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It can be shown that the total number of solutions in $[n]$ to the Sidon equation is $n^3/12 + O(n^2)$ and so, trivially, $AR_{X+Y = Z + T}^k (n) \\leq n^3 /12 + O (n^2)$. We improve this upper bound to \\[ AR_{X+Y = Z+ T}^k (n) \\leq \\left( \\frac{1}{12} - \\frac{1}{24k} \\right)n^3 + O_k(n^2) \\] for all $n \\geq k \\geq 4$. Furthermore, we give an explicit $k$-coloring of $[n]$ with more rainbow solutions to the Sidon equ"},"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":"1808.09846","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-08-29T14:21:04Z","cross_cats_sorted":[],"title_canon_sha256":"0e0b73ae3b332ab784309d2f9dacf869f700eefc3d66b92dd72e815e760e9b77","abstract_canon_sha256":"2dbc8915e0ad70c6779ffa3b12a5310356a6236326caae035c23b7654a43d03f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:54.277545Z","signature_b64":"lDhZBTsLol2JbK85Ji/Roro9rxekb34KDCVttmFKJmmEihmXvPPKGoDcvUUY+To4NJfULBjk8n18L4P7qUczBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b3cc246de5af5ea5206ed92d7651349ee00a1df65d40708a3e298b4fdb77db19","last_reissued_at":"2026-05-18T00:06:54.277072Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:54.277072Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Anti-Ramsey Problem for the Sidon equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Craig Timmons, Vladislav Taranchuk","submitted_at":"2018-08-29T14:21:04Z","abstract_excerpt":"For $n \\geq k \\geq 4$, let $AR_{X + Y = Z + T}^k (n)$ be the maximum number of rainbow solutions to the Sidon equation $X+Y = Z + T$ over all $k$-colorings $c:[n] \\rightarrow [k]$. It can be shown that the total number of solutions in $[n]$ to the Sidon equation is $n^3/12 + O(n^2)$ and so, trivially, $AR_{X+Y = Z + T}^k (n) \\leq n^3 /12 + O (n^2)$. We improve this upper bound to \\[ AR_{X+Y = Z+ T}^k (n) \\leq \\left( \\frac{1}{12} - \\frac{1}{24k} \\right)n^3 + O_k(n^2) \\] for all $n \\geq k \\geq 4$. 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