{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:HKH3D7CCPNPMK2RPNF4RZGMOZF","short_pith_number":"pith:HKH3D7CC","canonical_record":{"source":{"id":"1905.05639","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-05-14T14:29:16Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"185f0df2f5c98e7dc4215b58f1302008fb739d2425f04c9bcf103fb94ede66de","abstract_canon_sha256":"747593889aa0ec648eb07c804e54903cb30962955770dfd89e665a9dd31e0a67"},"schema_version":"1.0"},"canonical_sha256":"3a8fb1fc427b5ec56a2f69791c998ec96c1f235f99a5d1dd74ee0746592cf58c","source":{"kind":"arxiv","id":"1905.05639","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.05639","created_at":"2026-05-17T23:46:13Z"},{"alias_kind":"arxiv_version","alias_value":"1905.05639v1","created_at":"2026-05-17T23:46:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.05639","created_at":"2026-05-17T23:46:13Z"},{"alias_kind":"pith_short_12","alias_value":"HKH3D7CCPNPM","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"HKH3D7CCPNPMK2RP","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"HKH3D7CC","created_at":"2026-05-18T12:33:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:HKH3D7CCPNPMK2RPNF4RZGMOZF","target":"record","payload":{"canonical_record":{"source":{"id":"1905.05639","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-05-14T14:29:16Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"185f0df2f5c98e7dc4215b58f1302008fb739d2425f04c9bcf103fb94ede66de","abstract_canon_sha256":"747593889aa0ec648eb07c804e54903cb30962955770dfd89e665a9dd31e0a67"},"schema_version":"1.0"},"canonical_sha256":"3a8fb1fc427b5ec56a2f69791c998ec96c1f235f99a5d1dd74ee0746592cf58c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:13.972185Z","signature_b64":"iLwSDmGSUW0LTQrT9X9wnJAvauvizNzlG8h4SM6R7JXVeOh75Yt4L5ywPWKV3L5KGdJSVjxl5xGi1KMv4DhqAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3a8fb1fc427b5ec56a2f69791c998ec96c1f235f99a5d1dd74ee0746592cf58c","last_reissued_at":"2026-05-17T23:46:13.971574Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:13.971574Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1905.05639","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":"2026-05-17T23:46:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cLfgZll5RGJA8Qq55zZT8v6+BksfGylTm93DXno+gF27i5vRY582uLYSPwD5JSdLVTBs6cdTCfSzYDaa9lpzDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T14:49:33.990201Z"},"content_sha256":"d400c3e3493c132bc0a30dd4c1d44d57a4e5a136c87dc0a628c97d97fa80ecc8","schema_version":"1.0","event_id":"sha256:d400c3e3493c132bc0a30dd4c1d44d57a4e5a136c87dc0a628c97d97fa80ecc8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:HKH3D7CCPNPMK2RPNF4RZGMOZF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Low Complexity Algorithms for Robust Multigroup Multicast Beamforming","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Feng Yang, Guangda Zang, Hei Victor Cheng, Hui Liu, Lianghui Ding, Wei Liu, Ying Cui","submitted_at":"2019-05-14T14:29:16Z","abstract_excerpt":"Existing methods for robust multigroup multicast beamforming obtain feasible points using semidefinite relaxation (SDR) and Gaussian randomization, and have high computational complexity. In this letter, we consider the robust multigroup multicast beamforming design to minimize the sum power (SP) or per-antenna power (PAP) under the signal-to-interference-plus-noise ratio (SINR) constraints and to maximize the worst-case SINR under the SP constraint or PAP constraints, respectively. The resulting optimization problems are challenging non-convex problems with infinitely many constraints. For ea"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.05639","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":"2026-05-17T23:46:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xAa3cBhnhZCcJWTCkcik8Y9SVYKi10M1brP3OZseNy4SNaaVwJ6RIJADnvrcqdHbINlRct0zy1tKe8BGZWL4Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T14:49:33.990576Z"},"content_sha256":"34c9fd3d692ffb10f62b84dc3909072c603075c14ea67b7327078dc6869aa389","schema_version":"1.0","event_id":"sha256:34c9fd3d692ffb10f62b84dc3909072c603075c14ea67b7327078dc6869aa389"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HKH3D7CCPNPMK2RPNF4RZGMOZF/bundle.json","state_url":"https