{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:3N7BNGZFMXU4YAL3MOIS2VDBAI","short_pith_number":"pith:3N7BNGZF","canonical_record":{"source":{"id":"1104.1057","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-04-06T11:08:31Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"5bd8125c0502761c8083995c9cfca7aa4f228f6e7a89a934b1944f72177beb51","abstract_canon_sha256":"959360fa9261b6722c8c8672bc55467e981d9d4d4a3ebfdaadb1ad1960de1326"},"schema_version":"1.0"},"canonical_sha256":"db7e169b2565e9cc017b63912d5461020abc52a0622fd2b3efab0d6269dc6f56","source":{"kind":"arxiv","id":"1104.1057","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.1057","created_at":"2026-05-18T00:59:10Z"},{"alias_kind":"arxiv_version","alias_value":"1104.1057v1","created_at":"2026-05-18T00:59:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.1057","created_at":"2026-05-18T00:59:10Z"},{"alias_kind":"pith_short_12","alias_value":"3N7BNGZFMXU4","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"3N7BNGZFMXU4YAL3","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"3N7BNGZF","created_at":"2026-05-18T12:26:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:3N7BNGZFMXU4YAL3MOIS2VDBAI","target":"record","payload":{"canonical_record":{"source":{"id":"1104.1057","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-04-06T11:08:31Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"5bd8125c0502761c8083995c9cfca7aa4f228f6e7a89a934b1944f72177beb51","abstract_canon_sha256":"959360fa9261b6722c8c8672bc55467e981d9d4d4a3ebfdaadb1ad1960de1326"},"schema_version":"1.0"},"canonical_sha256":"db7e169b2565e9cc017b63912d5461020abc52a0622fd2b3efab0d6269dc6f56","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:59:10.384587Z","signature_b64":"oH+lo6oWMyId/p5w/pT1KgVgOCvW7a+qpkAQT6GbZ5EsG/CJs87YgUUOU7nPg77St4FdbwYVh2VpMNTuM0uMDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"db7e169b2565e9cc017b63912d5461020abc52a0622fd2b3efab0d6269dc6f56","last_reissued_at":"2026-05-18T00:59:10.383849Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:59:10.383849Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1104.1057","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":"2026-05-18T00:59:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i0d0xHlu258GPtrW60IN/3G2vj5ZLBFjFZaRSkj5x5UJPBRG+Y1B69vEkcIlUrlm7J6DmyVwasWLHMy5A9TxDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T21:32:08.917838Z"},"content_sha256":"2d2927604fc543ab3c987a9d7036212ab4476a1e22bbb9624973701de21cb5d6","schema_version":"1.0","event_id":"sha256:2d2927604fc543ab3c987a9d7036212ab4476a1e22bbb9624973701de21cb5d6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:3N7BNGZFMXU4YAL3MOIS2VDBAI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bounds on the Capacity of the Relay Channel with Noncausal State at Source","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Abdellatif Zaidi, Luc Vandendorpe, Pablo Piantanida, Shlomo Shamai (Shitz)","submitted_at":"2011-04-06T11:08:31Z","abstract_excerpt":"We consider a three-terminal state-dependent relay channel with the channel state available non-causally at only the source. Such a model may be of interest for node cooperation in the framework of cognition, i.e., collaborative signal transmission involving cognitive and non-cognitive radios. We study the capacity of this communication model. One principal problem is caused by the relay's not knowing the channel state. For the discrete memoryless (DM) model, we establish two lower bounds and an upper bound on channel capacity. The first lower bound is obtained by a coding scheme in which the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.1057","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":"2026-05-18T00:59:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EFSd+O1rCKWoWpBS4gpvA9t0sLbsudHYKU4eAsdCiNml9Ni6zkcP0qhex4xJik/sTxmeaPPx+nkh18DEMUW+Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T21:32:08.918499Z"},"content_sha256":"a9e0bb82e20daf064d3d8ffbf9b8193abbfd51d1e533f2c39759eadf80b9a795","schema_version":"1.0","event_id":"sha256:a9e0bb82e20daf064d3d8ffbf9b8193abbfd51d1e533f2c39759eadf80b9a795"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3N7BNGZFMXU4YAL3MOIS2VDBAI/bundle.json","state_url":