{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:RC2QY62DBOQYDR7M4TSMKAJGPH","short_pith_number":"pith:RC2QY62D","canonical_record":{"source":{"id":"1301.0178","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-01-02T07:08:32Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"683b7058a49e2c24f0bd99db833bee372e9282dd004f02dda4edc06760164005","abstract_canon_sha256":"e02169b8b21e8de3a597517b95eca6fd0ac2579cb92ceec1bdd573dbcf2cc058"},"schema_version":"1.0"},"canonical_sha256":"88b50c7b430ba181c7ece4e4c5012679d19232755111282f5bc3b3a886bf4b3b","source":{"kind":"arxiv","id":"1301.0178","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.0178","created_at":"2026-05-18T03:10:11Z"},{"alias_kind":"arxiv_version","alias_value":"1301.0178v1","created_at":"2026-05-18T03:10:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.0178","created_at":"2026-05-18T03:10:11Z"},{"alias_kind":"pith_short_12","alias_value":"RC2QY62DBOQY","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"RC2QY62DBOQYDR7M","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"RC2QY62D","created_at":"2026-05-18T12:27:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:RC2QY62DBOQYDR7M4TSMKAJGPH","target":"record","payload":{"canonical_record":{"source":{"id":"1301.0178","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-01-02T07:08:32Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"683b7058a49e2c24f0bd99db833bee372e9282dd004f02dda4edc06760164005","abstract_canon_sha256":"e02169b8b21e8de3a597517b95eca6fd0ac2579cb92ceec1bdd573dbcf2cc058"},"schema_version":"1.0"},"canonical_sha256":"88b50c7b430ba181c7ece4e4c5012679d19232755111282f5bc3b3a886bf4b3b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:10:11.974820Z","signature_b64":"wssExNHZ2yp9orzN3Ck0U7ZYHR0hdc5RzAMgUyXE3e0jyOWG1i0PVvF1Bgr4LMB4u/dzazlC8gOymAMBUpiFCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"88b50c7b430ba181c7ece4e4c5012679d19232755111282f5bc3b3a886bf4b3b","last_reissued_at":"2026-05-18T03:10:11.974225Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:10:11.974225Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.0178","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":"2026-05-18T03:10:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v2ALYr48kApTRATev7TcpsRdJfYVcmKhsj5jlEs9f/JF3eZpuH0bGq+nRn+bNYK6yJWxriQ0E7OyFV2CeqzbAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T16:45:24.769806Z"},"content_sha256":"a13c10c3d83b5a41873028387467121b71e3eda9a9ead12c4ade5d418228f65c","schema_version":"1.0","event_id":"sha256:a13c10c3d83b5a41873028387467121b71e3eda9a9ead12c4ade5d418228f65c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:RC2QY62DBOQYDR7M4TSMKAJGPH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Efficient Solutions for Weighted Sum Rate Maximization in Multicellular Networks With Channel Uncertainties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Antti T\\\"olli, Le-Nam Tran, Markku Juntti, Muhammad Fainan Hanif, Savo Glisic","submitted_at":"2013-01-02T07:08:32Z","abstract_excerpt":"The important problem of weighted sum rate maximization (WSRM) in a multicellular environment is intrinsically sensitive to channel estimation errors. In this paper, we study ways to maximize the weighted sum rate in a linearly precoded multicellular downlink system where the receivers are equipped with a single antenna. With perfect channel information available at the base stations, we first present a novel fast converging algorithm that solves the WSRM problem. Then, the assumption is relaxed to the case where the error vectors in the channel estimates are assumed to lie in an uncertainty