{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:FEQ4EHLWNIDIPIC5LE2CVRIHDI","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":"488d49d43cc1225b344d78ecd28336f871d8480387b6e7876a446ad739b95786","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-02-21T00:20:34Z","title_canon_sha256":"d2984ab820271fbecb6ec9746cee783aa48af354e4574f06ede8191b6fc93785"},"schema_version":"1.0","source":{"id":"1002.3943","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.3943","created_at":"2026-05-18T02:24:38Z"},{"alias_kind":"arxiv_version","alias_value":"1002.3943v4","created_at":"2026-05-18T02:24:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.3943","created_at":"2026-05-18T02:24:38Z"},{"alias_kind":"pith_short_12","alias_value":"FEQ4EHLWNIDI","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"FEQ4EHLWNIDIPIC5","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"FEQ4EHLW","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:47608f2fd11e7e176aa1d475bae2b420a1fd291e8fac8530a1d82509f929ea9e","target":"graph","created_at":"2026-05-18T02:24:38Z","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 paper, we analyze the signal-to-interference-plus-noise ratio (SINR) performance at a mobile station (MS) in a random cellular network. The cellular network is formed by base-stations (BSs) placed in a one, two or three dimensional space according to a possibly non-homogeneous Poisson point process, which is a generalization of the so-called shotgun cellular system. We develop a sequence of equivalence relations for the SCSs and use them to derive semi-analytical expressions for the coverage probability at the MS when the transmissions from each BS may be affected by random fading with","authors_text":"Juan G. Restrepo, Kenneth R. Baker, Prasanna Madhusudhanan, Timothy X Brown, Youjian Liu","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-02-21T00:20:34Z","title":"Downlink Performance Analysis for a Generalized Shotgun Cellular System"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.3943","kind":"arxiv","version":4},"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":"sha256:1c7505f3c4e94f6cf80b3597796e1139f92b4906fae919b18ad2dc2ff237af10","target":"record","created_at":"2026-05-18T02:24:38Z","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":"488d49d43cc1225b344d78ecd28336f871d8480387b6e7876a446ad739b95786","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-02-21T00:20:34Z","title_canon_sha256":"d2984ab820271fbecb6ec9746cee783aa48af354e4574f06ede8191b6fc93785"},"schema_version":"1.0","source":{"id":"1002.3943","kind":"arxiv","version":4}},"canonical_sha256":"2921c21d766a0687a05d59342ac5071a139b6d4ec8477053f80f6d4b8f7cbdeb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2921c21d766a0687a05d59342ac5071a139b6d4ec8477053f80f6d4b8f7cbdeb","first_computed_at":"2026-05-18T02:24:38.693933Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:24:38.693933Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"34nApdpzfwOXNYNa9j4ALD9JjDfS/Bgon7gOfTb1pngY0O4YdRuDKdnBYrl9nmDnsPC+pIDVqxZoiUFzp3efCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:24:38.694472Z","signed_message":"canonical_sha256_bytes"},"source_id":"1002.3943","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1c7505f3c4e94f6cf80b3597796e1139f92b4906fae919b18ad2dc2ff237af10","sha256:47608f2fd11e7e176aa1d475bae2b420a1fd291e8fac8530a1d82509f929ea9e"],"state_sha256":"04a8f2bacb805616d6e033c0d2e9d20dfb3b799ed88ee2e6be256b02f0fd4213"}