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What is the critical value of $C_0$ such that $C(C_0)$ first equals $C(\\infty)$? This is a long-standing open problem posed by Cover and named \"The Capacity of the Relay Channel,\" in $Open \\ Problems \\ in \\ Communication \\ and \\ Computation$, Springer-Verlag, 1987. In this paper, we answer this question in the Gaussian case and show that $C(C_0)$ can not equal to $C(\\infty)$ unless $C_0=\\infty$"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1701.02043","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-01-09T01:11:12Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"d4934997ef79af15faf536efcff07495766ffae254bba3640061f83f8e820903","abstract_canon_sha256":"701f23b7bada1ac8ab646429e993ba73749bb66d02926d978b03c6e39ee98bb3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:57.178535Z","signature_b64":"JCHtqFhLMtspZ+E5x2vVetg9kqGQdBedNFo7hdVn5Req51Qqg10iyEypJndALXQ4gwLy1dkevDfiZNKcMfANAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3fa0c1152d0f3f6a1433ec9290f699711f53b5ca7b181c38a9bfa3c82b74fc71","last_reissued_at":"2026-05-18T00:03:57.177814Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:57.177814Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"\"The Capacity of the Relay Channel\": Solution to Cover's Problem in the Gaussian Case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Ayfer Ozgur, Leighton Pate Barnes, Xiugang Wu","submitted_at":"2017-01-09T01:11:12Z","abstract_excerpt":"Consider a memoryless relay channel, where the relay is connected to the destination with an isolated bit pipe of capacity $C_0$. 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