s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.0178","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":"2026-05-18T03:10:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F5cRCCi5Wg4ghMlTY9lkOnRnqx9sM4NBFo8xGeeIFgmXIBT5lNyPJAQkwnwBwKHQxUJgf/RNV7vscvy0DER/Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T16:45:24.770145Z"},"content_sha256":"08c389af7629f7fba905bd9db6d950c88639ab29409868dfd51d2c55e493a6cd","schema_version":"1.0","event_id":"sha256:08c389af7629f7fba905bd9db6d950c88639ab29409868dfd51d2c55e493a6cd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RC2QY62DBOQYDR7M4TSMKAJGPH/bundle.json","state_url":"https://pith.science/pith/RC2QY62DBOQYDR7M4TSMKAJGPH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RC2QY62DBOQYDR7M4TSMKAJGPH/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":"2026-06-28T16:45:24Z","links":{"resolver":"https://pith.science/pith/RC2QY62DBOQYDR7M4TSMKAJGPH","bundle":"https://pith.science/pith/RC2QY62DBOQYDR7M4TSMKAJGPH/bundle.json","state":"https://pith.science/pith/RC2QY62DBOQYDR7M4TSMKAJGPH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RC2QY62DBOQYDR7M4TSMKAJGPH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:RC2QY62DBOQYDR7M4TSMKAJGPH","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":"e02169b8b21e8de3a597517b95eca6fd0ac2579cb92ceec1bdd573dbcf2cc058","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-01-02T07:08:32Z","title_canon_sha256":"683b7058a49e2c24f0bd99db833bee372e9282dd004f02dda4edc06760164005"},"schema_version":"1.0","source":{"id":"1301.0178","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.0178","created_at":"2026-05-18T03:10:11Z"},{"alias_kind":"arxiv_version","alias_value":"1301.0178v1","created_at":"2026-05-18T03:10:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.0178","created_at":"2026-05-18T03:10:11Z"},{"alias_kind":"pith_short_12","alias_value":"RC2QY62DBOQY","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"RC2QY62DBOQYDR7M","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"RC2QY62D","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:08c389af7629f7fba905bd9db6d950c88639ab29409868dfd51d2c55e493a6cd","target":"graph","created_at":"2026-05-18T03:10:11Z","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":"The important problem of weighted sum rate maximization (WSRM) in a multicellular environment is intrinsically sensitive to channel estimation errors. In this paper, we study ways to maximize the weighted sum rate in a linearly precoded multicellular downlink system where the receivers are equipped with a single antenna. With perfect channel information available at the base stations, we first present a novel fast converging algorithm that solves the WSRM problem. Then, the assumption is relaxed to the case where the error vectors in the channel estimates are assumed to lie in an uncertainty s","authors_text":"Antti T\\\"olli, Le-Nam Tran, Markku Juntti, Muhammad Fainan Hanif, Savo Glisic","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-01-02T07:08:32Z","title":"Efficient Solutions for Weighted Sum Rate Maximization in Multicellular Networks With Channel Uncertainties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.0178","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:a13c10c3d83b5a41873028387467121b71e3eda9a9ead12c4ade5d418228f65c","target":"record","created_at":"2026-05-18T03:10:11Z","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":"e02169b8b21e8de3a597517b95eca6fd0ac2579cb92ceec1bdd573dbcf2cc058","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-01-02T07:08:32Z","title_canon_sha256":"683b7058a49e2c24f0bd99db833bee372e9282dd004f02dda4edc06760164005"},"schema_version":"1.0","source":{"id":"1301.0178","kind":"arxiv","version":1}},"canonical_sha256":"88b50c7b430ba181c7ece4e4c5012679d19232755111282f5bc3b3a886bf4b3b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"88b50c7b430ba181c7ece4e4c5012679d19232755111282f5bc3b3a886bf4b3b","first_computed_at":"2026-05-18T03:10:11.974225Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:10:11.974225Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wssExNHZ2yp9orzN3Ck0U7ZYHR0hdc5RzAMgUyXE3e0jyOWG1i0PVvF1Bgr4LMB4u/dzazlC8gOymAMBUpiFCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:10:11.974820Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.0178","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a13c10c3d83b5a41873028387467121b71e3eda9a9ead12c4ade5d418228f65c","sha256:08c389af7629f7fba905bd9db6d950c88639ab29409868dfd51d2c55e493a6cd"],"state_sha256":"70f544d93e9609273068e12109900d16388f05dfa4b04a42cb2399a9c35944a1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3JeHGuy9UiKLNQt+TNj7eUdfeHHe1jw2iN368XJ+CPzNSCExU931lLE2I0OLyE9aAuvlx7nFKrGMb40QKoAQDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T16:45:24.772058Z","bundle_sha256":"6d0cff2e0a1ef7d989907651b2a7737f0538e5f62b29814c405510418df8e15e"}}