{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:42SBLBCK4FGLCRPQNQZ7WET34J","short_pith_number":"pith:42SBLBCK","canonical_record":{"source":{"id":"1503.01056","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-03-03T19:00:14Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"d4cb9d72c9738de0c61835e152f6d642a58c9b9d59089cb75a9de7df7487ddb5","abstract_canon_sha256":"f646e18ee129a7e75dacc7bb8818712dca099d49e6b93d4013cbdbf2c3cd631f"},"schema_version":"1.0"},"canonical_sha256":"e6a415844ae14cb145f06c33fb127be277390e0a4ed85046beb5f1e689514405","source":{"kind":"arxiv","id":"1503.01056","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.01056","created_at":"2026-05-18T01:41:47Z"},{"alias_kind":"arxiv_version","alias_value":"1503.01056v1","created_at":"2026-05-18T01:41:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.01056","created_at":"2026-05-18T01:41:47Z"},{"alias_kind":"pith_short_12","alias_value":"42SBLBCK4FGL","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"42SBLBCK4FGLCRPQ","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"42SBLBCK","created_at":"2026-05-18T12:29:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:42SBLBCK4FGLCRPQNQZ7WET34J","target":"record","payload":{"canonical_record":{"source":{"id":"1503.01056","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-03-03T19:00:14Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"d4cb9d72c9738de0c61835e152f6d642a58c9b9d59089cb75a9de7df7487ddb5","abstract_canon_sha256":"f646e18ee129a7e75dacc7bb8818712dca099d49e6b93d4013cbdbf2c3cd631f"},"schema_version":"1.0"},"canonical_sha256":"e6a415844ae14cb145f06c33fb127be277390e0a4ed85046beb5f1e689514405","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:41:47.599035Z","signature_b64":"gqtwpWxF7xvZocYnLYM2dD7Wml5zJJV40GfEXwbk6GsIvrViN58Cwv0FvAJjdaRlTs70WPCWgX+Se51Vg3EZDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e6a415844ae14cb145f06c33fb127be277390e0a4ed85046beb5f1e689514405","last_reissued_at":"2026-05-18T01:41:47.598548Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:41:47.598548Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.01056","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":"2026-05-18T01:41:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4/K7kdWod2tgWNiw7aY6Lhkoh64aZi0/FPak2wv9EXovzePQePYsOBChzkMJdXzNmU5hFNvLT/7qHV64rvElCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T12:43:14.918733Z"},"content_sha256":"e5c0136300c517b58450e8f8c9ff97fffdac30024228ff6c8ca463612e205d71","schema_version":"1.0","event_id":"sha256:e5c0136300c517b58450e8f8c9ff97fffdac30024228ff6c8ca463612e205d71"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:42SBLBCK4FGLCRPQNQZ7WET34J","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Secrecy Transmit Beamforming for Heterogeneous Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Hui Gao, Shaoshi Yang, Tiejun Lv","submitted_at":"2015-03-03T19:00:14Z","abstract_excerpt":"In this paper, we pioneer the study of physical-layer security in heterogeneous networks (HetNets). We investigate secure communications in a two-tier downlink HetNet, which comprises one macrocell and several femtocells. Each cell has multiple users and an eavesdropper attempts to wiretap the intended macrocell user. Firstly, we consider an orthogonal spectrum allocation strategy to eliminate co-channel interference, and propose the secrecy transmit beamforming only operating in the macrocell (STB-OM) as a partial solution for secure communication in HetNet. Next, we consider a secrecy-orient"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.01056","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":"2026-05-18T01:41:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"akP5+++L5vdH95L2SRy1LIpPJi08iLqPDwZjME7o2LjzzaM8eFBAB3Qe83FIC92ICqWZ7TRJnHCwd3iPOLIwAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T12:43:14.919380Z"},"content_sha256":"ea48f56ccb6a8b7b5fa693279bfcd21bc55abf3556c15e424102e209e2e48775","schema_version":"1.0","event_id":"sha256:ea48f56ccb6a8b7b5fa693279bfcd21bc55abf3556c15e424102e209e2e48775"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/42SBLBCK4FGLCRPQNQZ7WET34J/bundle.json","state_url