{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:3QNOPYYGBQZERUKNFHI3B43NCC","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":"4138f0ae88c6faaf1faeb627b0fb47ba4717bd44fa319254a56a070dd5d62853","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-03-01T02:55:39Z","title_canon_sha256":"4451ddcd96654974bf4da345c5f497f5cf080656113813c5c3addf4889ac7b08"},"schema_version":"1.0","source":{"id":"1803.00182","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.00182","created_at":"2026-05-18T00:22:13Z"},{"alias_kind":"arxiv_version","alias_value":"1803.00182v1","created_at":"2026-05-18T00:22:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.00182","created_at":"2026-05-18T00:22:13Z"},{"alias_kind":"pith_short_12","alias_value":"3QNOPYYGBQZE","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"3QNOPYYGBQZERUKN","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"3QNOPYYG","created_at":"2026-05-18T12:32:02Z"}],"graph_snapshots":[{"event_id":"sha256:d93d2306a70e1ab3d4b4a6b73dbabed82e0dc741ca7e29f0d276965f649fc4c4","target":"graph","created_at":"2026-05-18T00:22:13Z","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":"Heterogeneous cellular networks (HCNs) constitute a necessary step in the evolution of cellular networks. In this paper, we apply the signal-to-interference ratio (SIR) meta distribution framework for a refined SIR performance analysis of HCNs, focusing on K-tier heterogeneous cellular networks based on the homogeneous independent Poisson point process (HIP) model, with range expansion bias (offloading bias) in each tier. Expressions for the b-th moment of the conditional success probability for both the entire network and each tier are derived, based on which the exact meta distributions and ","authors_text":"Martin Haenggi, Yuanjie Wang, Zhenhui Tan","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-03-01T02:55:39Z","title":"SIR Meta Distribution of K-Tier Downlink Heterogeneous Cellular Networks with Cell Range Expansion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.00182","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:ec1aa740419ba4b43af642fdecc386b3ade56478738a866382899c88754a16f0","target":"record","created_at":"2026-05-18T00:22:13Z","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":"4138f0ae88c6faaf1faeb627b0fb47ba4717bd44fa319254a56a070dd5d62853","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-03-01T02:55:39Z","title_canon_sha256":"4451ddcd96654974bf4da345c5f497f5cf080656113813c5c3addf4889ac7b08"},"schema_version":"1.0","source":{"id":"1803.00182","kind":"arxiv","version":1}},"canonical_sha256":"dc1ae7e3060c3248d14d29d1b0f36d1097cac7dd5a43c57d469094ee02c22df9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dc1ae7e3060c3248d14d29d1b0f36d1097cac7dd5a43c57d469094ee02c22df9","first_computed_at":"2026-05-18T00:22:13.108843Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:13.108843Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LDFMwSNypP4uWKMscsBCtx9cM8wdlegYTsd7u36CY4NtzbEoQOuqWuLWF+C5Ptt15+c4wduknX9NO4PJhM67DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:13.109421Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.00182","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ec1aa740419ba4b43af642fdecc386b3ade56478738a866382899c88754a16f0","sha256:d93d2306a70e1ab3d4b4a6b73dbabed82e0dc741ca7e29f0d276965f649fc4c4"],"state_sha256":"171cbddc964557f27c82913fadd4c5c9d46cebbb2126ff34a1ca1b71a768f810"}