{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:GSR57A66TYHDX4SSJMU5N7EOT2","short_pith_number":"pith:GSR57A66","canonical_record":{"source":{"id":"1604.04457","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-04-15T12:18:43Z","cross_cats_sorted":["cs.NI","math.IT"],"title_canon_sha256":"f5768b1d94f845aebbf9f4d2a4169ad22daef97f1710aefc3edabf565a70ebe1","abstract_canon_sha256":"1f99e99f88fbc28a61180ad1bef6b80da8298d4401b60a4bb87dc8951a34f229"},"schema_version":"1.0"},"canonical_sha256":"34a3df83de9e0e3bf2524b29d6fc8e9eb6ba093c0d660a14cc623f0a7f86f085","source":{"kind":"arxiv","id":"1604.04457","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.04457","created_at":"2026-05-18T01:17:02Z"},{"alias_kind":"arxiv_version","alias_value":"1604.04457v1","created_at":"2026-05-18T01:17:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.04457","created_at":"2026-05-18T01:17:02Z"},{"alias_kind":"pith_short_12","alias_value":"GSR57A66TYHD","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GSR57A66TYHDX4SS","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GSR57A66","created_at":"2026-05-18T12:30:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:GSR57A66TYHDX4SSJMU5N7EOT2","target":"record","payload":{"canonical_record":{"source":{"id":"1604.04457","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-04-15T12:18:43Z","cross_cats_sorted":["cs.NI","math.IT"],"title_canon_sha256":"f5768b1d94f845aebbf9f4d2a4169ad22daef97f1710aefc3edabf565a70ebe1","abstract_canon_sha256":"1f99e99f88fbc28a61180ad1bef6b80da8298d4401b60a4bb87dc8951a34f229"},"schema_version":"1.0"},"canonical_sha256":"34a3df83de9e0e3bf2524b29d6fc8e9eb6ba093c0d660a14cc623f0a7f86f085","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:02.159698Z","signature_b64":"6rWZTr8chdcnZjVjL4eTI6WCJOm5qGTaMub+3SdkRArZQ6s2ed4ePYdde99qhMvniSUDG+dVVcJWCDKkcsMLCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"34a3df83de9e0e3bf2524b29d6fc8e9eb6ba093c0d660a14cc623f0a7f86f085","last_reissued_at":"2026-05-18T01:17:02.158992Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:02.158992Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.04457","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":"2026-05-18T01:17:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SmtDilr5ZfekWWTbIicZj2lmTihgbUHoGBnWPEYtU75err6rwnDlafwU6Pk22H5WSjjJtKoAnneCrGL3sOqCDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T02:07:01.490647Z"},"content_sha256":"92de93dd901107212bd95bcf4c98e914b799ed9c678c7e0638f351d897e5602e","schema_version":"1.0","event_id":"sha256:92de93dd901107212bd95bcf4c98e914b799ed9c678c7e0638f351d897e5602e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:GSR57A66TYHDX4SSJMU5N7EOT2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A 3D Spatial Fluid Model for Wireless Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NI","math.IT"],"primary_cat":"cs.IT","authors_text":"Jean-Marc Kelif, Marceau Coupechoux","submitted_at":"2016-04-15T12:18:43Z","abstract_excerpt":"In this article we develop a three dimensional (3D) analytical model of wireless networks. We establish an analytical expression of the SINR (Signal to Interference plus Noise Ratio) of user equipments (UE), by using a 3D fluid model approach of the network. This model enables to evaluate in a simple way the cumulative distribution function of the SINR, and therefore the performance, the quality of service and the coverage of wireless networks, with a high accuracy. The use of this 3D wireless network model, instead of a standard two-dimensional one, in order to analyze wireless networks, is p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.04457","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":"2026-05-18T01:17:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UGweoBNP7/ig3vN5JnhhnhgjSJaNKnBGh+/CFk98I+WyevxwWuftS0zvNWfwcgXLjP09zVeNX8lThs5cOjdHBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T02:07:01.490982Z"},"content_sha256":"340e84a91409c9d66e110939790387ab44130c99e1198586ffe811284deec38a","schema_version":"1.0","event_id":"sha256:340e84a91409c9d66e110939790387ab44130c99e1198586ffe811284deec38a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GSR57A66TYHDX4SSJMU5N7EOT2/bundle.json","state_url":