{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:SKUCRM7OJLS6EEH2GVCTLXILKG","short_pith_number":"pith:SKUCRM7O","canonical_record":{"source":{"id":"1401.6736","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NI","submitted_at":"2014-01-27T04:32:02Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"dcad26ca1510720bd42abbb7838adb8825e3b6e51e6a05e9968e2e7e97fd48ba","abstract_canon_sha256":"b1a94bee7806849f5b60de46b0d2a9313838d02a7c8d249702aea30041e51782"},"schema_version":"1.0"},"canonical_sha256":"92a828b3ee4ae5e210fa354535dd0b518b9eece3efe2634697fa2eea879653b8","source":{"kind":"arxiv","id":"1401.6736","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.6736","created_at":"2026-05-18T03:01:00Z"},{"alias_kind":"arxiv_version","alias_value":"1401.6736v1","created_at":"2026-05-18T03:01:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.6736","created_at":"2026-05-18T03:01:00Z"},{"alias_kind":"pith_short_12","alias_value":"SKUCRM7OJLS6","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"SKUCRM7OJLS6EEH2","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"SKUCRM7O","created_at":"2026-05-18T12:28:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:SKUCRM7OJLS6EEH2GVCTLXILKG","target":"record","payload":{"canonical_record":{"source":{"id":"1401.6736","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NI","submitted_at":"2014-01-27T04:32:02Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"dcad26ca1510720bd42abbb7838adb8825e3b6e51e6a05e9968e2e7e97fd48ba","abstract_canon_sha256":"b1a94bee7806849f5b60de46b0d2a9313838d02a7c8d249702aea30041e51782"},"schema_version":"1.0"},"canonical_sha256":"92a828b3ee4ae5e210fa354535dd0b518b9eece3efe2634697fa2eea879653b8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:01:00.820037Z","signature_b64":"erKveblnTUt/bgWQSIs/Bk5hgfUSCitjE7yENiChUQ/zpUOoJCebd0FVb4Tiw2cNtAStIOyqdwAbUMcWxWt9CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"92a828b3ee4ae5e210fa354535dd0b518b9eece3efe2634697fa2eea879653b8","last_reissued_at":"2026-05-18T03:01:00.819278Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:01:00.819278Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.6736","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":"2026-05-18T03:01:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N48W0LW8U/6wgk+qIhMEkMbZQl4rl+Ac91FV1Cb+7175gExulKhQmFdtaxawLaDkFPHd+YrYDMhaF9oLvBCQDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T15:54:32.918773Z"},"content_sha256":"43a7e47a3db53e0372d07dca7b3f13ad966e5c6cd8d0cced00c4b72c0e0bf7f4","schema_version":"1.0","event_id":"sha256:43a7e47a3db53e0372d07dca7b3f13ad966e5c6cd8d0cced00c4b72c0e0bf7f4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:SKUCRM7OJLS6EEH2GVCTLXILKG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multi-Channel Cognitive Radio Networks: Modeling, Analysis and Synthesis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"cs.NI","authors_text":"Navid Tadayon, Sonia Aissa","submitted_at":"2014-01-27T04:32:02Z","abstract_excerpt":"In this contribution, we establish a model for multichannel cognitive radio networks (CRNs) using the theory of priority queues. This model enables us to conduct a performance analysis in the most general form by the derivation of the probability mass function (PMF) of queue length at the secondary users (SUs). In the second part, a reverse problem is considered to answer the important top-down question of whether a service requirement can be satisfied in a multi-channel CRN knowing the network parameters and traffic situation with respect to the SUs and the primary users (PUs). Terming this p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.6736","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":"2026-05-18T03:01:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6Nxag9BIAzCr3SeGLmU3zrW7mowORgIEfwS64Xp/xd7a3z+J0fuBFA6fMQtTA8KtvoCI880Fhd+6bI9F3twnDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T15:54:32.919124Z"},"content_sha256":"c743fc0354e22981df7cf59f39fd5d9316762f497da3110e191d1050bd44ffc9","schema_version":"1.0","event_id":"sha256:c743fc0354e22981df7cf59f39fd5d9316762f497da3110e191d1050bd44ffc9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SKUCRM7OJLS6EEH2GVCTLXILKG/bundle.json","state_url":