{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:ADSFHIVDM7Q52QATQP6JTBEL2I","short_pith_number":"pith:ADSFHIVD","canonical_record":{"source":{"id":"1011.2109","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-11-09T15:04:47Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"4dbfdb4a6d1e098c6d9b0d4fc4d2c7c5fa9a13140985b199b7c5c3a0710d91dc","abstract_canon_sha256":"0b8e56ad14001dbfd93e4d01c4d63ac692071079d1d323ca3c69604481154e51"},"schema_version":"1.0"},"canonical_sha256":"00e453a2a367e1dd401383fc99848bd2163bd5b210f4a1f98d749a6b00769812","source":{"kind":"arxiv","id":"1011.2109","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.2109","created_at":"2026-05-18T04:36:42Z"},{"alias_kind":"arxiv_version","alias_value":"1011.2109v1","created_at":"2026-05-18T04:36:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.2109","created_at":"2026-05-18T04:36:42Z"},{"alias_kind":"pith_short_12","alias_value":"ADSFHIVDM7Q5","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"ADSFHIVDM7Q52QAT","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"ADSFHIVD","created_at":"2026-05-18T12:26:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:ADSFHIVDM7Q52QATQP6JTBEL2I","target":"record","payload":{"canonical_record":{"source":{"id":"1011.2109","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-11-09T15:04:47Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"4dbfdb4a6d1e098c6d9b0d4fc4d2c7c5fa9a13140985b199b7c5c3a0710d91dc","abstract_canon_sha256":"0b8e56ad14001dbfd93e4d01c4d63ac692071079d1d323ca3c69604481154e51"},"schema_version":"1.0"},"canonical_sha256":"00e453a2a367e1dd401383fc99848bd2163bd5b210f4a1f98d749a6b00769812","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:36:42.557302Z","signature_b64":"AQsmloXGRhsH6TXGQ643OeELrdsBg+kJuY2qL7iRXbWyTSl3KqYq67XLbydRCWegxsucZHYvPZGRYO2aV4j9Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"00e453a2a367e1dd401383fc99848bd2163bd5b210f4a1f98d749a6b00769812","last_reissued_at":"2026-05-18T04:36:42.556822Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:36:42.556822Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1011.2109","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":"2026-05-18T04:36:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hzJzXYDPzc+u7aCQ6w1lcXcVVscK4UYRK9nh4mp6IbIELmQeUfQYJiM9VzwvqduyY/P9PgMNAodQW+4dTBQTBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T22:19:46.729038Z"},"content_sha256":"f3cd53e46aeeb6ef7d2d9c416da534a1a0078464659663e335712ff649a59d30","schema_version":"1.0","event_id":"sha256:f3cd53e46aeeb6ef7d2d9c416da534a1a0078464659663e335712ff649a59d30"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:ADSFHIVDM7Q52QATQP6JTBEL2I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Secure Transmission over Parallel Relay Eavesdropper Channel","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Abdellatif Zaidi, Luc Vandendorpe, Zohaib Hassan Awan","submitted_at":"2010-11-09T15:04:47Z","abstract_excerpt":"We study a four terminal parallel relay-eavesdropper channel which consists of multiple independent relay-eavesdropper channels as subchannels. For the discrete memoryless case, we establish inner and outer bounds on the rate-equivocation region. For each subchannel, secure transmission is obtained through one of the two coding schemes at the relay: decoding-and-forwarding the source message or confusing the eavesdropper through noise injection. The inner bound allows relay mode selection. For the Gaussian model we establish lower and upper bounds on the perfect secrecy rate. We show that the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.2109","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":"2026-05-18T04:36:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J5AmrxjPFuXfy09zBbanVFV5Uy7AfXh5gFv0Qqq/kiOG+1boNVwhEfJqFA/MCTuuU5WKp65G0EM/vyeYYiGsCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T22:19:46.729467Z"},"content_sha256":"e9021ccab2094166d2f0a3e8e8556eae686b47ee3ed9f1501203418f7fea30da","schema_version":"1.0","event_id":"sha256:e9021ccab2094166d2f0a3e8e8556eae686b47ee3ed9f1501203418f7fea30da"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ADSFHIVDM7Q52QATQP6JTBEL2I/bundle.json","state_url":"https://