{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:BIAT3HJA7664AJDUMCCLNMNWJ3","short_pith_number":"pith:BIAT3HJA","canonical_record":{"source":{"id":"1604.03183","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-04-12T00:23:36Z","cross_cats_sorted":["cs.NI","math.IT"],"title_canon_sha256":"a0a7ea86ba2edcfb507e990f4904a9aa998b67b11c973d4c7109381fe1746202","abstract_canon_sha256":"f8e55c75272347f80043ff054c6e2cdbdd1f47d3b0afb090adbdd5f7c1074317"},"schema_version":"1.0"},"canonical_sha256":"0a013d9d20ffbdc024746084b6b1b64eca693b1cc12d357077deebef89370847","source":{"kind":"arxiv","id":"1604.03183","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.03183","created_at":"2026-05-18T01:03:07Z"},{"alias_kind":"arxiv_version","alias_value":"1604.03183v2","created_at":"2026-05-18T01:03:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.03183","created_at":"2026-05-18T01:03:07Z"},{"alias_kind":"pith_short_12","alias_value":"BIAT3HJA7664","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"BIAT3HJA7664AJDU","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"BIAT3HJA","created_at":"2026-05-18T12:30:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:BIAT3HJA7664AJDUMCCLNMNWJ3","target":"record","payload":{"canonical_record":{"source":{"id":"1604.03183","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-04-12T00:23:36Z","cross_cats_sorted":["cs.NI","math.IT"],"title_canon_sha256":"a0a7ea86ba2edcfb507e990f4904a9aa998b67b11c973d4c7109381fe1746202","abstract_canon_sha256":"f8e55c75272347f80043ff054c6e2cdbdd1f47d3b0afb090adbdd5f7c1074317"},"schema_version":"1.0"},"canonical_sha256":"0a013d9d20ffbdc024746084b6b1b64eca693b1cc12d357077deebef89370847","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:07.362893Z","signature_b64":"HhQ9OmpJ6LTiGaE9wVUGylsNjJl4l8drY965gcPTz4DQsbxC0hx2/QZ0W/EgsEM5Rjb6q9rXWG6Tsla/+IsIDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0a013d9d20ffbdc024746084b6b1b64eca693b1cc12d357077deebef89370847","last_reissued_at":"2026-05-18T01:03:07.362484Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:07.362484Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.03183","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:03:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f8Ldxuypq9nRSqk0bGUDmCjlMkQXfIsd9SQoh0P2x6Hl0Qpftd8oYHtTDkS2L4SZHUjklKx3ZaoC9klH3zkRBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T03:11:15.093019Z"},"content_sha256":"9e343e95046054f4321b4dba838f9369aee92f94b58d18e9be0178670dc422f2","schema_version":"1.0","event_id":"sha256:9e343e95046054f4321b4dba838f9369aee92f94b58d18e9be0178670dc422f2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:BIAT3HJA7664AJDUMCCLNMNWJ3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Primer on Cellular Network Analysis Using Stochastic Geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NI","math.IT"],"primary_cat":"cs.IT","authors_text":"Abhishek K. Gupta, Harpreet S. Dhillon, Jeffrey G. Andrews","submitted_at":"2016-04-12T00:23:36Z","abstract_excerpt":"This tutorial is intended as an accessible but rigorous first reference for someone interested in learning how to model and analyze cellular network performance using stochastic geometry. In particular, we focus on computing the signal-to-interference-plus-noise ratio (SINR) distribution, which can be characterized by the coverage probability (the SINR CCDF) or the outage probability (its CDF). We model base stations (BSs) in the network as a realization of a homogeneous Poisson point process of density $\\lambda$, and compute the SINR for three main cases: the downlink, uplink, and finally the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.03183","kind":"arxiv","version":2},"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":"2026-05-18T01:03:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cFnaMouPhvBII1f9+IvP5xOvY5maJDF1uHT2ENM3NJoCUQcYDhedXfbb/pSz8De2/VQol6O8Yc+gBJ9u/aGNBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T03:11:15.093414Z"},"content_sha256":"f0210299275f518fb78f5a911bf5fdfbc8851a5cf0752a0a48002ea083bdebd7","schema_version":"1.0","event_id":"sha256:f0210299275f518fb78f5a911bf5fdfbc8851a5cf0752a0a48002ea083bdebd7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BIAT3HJA7664AJDUMCCLNMNWJ3/bundle.json","state_url":"https://pith