":"https://pith.science/pith/42SBLBCK4FGLCRPQNQZ7WET34J/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/42SBLBCK4FGLCRPQNQZ7WET34J/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":"2026-05-27T12:43:14Z","links":{"resolver":"https://pith.science/pith/42SBLBCK4FGLCRPQNQZ7WET34J","bundle":"https://pith.science/pith/42SBLBCK4FGLCRPQNQZ7WET34J/bundle.json","state":"https://pith.science/pith/42SBLBCK4FGLCRPQNQZ7WET34J/state.json","well_known_bundle":"https://pith.science/.well-known/pith/42SBLBCK4FGLCRPQNQZ7WET34J/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:42SBLBCK4FGLCRPQNQZ7WET34J","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":"f646e18ee129a7e75dacc7bb8818712dca099d49e6b93d4013cbdbf2c3cd631f","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-03-03T19:00:14Z","title_canon_sha256":"d4cb9d72c9738de0c61835e152f6d642a58c9b9d59089cb75a9de7df7487ddb5"},"schema_version":"1.0","source":{"id":"1503.01056","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.01056","created_at":"2026-05-18T01:41:47Z"},{"alias_kind":"arxiv_version","alias_value":"1503.01056v1","created_at":"2026-05-18T01:41:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.01056","created_at":"2026-05-18T01:41:47Z"},{"alias_kind":"pith_short_12","alias_value":"42SBLBCK4FGL","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"42SBLBCK4FGLCRPQ","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"42SBLBCK","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:ea48f56ccb6a8b7b5fa693279bfcd21bc55abf3556c15e424102e209e2e48775","target":"graph","created_at":"2026-05-18T01:41:47Z","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 pioneer the study of physical-layer security in heterogeneous networks (HetNets). We investigate secure communications in a two-tier downlink HetNet, which comprises one macrocell and several femtocells. Each cell has multiple users and an eavesdropper attempts to wiretap the intended macrocell user. Firstly, we consider an orthogonal spectrum allocation strategy to eliminate co-channel interference, and propose the secrecy transmit beamforming only operating in the macrocell (STB-OM) as a partial solution for secure communication in HetNet. Next, we consider a secrecy-orient","authors_text":"Hui Gao, Shaoshi Yang, Tiejun Lv","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-03-03T19:00:14Z","title":"Secrecy Transmit Beamforming for Heterogeneous Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.01056","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:e5c0136300c517b58450e8f8c9ff97fffdac30024228ff6c8ca463612e205d71","target":"record","created_at":"2026-05-18T01:41:47Z","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":"f646e18ee129a7e75dacc7bb8818712dca099d49e6b93d4013cbdbf2c3cd631f","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-03-03T19:00:14Z","title_canon_sha256":"d4cb9d72c9738de0c61835e152f6d642a58c9b9d59089cb75a9de7df7487ddb5"},"schema_version":"1.0","source":{"id":"1503.01056","kind":"arxiv","version":1}},"canonical_sha256":"e6a415844ae14cb145f06c33fb127be277390e0a4ed85046beb5f1e689514405","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e6a415844ae14cb145f06c33fb127be277390e0a4ed85046beb5f1e689514405","first_computed_at":"2026-05-18T01:41:47.598548Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:41:47.598548Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gqtwpWxF7xvZocYnLYM2dD7Wml5zJJV40GfEXwbk6GsIvrViN58Cwv0FvAJjdaRlTs70WPCWgX+Se51Vg3EZDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:41:47.599035Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.01056","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e5c0136300c517b58450e8f8c9ff97fffdac30024228ff6c8ca463612e205d71","sha256:ea48f56ccb6a8b7b5fa693279bfcd21bc55abf3556c15e424102e209e2e48775"],"state_sha256":"4147bcb2ca4686169469bdc7a6bde738ac9ca3876a68f1f34eac32a9e6f03e82"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"brBAvoiX/i8gBsOLDHxtbhA7M1vuSeeK+39QmEyFp9H1cSxgjYxofdE/uVPFwe5wyGn/o81pZMm7BLQ5/fciBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T12:43:14.924103Z","bundle_sha256":"387314503d9564ff821a86e05591df00161d07a0142ee47e88cd8599b3b9b94c"}}