{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:NBB4V6WKAGFVRH5WOUTJJ3YSQQ","short_pith_number":"pith:NBB4V6WK","canonical_record":{"source":{"id":"1001.3187","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-01-19T03:11:46Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"e1b292484befe8c6a65cdfe55dd29a29f7a87e14b4afdd1c9bedebf1a905787b","abstract_canon_sha256":"1de821f26b06f6244f15560dcf4743a304c2f58fbc21cd096cfa75636f6c182e"},"schema_version":"1.0"},"canonical_sha256":"6843cafaca018b589fb6752694ef12842fb72d74b1dea5d76f14c1d989f0fbfd","source":{"kind":"arxiv","id":"1001.3187","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.3187","created_at":"2026-05-18T00:58:47Z"},{"alias_kind":"arxiv_version","alias_value":"1001.3187v1","created_at":"2026-05-18T00:58:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.3187","created_at":"2026-05-18T00:58:47Z"},{"alias_kind":"pith_short_12","alias_value":"NBB4V6WKAGFV","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"NBB4V6WKAGFVRH5W","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"NBB4V6WK","created_at":"2026-05-18T12:26:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:NBB4V6WKAGFVRH5WOUTJJ3YSQQ","target":"record","payload":{"canonical_record":{"source":{"id":"1001.3187","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-01-19T03:11:46Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"e1b292484befe8c6a65cdfe55dd29a29f7a87e14b4afdd1c9bedebf1a905787b","abstract_canon_sha256":"1de821f26b06f6244f15560dcf4743a304c2f58fbc21cd096cfa75636f6c182e"},"schema_version":"1.0"},"canonical_sha256":"6843cafaca018b589fb6752694ef12842fb72d74b1dea5d76f14c1d989f0fbfd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:58:47.758682Z","signature_b64":"CPeMaVIN3ytVJyNE3A19YmR1ht1oLoxxK99Tn/CuCppUm1bHROzbLt/phYDKXv4+I3koBt4QoEX1TcPgc9TMDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6843cafaca018b589fb6752694ef12842fb72d74b1dea5d76f14c1d989f0fbfd","last_reissued_at":"2026-05-18T00:58:47.758169Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:58:47.758169Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1001.3187","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":"2026-05-18T00:58:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HHG3Hs8Ot9DSREZUheQhXC7YKTDisRAjddP8nBkrRX8FgBB4F1rinQ3oTgFr08L7xgt7TKK20Qw/aYay6/rjCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T09:05:59.147973Z"},"content_sha256":"9357a5ffb6dbeb52d4b75afb580354142cc3909c42283c6f44a49cb73e692d87","schema_version":"1.0","event_id":"sha256:9357a5ffb6dbeb52d4b75afb580354142cc3909c42283c6f44a49cb73e692d87"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:NBB4V6WKAGFVRH5WOUTJJ3YSQQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dynamic Resource Allocation in Cognitive Radio Networks: A Convex Optimization Perspective","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Rui Zhang, Shuguang Cui, Ying-Chang Liang","submitted_at":"2010-01-19T03:11:46Z","abstract_excerpt":"This article provides an overview of the state-of-art results on communication resource allocation over space, time, and frequency for emerging cognitive radio (CR) wireless networks. Focusing on the interference-power/interference-temperature (IT) constraint approach for CRs to protect primary radio transmissions, many new and challenging problems regarding the design of CR systems are formulated, and some of the corresponding solutions are shown to be obtainable by restructuring some classic results known for traditional (non-CR) wireless networks. It is demonstrated that convex optimization"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.3187","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":"2026-05-18T00:58:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rd1JD1p1c9HWIzjvRUVEcJrzZ0AN2lNiDz2Wvi069oRVMcOlBYphxDa/bToj6JvWadcsr9Bpi3qEsHB5215GAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T09:05:59.148338Z"},"content_sha256":"bbfc8b1e69397e444289ac70e6d1a0a4d221a3cfef9af536c9c8026dc4a59abc","schema_version":"1.0","event_id":"sha256:bbfc8b1e69397e444289ac70e6d1a0a4d221a3cfef9af536c9c8026dc4a59abc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NBB4V6WKAGFVRH5WOUTJJ3YSQQ/bundle.json","state_url":"https://pith.science