{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:HOD2NBKZBD3TGFEJNOVV4KJTCJ","short_pith_number":"pith:HOD2NBKZ","canonical_record":{"source":{"id":"1607.04352","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-07-15T01:16:17Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"c5f52bb48e70b657f6823f5f99e6b4ef6596060eb32aae30ea35d66cd34006dc","abstract_canon_sha256":"79bd4cdd8192c7d79448109a13d5e6be29b0fa6a8ed34a3cf17ef056092075b6"},"schema_version":"1.0"},"canonical_sha256":"3b87a6855908f73314896bab5e2933124bd8679297e00b8d23590e3dc5cb7f95","source":{"kind":"arxiv","id":"1607.04352","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.04352","created_at":"2026-05-18T00:38:42Z"},{"alias_kind":"arxiv_version","alias_value":"1607.04352v4","created_at":"2026-05-18T00:38:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.04352","created_at":"2026-05-18T00:38:42Z"},{"alias_kind":"pith_short_12","alias_value":"HOD2NBKZBD3T","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"HOD2NBKZBD3TGFEJ","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"HOD2NBKZ","created_at":"2026-05-18T12:30:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:HOD2NBKZBD3TGFEJNOVV4KJTCJ","target":"record","payload":{"canonical_record":{"source":{"id":"1607.04352","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-07-15T01:16:17Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"c5f52bb48e70b657f6823f5f99e6b4ef6596060eb32aae30ea35d66cd34006dc","abstract_canon_sha256":"79bd4cdd8192c7d79448109a13d5e6be29b0fa6a8ed34a3cf17ef056092075b6"},"schema_version":"1.0"},"canonical_sha256":"3b87a6855908f73314896bab5e2933124bd8679297e00b8d23590e3dc5cb7f95","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:42.227134Z","signature_b64":"6gjo59OP/iLbIKX0tAl8MTMnvhF3zdVxHQJb0vwPgdDVN1h0+T/0QsCw2m4q8vwK1cgGjg123ovWmd2UukPXCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3b87a6855908f73314896bab5e2933124bd8679297e00b8d23590e3dc5cb7f95","last_reissued_at":"2026-05-18T00:38:42.226506Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:42.226506Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1607.04352","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:38:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ntzouMg6o0LSeEFMZhKkymakXFOYrep4KVMLQr3xP6jQ+kZG4LCsstfdsQAvvWcRbZ4t1+MLXGV8w2vMp0TmAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T18:28:59.373835Z"},"content_sha256":"3d8cd16b5aceb784a73765902b8c6d00c3ef4b59b8a664a9c41a6ad21486d797","schema_version":"1.0","event_id":"sha256:3d8cd16b5aceb784a73765902b8c6d00c3ef4b59b8a664a9c41a6ad21486d797"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:HOD2NBKZBD3TGFEJNOVV4KJTCJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Ergodic Spectral Efficiency in MIMO Cellular Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Angel Lozano, Geordie George, Martin Haenggi, Ratheesh K. Mungara","submitted_at":"2016-07-15T01:16:17Z","abstract_excerpt":"This paper shows how the application of stochastic geometry to the analysis of wireless networks is greatly facilitated by (i) a clear separation of time scales, (ii) the abstraction of small-scale effects via ergodicity, and (iii) an interference model that reflects the receiver's lack of knowledge of how each individual interference term is faded. These procedures render the analysis both more manageable and more precise, as well as more amenable to the incorporation of subsequent features. In particular, the paper presents analytical characterizations of the ergodic spectral efficiency of c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.04352","kind":"arxiv","version":4},"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":"2026-05-18T00:38:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2PynizV6ouCGIGvDma4hwS9ppgzdSnsodUrbc+lkdPANY97JP0NjhHM5gly2ESylFdyTxeGg+dva/ARPz4B8AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T18:28:59.374428Z"},"content_sha256":"52820bc1e8c9f13b023a095d9297c3e266cd8bd4f3a10e6ac0145a4f5776ae79","schema_version":"1.0","event_id":"sha256:52820bc1e8c9f13b023a095d9297c3e266cd8bd4f3a10e6ac0145a4f5776ae79"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HOD2NBKZBD3TGFEJNOVV4KJTCJ/bundle.json","state