{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:LOE46ZGDQ4SYJ4RXXZ7B7PQONN","short_pith_number":"pith:LOE46ZGD","canonical_record":{"source":{"id":"1510.03191","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-10-12T09:17:08Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"03ee88a84e7ed4054c9c98f415f8329a0a79d7e7e4055cbe80d4b0e421a9a252","abstract_canon_sha256":"b17181d69f27b07e94eb02e519ed653fd8b55ff533a9abc6b903d703139705dc"},"schema_version":"1.0"},"canonical_sha256":"5b89cf64c3872584f237be7e1fbe0e6b4af59c6bae5d928255d88dda462954f7","source":{"kind":"arxiv","id":"1510.03191","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.03191","created_at":"2026-05-18T01:30:32Z"},{"alias_kind":"arxiv_version","alias_value":"1510.03191v1","created_at":"2026-05-18T01:30:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.03191","created_at":"2026-05-18T01:30:32Z"},{"alias_kind":"pith_short_12","alias_value":"LOE46ZGDQ4SY","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"LOE46ZGDQ4SYJ4RX","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"LOE46ZGD","created_at":"2026-05-18T12:29:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:LOE46ZGDQ4SYJ4RXXZ7B7PQONN","target":"record","payload":{"canonical_record":{"source":{"id":"1510.03191","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-10-12T09:17:08Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"03ee88a84e7ed4054c9c98f415f8329a0a79d7e7e4055cbe80d4b0e421a9a252","abstract_canon_sha256":"b17181d69f27b07e94eb02e519ed653fd8b55ff533a9abc6b903d703139705dc"},"schema_version":"1.0"},"canonical_sha256":"5b89cf64c3872584f237be7e1fbe0e6b4af59c6bae5d928255d88dda462954f7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:32.515681Z","signature_b64":"8mdKMcWGHWcJpsnF2SD7TJKlhRKLM0CP3JkqZhvG8y7veFL26Jx5ygp56pFGqZzAe/A4w8ScnAGumWjTgbliDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5b89cf64c3872584f237be7e1fbe0e6b4af59c6bae5d928255d88dda462954f7","last_reissued_at":"2026-05-18T01:30:32.514985Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:32.514985Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.03191","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":"2026-05-18T01:30:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HnQplRLN3+42zMW2n8ws7qem9hs0jWro6LAKI5c2PJbz+I7k30Oa/KbwjT6aKjK+DM72iB+UTgk1eKkSIrl3Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T22:32:57.251889Z"},"content_sha256":"26b1f056af944c05cdb58ee27317a050f2d0d0f1e5671c34303046e4372b7f92","schema_version":"1.0","event_id":"sha256:26b1f056af944c05cdb58ee27317a050f2d0d0f1e5671c34303046e4372b7f92"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:LOE46ZGDQ4SYJ4RXXZ7B7PQONN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Capacity of the Two-Hop Half-Duplex Relay Channel","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Nikola Zlatanov, Robert Schober, Vahid Jamali","submitted_at":"2015-10-12T09:17:08Z","abstract_excerpt":"Although extensively investigated, the capacity of the two-hop half-duplex (HD) relay channel is not fully understood. In particular, a capacity expression which can be evaluated straightforwardly is not available and an explicit coding scheme which achieves the capacity is not known either. In this paper, we derive a new expression for the capacity of the two-hop HD relay channel based on a simplified converse. Compared to previous results, this capacity expression can be easily evaluated. Moreover, we propose an explicit coding scheme which achieves the capacity. To achieve the capacity, the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03191","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":"2026-05-18T01:30:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CJXaVQouVdEp151VoRnQnLCthE34QKJhd0qOLUz54fjdbTqwtrK7i+bVdCJb6JQY1wMHSMhXFL/lMCQtHPDCAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T22:32:57.252232Z"},"content_sha256":"680c07b2f66319e796d805caa281e91f6d5a49f9079d36dc956d632a43b3bde7","schema_version":"1.0","event_id":"sha256:680c07b2f66319e796d805caa281e91f6d5a49f9079d36dc956d632a43b3bde7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LOE46ZGDQ4SYJ4RXXZ7B7PQONN/bundle.json","state_url":"https