":"93e8c9928f53f5eed3fc3e91b4645a3ec38e510d6787cbd6babc352da7b8ea0d","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-07-19T14:44:46Z","title_canon_sha256":"021615edb83fa3c3635ff46870959bffb48d912168e734c1928494d1ed452d7e"},"schema_version":"1.0","source":{"id":"1307.5240","kind":"arxiv","version":1}},"canonical_sha256":"1c123a07706719840c0382dfcb237122f5f337988988d61f91b66478840804da","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1c123a07706719840c0382dfcb237122f5f337988988d61f91b66478840804da","first_computed_at":"2026-05-18T03:18:05.359995Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:18:05.359995Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4EC//M1UqMgMYle0SfNF05GYsC+x/IdDKiakvNjrcIXqBY1bNL8XaXAcMdw4PQXWHZY0uQS5EqWU+DyqmRSCDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:18:05.360695Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.5240","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a235e11e0926de8549780827569392361af6dee4ab7ae458aabaaba01437b435","sha256:9a4d1c76b8daf7c4335fd7c0a917f9f3672e1293e03897e42f7cae64474b7295"],"state_sha256":"9066d97fb7c64f39ccc5bfd972fd1c19eb7df14457191c4e63668ed689da402b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zzSKBUWPTgnd2WKQYlkqTA4Xg4YkWlI+IKYeVtW1p0UyE2Wmq/vYEGhD+N6Wh3MrDTgNb0wWNy6hrVymqrzlCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T11:17:24.629193Z","bundle_sha256":"7a0425b19a369002f39a852e774937fce5a1c604986ddf12fc1cd57d10fba172"}}