.science/pith/BIAT3HJA7664AJDUMCCLNMNWJ3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BIAT3HJA7664AJDUMCCLNMNWJ3/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":"2026-06-01T03:11:15Z","links":{"resolver":"https://pith.science/pith/BIAT3HJA7664AJDUMCCLNMNWJ3","bundle":"https://pith.science/pith/BIAT3HJA7664AJDUMCCLNMNWJ3/bundle.json","state":"https://pith.science/pith/BIAT3HJA7664AJDUMCCLNMNWJ3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BIAT3HJA7664AJDUMCCLNMNWJ3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:BIAT3HJA7664AJDUMCCLNMNWJ3","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":"f8e55c75272347f80043ff054c6e2cdbdd1f47d3b0afb090adbdd5f7c1074317","cross_cats_sorted":["cs.NI","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-04-12T00:23:36Z","title_canon_sha256":"a0a7ea86ba2edcfb507e990f4904a9aa998b67b11c973d4c7109381fe1746202"},"schema_version":"1.0","source":{"id":"1604.03183","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.03183","created_at":"2026-05-18T01:03:07Z"},{"alias_kind":"arxiv_version","alias_value":"1604.03183v2","created_at":"2026-05-18T01:03:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.03183","created_at":"2026-05-18T01:03:07Z"},{"alias_kind":"pith_short_12","alias_value":"BIAT3HJA7664","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"BIAT3HJA7664AJDU","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"BIAT3HJA","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:f0210299275f518fb78f5a911bf5fdfbc8851a5cf0752a0a48002ea083bdebd7","target":"graph","created_at":"2026-05-18T01:03:07Z","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 tutorial is intended as an accessible but rigorous first reference for someone interested in learning how to model and analyze cellular network performance using stochastic geometry. In particular, we focus on computing the signal-to-interference-plus-noise ratio (SINR) distribution, which can be characterized by the coverage probability (the SINR CCDF) or the outage probability (its CDF). We model base stations (BSs) in the network as a realization of a homogeneous Poisson point process of density $\\lambda$, and compute the SINR for three main cases: the downlink, uplink, and finally the","authors_text":"Abhishek K. Gupta, Harpreet S. Dhillon, Jeffrey G. Andrews","cross_cats":["cs.NI","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-04-12T00:23:36Z","title":"A Primer on Cellular Network Analysis Using Stochastic Geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.03183","kind":"arxiv","version":2},"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":"sha256:9e343e95046054f4321b4dba838f9369aee92f94b58d18e9be0178670dc422f2","target":"record","created_at":"2026-05-18T01:03:07Z","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":"f8e55c75272347f80043ff054c6e2cdbdd1f47d3b0afb090adbdd5f7c1074317","cross_cats_sorted":["cs.NI","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-04-12T00:23:36Z","title_canon_sha256":"a0a7ea86ba2edcfb507e990f4904a9aa998b67b11c973d4c7109381fe1746202"},"schema_version":"1.0","source":{"id":"1604.03183","kind":"arxiv","version":2}},"canonical_sha256":"0a013d9d20ffbdc024746084b6b1b64eca693b1cc12d357077deebef89370847","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0a013d9d20ffbdc024746084b6b1b64eca693b1cc12d357077deebef89370847","first_computed_at":"2026-05-18T01:03:07.362484Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:07.362484Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HhQ9OmpJ6LTiGaE9wVUGylsNjJl4l8drY965gcPTz4DQsbxC0hx2/QZ0W/EgsEM5Rjb6q9rXWG6Tsla/+IsIDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:07.362893Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.03183","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9e343e95046054f4321b4dba838f9369aee92f94b58d18e9be0178670dc422f2","sha256:f0210299275f518fb78f5a911bf5fdfbc8851a5cf0752a0a48002ea083bdebd7"],"state_sha256":"654861618a38fe119254d674837f3804f75e85035330e981b11168c25fd76a2c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xhOvU/iBpnMUIKAiee9SaiF7oF3PR+xovOQj8iTt+uZ0dr10lAPKdOtWZ3SuZBWfz6Fqpyz1qD1JUolq1k3CDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T03:11:15.096264Z","bundle_sha256":"83719267e4b7a2bd69a98985bac12a63d6fdd9e8f38d003db6cbd16edc7350f4"}}