Functions and Analysis

The Exact Sidon Constant of {0, 1, 2, 3} and Its Formalization

Authors: Haoxiang Yu

We determine the exact value of the Sidon constant of the four-element set {0,1,2,3} to be 5/3. The lower bound was established by Neuwirth via an explicit family of trigonometric polynomials; we prove the matching upper bound. Our proof introduces a new method: given a point on the unit circle we construct a cubic self-inversive polynomial whose three roots lie on the unit circle, extract positive real weights from these roots, and use a weighted square-sum identity to obtain the sharp estimate. The entire proof is formalized in Lean 4 using mathlib.

Comments: 11 Pages. See https://github.com/yhx-12243/Sidon3 for formalization

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Submission history

[v1] 2026-06-03 20:02:38

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