{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:5P2M4HZMEAUATZ4GBQN77APNRR","short_pith_number":"pith:5P2M4HZM","schema_version":"1.0","canonical_sha256":"ebf4ce1f2c202809e7860c1bff81ed8c7e50eb79e13ba269df4d90e8e0b88951","source":{"kind":"arxiv","id":"1709.07129","version":1},"attestation_state":"computed","paper":{"title":"Hypergraph Theory: Applications in 5G Heterogeneous Ultra-Dense Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Geoffrey Ye Li, Hongliang Zhang, Lingyang Song, Yonghui Li","submitted_at":"2017-09-21T02:07:36Z","abstract_excerpt":"Heterogeneous ultra-dense network (HUDN) can significantly increase the spectral efficiency of cellular networks and cater for the explosive growth of data traffic in the fifth-generation (5G) communications. Due to the dense deployment of small cells (SCs), interference among neighboring cells becomes severe. As a result, the effective resource allocation and user association algorithms are essential to minimize inter-cell interference and optimize network performance. However, optimizing network resources in HUDN is extremely complicated as resource allocation and user association are couple"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1709.07129","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-09-21T02:07:36Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"4baf5649898bc01982ab5c86f946da14fcecbd53b3b73c50c3b8207a469836d8","abstract_canon_sha256":"81cc666625e1e3552fbdd12d964e7783ac1a9b4ae5f2ae09915c577b7e1ab9eb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:36.508267Z","signature_b64":"NXdcsdS76YD12lTZraerhH/GxJiM3kEyP9YVMyl5DFx3xcjJLiJWzAgD8Lv8Bc/bPrAndSHLGfu6IsBooEfLCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ebf4ce1f2c202809e7860c1bff81ed8c7e50eb79e13ba269df4d90e8e0b88951","last_reissued_at":"2026-05-18T00:34:36.507804Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:36.507804Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hypergraph Theory: Applications in 5G Heterogeneous Ultra-Dense Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Geoffrey Ye Li, Hongliang Zhang, Lingyang Song, Yonghui Li","submitted_at":"2017-09-21T02:07:36Z","abstract_excerpt":"Heterogeneous ultra-dense network (HUDN) can significantly increase the spectral efficiency of cellular networks and cater for the explosive growth of data traffic in the fifth-generation (5G) communications. Due to the dense deployment of small cells (SCs), interference among neighboring cells becomes severe. As a result, the effective resource allocation and user association algorithms are essential to minimize inter-cell interference and optimize network performance. However, optimizing network resources in HUDN is extremely complicated as resource allocation and user association are couple"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.07129","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1709.07129","created_at":"2026-05-18T00:34:36.507889+00:00"},{"alias_kind":"arxiv_version","alias_value":"1709.07129v1","created_at":"2026-05-18T00:34:36.507889+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.07129","created_at":"2026-05-18T00:34:36.507889+00:00"},{"alias_kind":"pith_short_12","alias_value":"5P2M4HZMEAUA","created_at":"2026-05-18T12:31:00.734936+00:00"},{"alias_kind":"pith_short_16","alias_value":"5P2M4HZMEAUATZ4G","created_at":"2026-05-18T12:31:00.734936+00:00"},{"alias_kind":"pith_short_8","alias_value":"5P2M4HZM","created_at":"2026-05-18T12:31:00.734936+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/5P2M4HZMEAUATZ4GBQN77APNRR","json":"https://pith.science/pith/5P2M4HZMEAUATZ4GBQN77APNRR.json","graph_json":"https://pith.science/api/pith-number/5P2M4HZMEAUATZ4GBQN77APNRR/graph.json","events_json":"https://pith.science/api/pith-number/5P2M4HZMEAUATZ4GBQN77APNRR/events.json","paper":"https://pith.science/paper/5P2M4HZM"},"agent_actions":{"view_html":"https://pith.science/pith/5P2M4HZMEAUATZ4GBQN77APNRR","download_json":"https://pith.science/pith/5P2M4HZMEAUATZ4GBQN77APNRR.json","view_paper":"https://pith.science/paper/5P2M4HZM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1709.07129&json=true","fetch_graph":"https://pith.science/api/pith-number/5P2M4HZMEAUATZ4GBQN77APNRR/graph.json","fetch_events":"https://pith.science/api/pith-number/5P2M4HZMEAUATZ4GBQN77APNRR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5P2M4HZMEAUATZ4GBQN77APNRR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5P2M4HZMEAUATZ4GBQN77APNRR/action/storage_attestation","attest_author":"https://pith.science/pith/5P2M4HZMEAUATZ4GBQN77APNRR/action/author_attestation","sign_citation":"https://pith.science/pith/5P2M4HZMEAUATZ4GBQN77APNRR/action/citation_signature","submit_replication":"https://pith.science/pith/5P2M4HZMEAUATZ4GBQN77APNRR/action/replication_record"}},"created_at":"2026-05-18T00:34:36.507889+00:00","updated_at":"2026-05-18T00:34:36.507889+00:00"}