://pith.science/pith/HKH3D7CCPNPMK2RPNF4RZGMOZF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HKH3D7CCPNPMK2RPNF4RZGMOZF/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":"2026-05-26T14:49:33Z","links":{"resolver":"https://pith.science/pith/HKH3D7CCPNPMK2RPNF4RZGMOZF","bundle":"https://pith.science/pith/HKH3D7CCPNPMK2RPNF4RZGMOZF/bundle.json","state":"https://pith.science/pith/HKH3D7CCPNPMK2RPNF4RZGMOZF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HKH3D7CCPNPMK2RPNF4RZGMOZF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:HKH3D7CCPNPMK2RPNF4RZGMOZF","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":"747593889aa0ec648eb07c804e54903cb30962955770dfd89e665a9dd31e0a67","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-05-14T14:29:16Z","title_canon_sha256":"185f0df2f5c98e7dc4215b58f1302008fb739d2425f04c9bcf103fb94ede66de"},"schema_version":"1.0","source":{"id":"1905.05639","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.05639","created_at":"2026-05-17T23:46:13Z"},{"alias_kind":"arxiv_version","alias_value":"1905.05639v1","created_at":"2026-05-17T23:46:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.05639","created_at":"2026-05-17T23:46:13Z"},{"alias_kind":"pith_short_12","alias_value":"HKH3D7CCPNPM","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"HKH3D7CCPNPMK2RP","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"HKH3D7CC","created_at":"2026-05-18T12:33:18Z"}],"graph_snapshots":[{"event_id":"sha256:34c9fd3d692ffb10f62b84dc3909072c603075c14ea67b7327078dc6869aa389","target":"graph","created_at":"2026-05-17T23:46:13Z","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":"Existing methods for robust multigroup multicast beamforming obtain feasible points using semidefinite relaxation (SDR) and Gaussian randomization, and have high computational complexity. In this letter, we consider the robust multigroup multicast beamforming design to minimize the sum power (SP) or per-antenna power (PAP) under the signal-to-interference-plus-noise ratio (SINR) constraints and to maximize the worst-case SINR under the SP constraint or PAP constraints, respectively. The resulting optimization problems are challenging non-convex problems with infinitely many constraints. For ea","authors_text":"Feng Yang, Guangda Zang, Hei Victor Cheng, Hui Liu, Lianghui Ding, Wei Liu, Ying Cui","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-05-14T14:29:16Z","title":"Low Complexity Algorithms for Robust Multigroup Multicast Beamforming"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.05639","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:d400c3e3493c132bc0a30dd4c1d44d57a4e5a136c87dc0a628c97d97fa80ecc8","target":"record","created_at":"2026-05-17T23:46:13Z","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":"747593889aa0ec648eb07c804e54903cb30962955770dfd89e665a9dd31e0a67","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-05-14T14:29:16Z","title_canon_sha256":"185f0df2f5c98e7dc4215b58f1302008fb739d2425f04c9bcf103fb94ede66de"},"schema_version":"1.0","source":{"id":"1905.05639","kind":"arxiv","version":1}},"canonical_sha256":"3a8fb1fc427b5ec56a2f69791c998ec96c1f235f99a5d1dd74ee0746592cf58c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3a8fb1fc427b5ec56a2f69791c998ec96c1f235f99a5d1dd74ee0746592cf58c","first_computed_at":"2026-05-17T23:46:13.971574Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:13.971574Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iLwSDmGSUW0LTQrT9X9wnJAvauvizNzlG8h4SM6R7JXVeOh75Yt4L5ywPWKV3L5KGdJSVjxl5xGi1KMv4DhqAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:13.972185Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.05639","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d400c3e3493c132bc0a30dd4c1d44d57a4e5a136c87dc0a628c97d97fa80ecc8","sha256:34c9fd3d692ffb10f62b84dc3909072c603075c14ea67b7327078dc6869aa389"],"state_sha256":"18b71b925672c2cb3b65ae9b87109b3bfa0adb327f3eed723d4055250ebc96da"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LocJwsuWDeBomzeh3k3l58w3tDMLsNb1uVSfrCsOrzZqhgD7Rd9RZeHdkd8pDUaOrPfaEQgbcH7tyA6sHtB5BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T14:49:33.993591Z","bundle_sha256":"ca077098ee5ba1fd5662f55915a800330495b8ca1773f1f19a39b09abd39a2b2"}}