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Self-similar counterexamples to three conjectures of Lorentz

Yimin Zhong

Palomar Registrypalomar/PALOMAR-2026-10-29-000002Oct 29, 2026math.CAscore 0

Three continuous counterexamples in uniform polynomial approximation: a nonodd function whose best approximants all vanish at zero, a nonodd function with plateaus at degrees (2k+1,2k+2), and a noneven function with plateaus at degrees (2k,2k+1). Exact algebraic certificates, analytic contact persistence, and cubic self-similarity prove all three results. This repository contains the substantive formalization and formalizes the owner-supplied mathematical manuscripts.

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