_url":"https://pith.science/pith/HOD2NBKZBD3TGFEJNOVV4KJTCJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HOD2NBKZBD3TGFEJNOVV4KJTCJ/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":"2026-05-28T18:28:59Z","links":{"resolver":"https://pith.science/pith/HOD2NBKZBD3TGFEJNOVV4KJTCJ","bundle":"https://pith.science/pith/HOD2NBKZBD3TGFEJNOVV4KJTCJ/bundle.json","state":"https://pith.science/pith/HOD2NBKZBD3TGFEJNOVV4KJTCJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HOD2NBKZBD3TGFEJNOVV4KJTCJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:HOD2NBKZBD3TGFEJNOVV4KJTCJ","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":"79bd4cdd8192c7d79448109a13d5e6be29b0fa6a8ed34a3cf17ef056092075b6","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-07-15T01:16:17Z","title_canon_sha256":"c5f52bb48e70b657f6823f5f99e6b4ef6596060eb32aae30ea35d66cd34006dc"},"schema_version":"1.0","source":{"id":"1607.04352","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.04352","created_at":"2026-05-18T00:38:42Z"},{"alias_kind":"arxiv_version","alias_value":"1607.04352v4","created_at":"2026-05-18T00:38:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.04352","created_at":"2026-05-18T00:38:42Z"},{"alias_kind":"pith_short_12","alias_value":"HOD2NBKZBD3T","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"HOD2NBKZBD3TGFEJ","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"HOD2NBKZ","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:52820bc1e8c9f13b023a095d9297c3e266cd8bd4f3a10e6ac0145a4f5776ae79","target":"graph","created_at":"2026-05-18T00:38:42Z","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 paper shows how the application of stochastic geometry to the analysis of wireless networks is greatly facilitated by (i) a clear separation of time scales, (ii) the abstraction of small-scale effects via ergodicity, and (iii) an interference model that reflects the receiver's lack of knowledge of how each individual interference term is faded. These procedures render the analysis both more manageable and more precise, as well as more amenable to the incorporation of subsequent features. In particular, the paper presents analytical characterizations of the ergodic spectral efficiency of c","authors_text":"Angel Lozano, Geordie George, Martin Haenggi, Ratheesh K. Mungara","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-07-15T01:16:17Z","title":"Ergodic Spectral Efficiency in MIMO Cellular Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.04352","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":"sha256:3d8cd16b5aceb784a73765902b8c6d00c3ef4b59b8a664a9c41a6ad21486d797","target":"record","created_at":"2026-05-18T00:38:42Z","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":"79bd4cdd8192c7d79448109a13d5e6be29b0fa6a8ed34a3cf17ef056092075b6","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-07-15T01:16:17Z","title_canon_sha256":"c5f52bb48e70b657f6823f5f99e6b4ef6596060eb32aae30ea35d66cd34006dc"},"schema_version":"1.0","source":{"id":"1607.04352","kind":"arxiv","version":4}},"canonical_sha256":"3b87a6855908f73314896bab5e2933124bd8679297e00b8d23590e3dc5cb7f95","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3b87a6855908f73314896bab5e2933124bd8679297e00b8d23590e3dc5cb7f95","first_computed_at":"2026-05-18T00:38:42.226506Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:38:42.226506Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6gjo59OP/iLbIKX0tAl8MTMnvhF3zdVxHQJb0vwPgdDVN1h0+T/0QsCw2m4q8vwK1cgGjg123ovWmd2UukPXCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:38:42.227134Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.04352","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3d8cd16b5aceb784a73765902b8c6d00c3ef4b59b8a664a9c41a6ad21486d797","sha256:52820bc1e8c9f13b023a095d9297c3e266cd8bd4f3a10e6ac0145a4f5776ae79"],"state_sha256":"72be0d1e6498742bba4438868c7cb00468dc83756c2e1cf791aff68c9485cc6c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iFsTKgVnNKUHHHs1IcYQxEIr4FJFoRkqf4KU9dWAbobqBshlml3Q/xn0prVxx36ccmHfqiE0vSDtynTzOkBfDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T18:28:59.378038Z","bundle_sha256":"875ca191911533cfdad0d751463313d652df5dba0423ae596aa23a35a9c5ff2e"}}