pith.science/pith/ADSFHIVDM7Q52QATQP6JTBEL2I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ADSFHIVDM7Q52QATQP6JTBEL2I/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":"2026-05-25T22:19:46Z","links":{"resolver":"https://pith.science/pith/ADSFHIVDM7Q52QATQP6JTBEL2I","bundle":"https://pith.science/pith/ADSFHIVDM7Q52QATQP6JTBEL2I/bundle.json","state":"https://pith.science/pith/ADSFHIVDM7Q52QATQP6JTBEL2I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ADSFHIVDM7Q52QATQP6JTBEL2I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:ADSFHIVDM7Q52QATQP6JTBEL2I","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":"0b8e56ad14001dbfd93e4d01c4d63ac692071079d1d323ca3c69604481154e51","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-11-09T15:04:47Z","title_canon_sha256":"4dbfdb4a6d1e098c6d9b0d4fc4d2c7c5fa9a13140985b199b7c5c3a0710d91dc"},"schema_version":"1.0","source":{"id":"1011.2109","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.2109","created_at":"2026-05-18T04:36:42Z"},{"alias_kind":"arxiv_version","alias_value":"1011.2109v1","created_at":"2026-05-18T04:36:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.2109","created_at":"2026-05-18T04:36:42Z"},{"alias_kind":"pith_short_12","alias_value":"ADSFHIVDM7Q5","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"ADSFHIVDM7Q52QAT","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"ADSFHIVD","created_at":"2026-05-18T12:26:05Z"}],"graph_snapshots":[{"event_id":"sha256:e9021ccab2094166d2f0a3e8e8556eae686b47ee3ed9f1501203418f7fea30da","target":"graph","created_at":"2026-05-18T04:36:42Z","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":"We study a four terminal parallel relay-eavesdropper channel which consists of multiple independent relay-eavesdropper channels as subchannels. For the discrete memoryless case, we establish inner and outer bounds on the rate-equivocation region. For each subchannel, secure transmission is obtained through one of the two coding schemes at the relay: decoding-and-forwarding the source message or confusing the eavesdropper through noise injection. The inner bound allows relay mode selection. For the Gaussian model we establish lower and upper bounds on the perfect secrecy rate. We show that the ","authors_text":"Abdellatif Zaidi, Luc Vandendorpe, Zohaib Hassan Awan","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-11-09T15:04:47Z","title":"On Secure Transmission over Parallel Relay Eavesdropper Channel"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.2109","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:f3cd53e46aeeb6ef7d2d9c416da534a1a0078464659663e335712ff649a59d30","target":"record","created_at":"2026-05-18T04:36:42Z","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":"0b8e56ad14001dbfd93e4d01c4d63ac692071079d1d323ca3c69604481154e51","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-11-09T15:04:47Z","title_canon_sha256":"4dbfdb4a6d1e098c6d9b0d4fc4d2c7c5fa9a13140985b199b7c5c3a0710d91dc"},"schema_version":"1.0","source":{"id":"1011.2109","kind":"arxiv","version":1}},"canonical_sha256":"00e453a2a367e1dd401383fc99848bd2163bd5b210f4a1f98d749a6b00769812","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"00e453a2a367e1dd401383fc99848bd2163bd5b210f4a1f98d749a6b00769812","first_computed_at":"2026-05-18T04:36:42.556822Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:36:42.556822Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AQsmloXGRhsH6TXGQ643OeELrdsBg+kJuY2qL7iRXbWyTSl3KqYq67XLbydRCWegxsucZHYvPZGRYO2aV4j9Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:36:42.557302Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.2109","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f3cd53e46aeeb6ef7d2d9c416da534a1a0078464659663e335712ff649a59d30","sha256:e9021ccab2094166d2f0a3e8e8556eae686b47ee3ed9f1501203418f7fea30da"],"state_sha256":"347dff000116fd245c990dd8daa73590addc1e27e3aaecbbb41225b2a82c9ae0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"URbWEqHJb9/R5U8qmr1vsJxe2xWP+5pu0H5/aBI7QYYwm0bKWEnfPcupMhakkl6Drjqx6hQwohbv7gSM6XggDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T22:19:46.732294Z","bundle_sha256":"bdcd6068ef3edae09aee520d3544754a36f329226ec70e572d2a0942be520889"}}