"https://pith.science/pith/3N7BNGZFMXU4YAL3MOIS2VDBAI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3N7BNGZFMXU4YAL3MOIS2VDBAI/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":"2026-05-25T21:32:08Z","links":{"resolver":"https://pith.science/pith/3N7BNGZFMXU4YAL3MOIS2VDBAI","bundle":"https://pith.science/pith/3N7BNGZFMXU4YAL3MOIS2VDBAI/bundle.json","state":"https://pith.science/pith/3N7BNGZFMXU4YAL3MOIS2VDBAI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3N7BNGZFMXU4YAL3MOIS2VDBAI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:3N7BNGZFMXU4YAL3MOIS2VDBAI","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":"959360fa9261b6722c8c8672bc55467e981d9d4d4a3ebfdaadb1ad1960de1326","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-04-06T11:08:31Z","title_canon_sha256":"5bd8125c0502761c8083995c9cfca7aa4f228f6e7a89a934b1944f72177beb51"},"schema_version":"1.0","source":{"id":"1104.1057","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.1057","created_at":"2026-05-18T00:59:10Z"},{"alias_kind":"arxiv_version","alias_value":"1104.1057v1","created_at":"2026-05-18T00:59:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.1057","created_at":"2026-05-18T00:59:10Z"},{"alias_kind":"pith_short_12","alias_value":"3N7BNGZFMXU4","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"3N7BNGZFMXU4YAL3","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"3N7BNGZF","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:a9e0bb82e20daf064d3d8ffbf9b8193abbfd51d1e533f2c39759eadf80b9a795","target":"graph","created_at":"2026-05-18T00:59:10Z","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 consider a three-terminal state-dependent relay channel with the channel state available non-causally at only the source. Such a model may be of interest for node cooperation in the framework of cognition, i.e., collaborative signal transmission involving cognitive and non-cognitive radios. We study the capacity of this communication model. One principal problem is caused by the relay's not knowing the channel state. For the discrete memoryless (DM) model, we establish two lower bounds and an upper bound on channel capacity. The first lower bound is obtained by a coding scheme in which the ","authors_text":"Abdellatif Zaidi, Luc Vandendorpe, Pablo Piantanida, Shlomo Shamai (Shitz)","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-04-06T11:08:31Z","title":"Bounds on the Capacity of the Relay Channel with Noncausal State at Source"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.1057","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":"sha256:2d2927604fc543ab3c987a9d7036212ab4476a1e22bbb9624973701de21cb5d6","target":"record","created_at":"2026-05-18T00:59:10Z","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":"959360fa9261b6722c8c8672bc55467e981d9d4d4a3ebfdaadb1ad1960de1326","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-04-06T11:08:31Z","title_canon_sha256":"5bd8125c0502761c8083995c9cfca7aa4f228f6e7a89a934b1944f72177beb51"},"schema_version":"1.0","source":{"id":"1104.1057","kind":"arxiv","version":1}},"canonical_sha256":"db7e169b2565e9cc017b63912d5461020abc52a0622fd2b3efab0d6269dc6f56","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"db7e169b2565e9cc017b63912d5461020abc52a0622fd2b3efab0d6269dc6f56","first_computed_at":"2026-05-18T00:59:10.383849Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:59:10.383849Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oH+lo6oWMyId/p5w/pT1KgVgOCvW7a+qpkAQT6GbZ5EsG/CJs87YgUUOU7nPg77St4FdbwYVh2VpMNTuM0uMDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:59:10.384587Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.1057","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2d2927604fc543ab3c987a9d7036212ab4476a1e22bbb9624973701de21cb5d6","sha256:a9e0bb82e20daf064d3d8ffbf9b8193abbfd51d1e533f2c39759eadf80b9a795"],"state_sha256":"cb632f2aee9b1980e901dc66e29042123f4bba15aaa4b1d3d2082ece29446984"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C/AmmTB524vTjrPH+z2DfG79kET+RRfEk+xYkw1YaxVr94EQRXQMWM7UkgdGrbCUeMC6rWiIFYvCDOBio+MkDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T21:32:08.922365Z","bundle_sha256":"2c8f0aa3b4955413957a55a9e5cc8bdc02a73459c27b5c513435dd3a2cf99008"}}