/pith/NBB4V6WKAGFVRH5WOUTJJ3YSQQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NBB4V6WKAGFVRH5WOUTJJ3YSQQ/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":"2026-05-28T09:05:59Z","links":{"resolver":"https://pith.science/pith/NBB4V6WKAGFVRH5WOUTJJ3YSQQ","bundle":"https://pith.science/pith/NBB4V6WKAGFVRH5WOUTJJ3YSQQ/bundle.json","state":"https://pith.science/pith/NBB4V6WKAGFVRH5WOUTJJ3YSQQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NBB4V6WKAGFVRH5WOUTJJ3YSQQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:NBB4V6WKAGFVRH5WOUTJJ3YSQQ","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":"1de821f26b06f6244f15560dcf4743a304c2f58fbc21cd096cfa75636f6c182e","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-01-19T03:11:46Z","title_canon_sha256":"e1b292484befe8c6a65cdfe55dd29a29f7a87e14b4afdd1c9bedebf1a905787b"},"schema_version":"1.0","source":{"id":"1001.3187","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.3187","created_at":"2026-05-18T00:58:47Z"},{"alias_kind":"arxiv_version","alias_value":"1001.3187v1","created_at":"2026-05-18T00:58:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.3187","created_at":"2026-05-18T00:58:47Z"},{"alias_kind":"pith_short_12","alias_value":"NBB4V6WKAGFV","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"NBB4V6WKAGFVRH5W","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"NBB4V6WK","created_at":"2026-05-18T12:26:10Z"}],"graph_snapshots":[{"event_id":"sha256:bbfc8b1e69397e444289ac70e6d1a0a4d221a3cfef9af536c9c8026dc4a59abc","target":"graph","created_at":"2026-05-18T00:58:47Z","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":"This article provides an overview of the state-of-art results on communication resource allocation over space, time, and frequency for emerging cognitive radio (CR) wireless networks. Focusing on the interference-power/interference-temperature (IT) constraint approach for CRs to protect primary radio transmissions, many new and challenging problems regarding the design of CR systems are formulated, and some of the corresponding solutions are shown to be obtainable by restructuring some classic results known for traditional (non-CR) wireless networks. It is demonstrated that convex optimization","authors_text":"Rui Zhang, Shuguang Cui, Ying-Chang Liang","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-01-19T03:11:46Z","title":"Dynamic Resource Allocation in Cognitive Radio Networks: A Convex Optimization Perspective"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.3187","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":"sha256:9357a5ffb6dbeb52d4b75afb580354142cc3909c42283c6f44a49cb73e692d87","target":"record","created_at":"2026-05-18T00:58:47Z","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":"1de821f26b06f6244f15560dcf4743a304c2f58fbc21cd096cfa75636f6c182e","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-01-19T03:11:46Z","title_canon_sha256":"e1b292484befe8c6a65cdfe55dd29a29f7a87e14b4afdd1c9bedebf1a905787b"},"schema_version":"1.0","source":{"id":"1001.3187","kind":"arxiv","version":1}},"canonical_sha256":"6843cafaca018b589fb6752694ef12842fb72d74b1dea5d76f14c1d989f0fbfd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6843cafaca018b589fb6752694ef12842fb72d74b1dea5d76f14c1d989f0fbfd","first_computed_at":"2026-05-18T00:58:47.758169Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:58:47.758169Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CPeMaVIN3ytVJyNE3A19YmR1ht1oLoxxK99Tn/CuCppUm1bHROzbLt/phYDKXv4+I3koBt4QoEX1TcPgc9TMDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:58:47.758682Z","signed_message":"canonical_sha256_bytes"},"source_id":"1001.3187","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9357a5ffb6dbeb52d4b75afb580354142cc3909c42283c6f44a49cb73e692d87","sha256:bbfc8b1e69397e444289ac70e6d1a0a4d221a3cfef9af536c9c8026dc4a59abc"],"state_sha256":"e1e3b76ac50f9b4ab528f1928725cc025c2a0aa49930d56bdbf76dbd11d8d103"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aGfbRRXYJEc23HSLAUi9kxjH0/UZgQqYnt8L0Gn1Y5PnCErDosJpcJ8sZse3owjmChgwWf2s7LWGe9amiT8OBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T09:05:59.150256Z","bundle_sha256":"83a076e9ddc3b51c9b0253c9da805cdd17c19110c7f343e48f0b8a5470ec48fd"}}