"https://pith.science/pith/GSR57A66TYHDX4SSJMU5N7EOT2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GSR57A66TYHDX4SSJMU5N7EOT2/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":"2026-06-27T02:07:01Z","links":{"resolver":"https://pith.science/pith/GSR57A66TYHDX4SSJMU5N7EOT2","bundle":"https://pith.science/pith/GSR57A66TYHDX4SSJMU5N7EOT2/bundle.json","state":"https://pith.science/pith/GSR57A66TYHDX4SSJMU5N7EOT2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GSR57A66TYHDX4SSJMU5N7EOT2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:GSR57A66TYHDX4SSJMU5N7EOT2","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":"1f99e99f88fbc28a61180ad1bef6b80da8298d4401b60a4bb87dc8951a34f229","cross_cats_sorted":["cs.NI","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-04-15T12:18:43Z","title_canon_sha256":"f5768b1d94f845aebbf9f4d2a4169ad22daef97f1710aefc3edabf565a70ebe1"},"schema_version":"1.0","source":{"id":"1604.04457","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.04457","created_at":"2026-05-18T01:17:02Z"},{"alias_kind":"arxiv_version","alias_value":"1604.04457v1","created_at":"2026-05-18T01:17:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.04457","created_at":"2026-05-18T01:17:02Z"},{"alias_kind":"pith_short_12","alias_value":"GSR57A66TYHD","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GSR57A66TYHDX4SS","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GSR57A66","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:340e84a91409c9d66e110939790387ab44130c99e1198586ffe811284deec38a","target":"graph","created_at":"2026-05-18T01:17:02Z","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 article we develop a three dimensional (3D) analytical model of wireless networks. We establish an analytical expression of the SINR (Signal to Interference plus Noise Ratio) of user equipments (UE), by using a 3D fluid model approach of the network. This model enables to evaluate in a simple way the cumulative distribution function of the SINR, and therefore the performance, the quality of service and the coverage of wireless networks, with a high accuracy. The use of this 3D wireless network model, instead of a standard two-dimensional one, in order to analyze wireless networks, is p","authors_text":"Jean-Marc Kelif, Marceau Coupechoux","cross_cats":["cs.NI","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-04-15T12:18:43Z","title":"A 3D Spatial Fluid Model for Wireless Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.04457","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":"sha256:92de93dd901107212bd95bcf4c98e914b799ed9c678c7e0638f351d897e5602e","target":"record","created_at":"2026-05-18T01:17:02Z","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":"1f99e99f88fbc28a61180ad1bef6b80da8298d4401b60a4bb87dc8951a34f229","cross_cats_sorted":["cs.NI","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-04-15T12:18:43Z","title_canon_sha256":"f5768b1d94f845aebbf9f4d2a4169ad22daef97f1710aefc3edabf565a70ebe1"},"schema_version":"1.0","source":{"id":"1604.04457","kind":"arxiv","version":1}},"canonical_sha256":"34a3df83de9e0e3bf2524b29d6fc8e9eb6ba093c0d660a14cc623f0a7f86f085","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"34a3df83de9e0e3bf2524b29d6fc8e9eb6ba093c0d660a14cc623f0a7f86f085","first_computed_at":"2026-05-18T01:17:02.158992Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:02.158992Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6rWZTr8chdcnZjVjL4eTI6WCJOm5qGTaMub+3SdkRArZQ6s2ed4ePYdde99qhMvniSUDG+dVVcJWCDKkcsMLCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:02.159698Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.04457","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:92de93dd901107212bd95bcf4c98e914b799ed9c678c7e0638f351d897e5602e","sha256:340e84a91409c9d66e110939790387ab44130c99e1198586ffe811284deec38a"],"state_sha256":"75fd82f6a5c84e98ab27ad175ecedf2bb10d254f017b5c0dd411c701370368c7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9P7yOEr3o5twnqwUEFM1Ypag7SNSgoppdIZT0fXJU6d8s5sRJB1vz3jmkwRyBfnBnm6wV4ly/q2vm+BFUf9GCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T02:07:01.492830Z","bundle_sha256":"291af9140cec2e19dec60dc806a2e4c549d8ad8a3689d1f285b41e63af3ef9b2"}}