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For a given finite $R \\subset \\mathbb{Z}^+$, the clock network $N_n(R)$ has edge $v_iv_k$ if and only if $k>r$ and $k-i \\in R$. We show that the information flow problem on $N_n(\\{1,2, \\ldots ,r\\})$ can be solved for all $n \\geq r$. We also show that for any finite $R$ such that $\\gcd(R)=1$ and $r = \\max(R)$, we show that the information flow problem can be solved on $N_n(R)$ fo"},"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":"1605.05391","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-05-17T22:44:20Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"ad5fedf7bf8e1ea8b8c47c36f416c3f5ec9476e67efce3d4e0f3713a37718eeb","abstract_canon_sha256":"4537643a6530a0a99df43f1f087cbd0482f21d07d904fd1a2527632520fe97ab"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:14:35.137050Z","signature_b64":"vAmkHIeKArZnkCWHL6Z1lDvNhS8DsuNPWudm4kCvVoSziFTOl3nHwSp6VihPYO9Tz/FKIJlZHVOAmjYcpfk+Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c40e16bd1a4e56acd57ba36495b37303ea09d245e24f53b0ebf46d1ea42358c5","last_reissued_at":"2026-05-18T01:14:35.136283Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:14:35.136283Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Information Flow Problem on Clock Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Ross Atkins","submitted_at":"2016-05-17T22:44:20Z","abstract_excerpt":"The information flow problem on a network asks whether $r$ senders, $v_1,v_2, \\ldots ,v_r$ can each send messages to $r$ corresponding receivers $v_{n+1}, \\ldots ,v_{n+r}$ via intermediate nodes $v_{r+1}, \\ldots ,v_n$. 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