"https://pith.science/pith/SKUCRM7OJLS6EEH2GVCTLXILKG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SKUCRM7OJLS6EEH2GVCTLXILKG/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":"2026-06-26T15:54:32Z","links":{"resolver":"https://pith.science/pith/SKUCRM7OJLS6EEH2GVCTLXILKG","bundle":"https://pith.science/pith/SKUCRM7OJLS6EEH2GVCTLXILKG/bundle.json","state":"https://pith.science/pith/SKUCRM7OJLS6EEH2GVCTLXILKG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SKUCRM7OJLS6EEH2GVCTLXILKG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:SKUCRM7OJLS6EEH2GVCTLXILKG","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":"b1a94bee7806849f5b60de46b0d2a9313838d02a7c8d249702aea30041e51782","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NI","submitted_at":"2014-01-27T04:32:02Z","title_canon_sha256":"dcad26ca1510720bd42abbb7838adb8825e3b6e51e6a05e9968e2e7e97fd48ba"},"schema_version":"1.0","source":{"id":"1401.6736","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.6736","created_at":"2026-05-18T03:01:00Z"},{"alias_kind":"arxiv_version","alias_value":"1401.6736v1","created_at":"2026-05-18T03:01:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.6736","created_at":"2026-05-18T03:01:00Z"},{"alias_kind":"pith_short_12","alias_value":"SKUCRM7OJLS6","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"SKUCRM7OJLS6EEH2","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"SKUCRM7O","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:c743fc0354e22981df7cf59f39fd5d9316762f497da3110e191d1050bd44ffc9","target":"graph","created_at":"2026-05-18T03:01:00Z","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 contribution, we establish a model for multichannel cognitive radio networks (CRNs) using the theory of priority queues. This model enables us to conduct a performance analysis in the most general form by the derivation of the probability mass function (PMF) of queue length at the secondary users (SUs). In the second part, a reverse problem is considered to answer the important top-down question of whether a service requirement can be satisfied in a multi-channel CRN knowing the network parameters and traffic situation with respect to the SUs and the primary users (PUs). Terming this p","authors_text":"Navid Tadayon, Sonia Aissa","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NI","submitted_at":"2014-01-27T04:32:02Z","title":"Multi-Channel Cognitive Radio Networks: Modeling, Analysis and Synthesis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.6736","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":"sha256:43a7e47a3db53e0372d07dca7b3f13ad966e5c6cd8d0cced00c4b72c0e0bf7f4","target":"record","created_at":"2026-05-18T03:01:00Z","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":"b1a94bee7806849f5b60de46b0d2a9313838d02a7c8d249702aea30041e51782","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NI","submitted_at":"2014-01-27T04:32:02Z","title_canon_sha256":"dcad26ca1510720bd42abbb7838adb8825e3b6e51e6a05e9968e2e7e97fd48ba"},"schema_version":"1.0","source":{"id":"1401.6736","kind":"arxiv","version":1}},"canonical_sha256":"92a828b3ee4ae5e210fa354535dd0b518b9eece3efe2634697fa2eea879653b8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"92a828b3ee4ae5e210fa354535dd0b518b9eece3efe2634697fa2eea879653b8","first_computed_at":"2026-05-18T03:01:00.819278Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:01:00.819278Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"erKveblnTUt/bgWQSIs/Bk5hgfUSCitjE7yENiChUQ/zpUOoJCebd0FVb4Tiw2cNtAStIOyqdwAbUMcWxWt9CA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:01:00.820037Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.6736","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:43a7e47a3db53e0372d07dca7b3f13ad966e5c6cd8d0cced00c4b72c0e0bf7f4","sha256:c743fc0354e22981df7cf59f39fd5d9316762f497da3110e191d1050bd44ffc9"],"state_sha256":"2dbba22a00c203f46e114e0b49d537ee83714cf8d8ef9cc47785cab25d27eab8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3sSWrHaZgrobO8BKKFjd2HDQEfiPSjkeiyi6lYfCjIlImdjZebhdQ49EH8lanyFzFApUfjP3u1MFtEYv3pQUAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T15:54:32.921078Z","bundle_sha256":"7d5e0b783a1f4814db4b82ffe39669f1f8adef3de6b532edd2958ebbabd8ab34"}}