{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:U465DNXHNB5KFXCBT2TFKUNNIF","short_pith_number":"pith:U465DNXH","canonical_record":{"source":{"id":"1509.05506","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-09-18T04:50:44Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"8103278aea212a8885dccc9d44c872b36a5b0b2097b2aeb9b83854af02f61930","abstract_canon_sha256":"b417f3e5ecbf69a006ecd26a332ca5d7e54d808e27660c823694f373dc1ba546"},"schema_version":"1.0"},"canonical_sha256":"a73dd1b6e7687aa2dc419ea65551ad4168523ebda1a8b578b57b3ff0a32b9bcc","source":{"kind":"arxiv","id":"1509.05506","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.05506","created_at":"2026-05-18T01:18:09Z"},{"alias_kind":"arxiv_version","alias_value":"1509.05506v2","created_at":"2026-05-18T01:18:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.05506","created_at":"2026-05-18T01:18:09Z"},{"alias_kind":"pith_short_12","alias_value":"U465DNXHNB5K","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"U465DNXHNB5KFXCB","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"U465DNXH","created_at":"2026-05-18T12:29:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:U465DNXHNB5KFXCBT2TFKUNNIF","target":"record","payload":{"canonical_record":{"source":{"id":"1509.05506","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-09-18T04:50:44Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"8103278aea212a8885dccc9d44c872b36a5b0b2097b2aeb9b83854af02f61930","abstract_canon_sha256":"b417f3e5ecbf69a006ecd26a332ca5d7e54d808e27660c823694f373dc1ba546"},"schema_version":"1.0"},"canonical_sha256":"a73dd1b6e7687aa2dc419ea65551ad4168523ebda1a8b578b57b3ff0a32b9bcc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:09.467715Z","signature_b64":"bFZVE2iicBU5+E/D5FJmBfRXJOKLg/ZbKXaUlH6MlGj7SkjcxJOUua7T04wvYJ39Jg6mkfVm+LXDCfnvR4r3DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a73dd1b6e7687aa2dc419ea65551ad4168523ebda1a8b578b57b3ff0a32b9bcc","last_reissued_at":"2026-05-18T01:18:09.467252Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:09.467252Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.05506","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":"2026-05-18T01:18:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yWew8cwKl8AJwDJns1brdfbmg73Xy57CTkn/4JgECftuneARu1G3QPxLd3ouKIR/zc+4swsbSUVbDnzHeaPcAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T17:00:40.260114Z"},"content_sha256":"28cbda02250ad45c410869bb43aa7b4f95922a6ed9565db0e8f149ce010d97dd","schema_version":"1.0","event_id":"sha256:28cbda02250ad45c410869bb43aa7b4f95922a6ed9565db0e8f149ce010d97dd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:U465DNXHNB5KFXCBT2TFKUNNIF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Energy-Efficient Design of MIMO Heterogeneous Networks with Wireless Backhaul","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Giovanni Geraci, Howard H. Yang, Tony Q. S. Quek","submitted_at":"2015-09-18T04:50:44Z","abstract_excerpt":"As future networks aim to meet the ever-increasing requirements of high data rate applications, dense and heterogeneous networks (HetNets) will be deployed to provide better coverage and throughput. Besides the important implications for energy consumption, the trend towards densification calls for more and more wireless links to forward a massive backhaul traffic into the core network. It is critically important to take into account the presence of a wireless backhaul for the energy-efficient design of HetNets. In this paper, we provide a general framework to analyze the energy efficiency of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.05506","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":"2026-05-18T01:18:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"36jJdkXJrWC1l1JF65Y5mi8HnwpQ/Wz63MW2YeaUQPrgbnT0iLpi5VyBk0WswkKGDoC2NHCHiH0CJIGowKKMCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T17:00:40.260920Z"},"content_sha256":"1def6e0ec4f9f0cebe3b874e425cfcb20280caae8f04d7442ea3d3b4edb98d55","schema_version":"1.0","event_id":"sha256:1def6e0ec4f9f0cebe3b874e425cfcb20280caae8f04d7442ea3d3b4edb98d55"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U465DNXHNB5KFXCBT2TFKUNNIF/bundle.json","state_url":"https