://pith.science/pith/LOE46ZGDQ4SYJ4RXXZ7B7PQONN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LOE46ZGDQ4SYJ4RXXZ7B7PQONN/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":"2026-05-30T22:32:57Z","links":{"resolver":"https://pith.science/pith/LOE46ZGDQ4SYJ4RXXZ7B7PQONN","bundle":"https://pith.science/pith/LOE46ZGDQ4SYJ4RXXZ7B7PQONN/bundle.json","state":"https://pith.science/pith/LOE46ZGDQ4SYJ4RXXZ7B7PQONN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LOE46ZGDQ4SYJ4RXXZ7B7PQONN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:LOE46ZGDQ4SYJ4RXXZ7B7PQONN","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":"b17181d69f27b07e94eb02e519ed653fd8b55ff533a9abc6b903d703139705dc","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-10-12T09:17:08Z","title_canon_sha256":"03ee88a84e7ed4054c9c98f415f8329a0a79d7e7e4055cbe80d4b0e421a9a252"},"schema_version":"1.0","source":{"id":"1510.03191","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.03191","created_at":"2026-05-18T01:30:32Z"},{"alias_kind":"arxiv_version","alias_value":"1510.03191v1","created_at":"2026-05-18T01:30:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.03191","created_at":"2026-05-18T01:30:32Z"},{"alias_kind":"pith_short_12","alias_value":"LOE46ZGDQ4SY","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"LOE46ZGDQ4SYJ4RX","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"LOE46ZGD","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:680c07b2f66319e796d805caa281e91f6d5a49f9079d36dc956d632a43b3bde7","target":"graph","created_at":"2026-05-18T01:30:32Z","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":"Although extensively investigated, the capacity of the two-hop half-duplex (HD) relay channel is not fully understood. In particular, a capacity expression which can be evaluated straightforwardly is not available and an explicit coding scheme which achieves the capacity is not known either. In this paper, we derive a new expression for the capacity of the two-hop HD relay channel based on a simplified converse. Compared to previous results, this capacity expression can be easily evaluated. Moreover, we propose an explicit coding scheme which achieves the capacity. To achieve the capacity, the","authors_text":"Nikola Zlatanov, Robert Schober, Vahid Jamali","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-10-12T09:17:08Z","title":"On the Capacity of the Two-Hop Half-Duplex Relay Channel"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03191","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":"sha256:26b1f056af944c05cdb58ee27317a050f2d0d0f1e5671c34303046e4372b7f92","target":"record","created_at":"2026-05-18T01:30:32Z","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":"b17181d69f27b07e94eb02e519ed653fd8b55ff533a9abc6b903d703139705dc","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-10-12T09:17:08Z","title_canon_sha256":"03ee88a84e7ed4054c9c98f415f8329a0a79d7e7e4055cbe80d4b0e421a9a252"},"schema_version":"1.0","source":{"id":"1510.03191","kind":"arxiv","version":1}},"canonical_sha256":"5b89cf64c3872584f237be7e1fbe0e6b4af59c6bae5d928255d88dda462954f7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5b89cf64c3872584f237be7e1fbe0e6b4af59c6bae5d928255d88dda462954f7","first_computed_at":"2026-05-18T01:30:32.514985Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:32.514985Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8mdKMcWGHWcJpsnF2SD7TJKlhRKLM0CP3JkqZhvG8y7veFL26Jx5ygp56pFGqZzAe/A4w8ScnAGumWjTgbliDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:32.515681Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.03191","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:26b1f056af944c05cdb58ee27317a050f2d0d0f1e5671c34303046e4372b7f92","sha256:680c07b2f66319e796d805caa281e91f6d5a49f9079d36dc956d632a43b3bde7"],"state_sha256":"773ffc9a46951646243230457cb7ad38eacc8d6e21a6877c77cbcca9d4c4eca9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q9T7DHCk5l/53rbXNrzYnH+fHnYxd/NfxvSl/n9pGO0R2FfTi7rMxW1jXkGrCTB9LHBnCgCx5U/gw2AjAbxpAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T22:32:57.254585Z","bundle_sha256":"420f90e72e32460c81bcc3e7d95da4f50b5e12484c83a45f6fba7b5d57fcc113"}}