://pith.science/pith/U465DNXHNB5KFXCBT2TFKUNNIF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U465DNXHNB5KFXCBT2TFKUNNIF/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":"2026-06-01T17:00:40Z","links":{"resolver":"https://pith.science/pith/U465DNXHNB5KFXCBT2TFKUNNIF","bundle":"https://pith.science/pith/U465DNXHNB5KFXCBT2TFKUNNIF/bundle.json","state":"https://pith.science/pith/U465DNXHNB5KFXCBT2TFKUNNIF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U465DNXHNB5KFXCBT2TFKUNNIF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:U465DNXHNB5KFXCBT2TFKUNNIF","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":"b417f3e5ecbf69a006ecd26a332ca5d7e54d808e27660c823694f373dc1ba546","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-09-18T04:50:44Z","title_canon_sha256":"8103278aea212a8885dccc9d44c872b36a5b0b2097b2aeb9b83854af02f61930"},"schema_version":"1.0","source":{"id":"1509.05506","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.05506","created_at":"2026-05-18T01:18:09Z"},{"alias_kind":"arxiv_version","alias_value":"1509.05506v2","created_at":"2026-05-18T01:18:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.05506","created_at":"2026-05-18T01:18:09Z"},{"alias_kind":"pith_short_12","alias_value":"U465DNXHNB5K","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"U465DNXHNB5KFXCB","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"U465DNXH","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:1def6e0ec4f9f0cebe3b874e425cfcb20280caae8f04d7442ea3d3b4edb98d55","target":"graph","created_at":"2026-05-18T01:18:09Z","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":"As future networks aim to meet the ever-increasing requirements of high data rate applications, dense and heterogeneous networks (HetNets) will be deployed to provide better coverage and throughput. Besides the important implications for energy consumption, the trend towards densification calls for more and more wireless links to forward a massive backhaul traffic into the core network. It is critically important to take into account the presence of a wireless backhaul for the energy-efficient design of HetNets. In this paper, we provide a general framework to analyze the energy efficiency of ","authors_text":"Giovanni Geraci, Howard H. Yang, Tony Q. S. Quek","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-09-18T04:50:44Z","title":"Energy-Efficient Design of MIMO Heterogeneous Networks with Wireless Backhaul"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.05506","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":"sha256:28cbda02250ad45c410869bb43aa7b4f95922a6ed9565db0e8f149ce010d97dd","target":"record","created_at":"2026-05-18T01:18:09Z","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":"b417f3e5ecbf69a006ecd26a332ca5d7e54d808e27660c823694f373dc1ba546","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-09-18T04:50:44Z","title_canon_sha256":"8103278aea212a8885dccc9d44c872b36a5b0b2097b2aeb9b83854af02f61930"},"schema_version":"1.0","source":{"id":"1509.05506","kind":"arxiv","version":2}},"canonical_sha256":"a73dd1b6e7687aa2dc419ea65551ad4168523ebda1a8b578b57b3ff0a32b9bcc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a73dd1b6e7687aa2dc419ea65551ad4168523ebda1a8b578b57b3ff0a32b9bcc","first_computed_at":"2026-05-18T01:18:09.467252Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:09.467252Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bFZVE2iicBU5+E/D5FJmBfRXJOKLg/ZbKXaUlH6MlGj7SkjcxJOUua7T04wvYJ39Jg6mkfVm+LXDCfnvR4r3DA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:09.467715Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.05506","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:28cbda02250ad45c410869bb43aa7b4f95922a6ed9565db0e8f149ce010d97dd","sha256:1def6e0ec4f9f0cebe3b874e425cfcb20280caae8f04d7442ea3d3b4edb98d55"],"state_sha256":"5f83cc54c8c756290208ee8c4f6568d376a3ae7e3514ab08cc3b09bd156d9283"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mvTVkL9m0zWal/vl5TQDpv2TD6k+bah1EGLWNmv4u/WT5yXHJsq59vhN8XZUTJeASLz8zKLrdTIpPAyA0UQJBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T17:00:40.262963Z","bundle_sha256":"da4c6e1ef1fbb1177fcbb7f3da41fe735e833c6c02e99f4c32052255749422fa"}}