Vector-valued smoothing for finite Sidon sets

Let $F(N)$ denote the largest cardinality of a Sidon subset of $\{0,1,\dots ,N-1\}$. We prove $$F(N)\le N^{1\mathrm{/}2}+0.9435N^{1\mathrm{/}4}+O(1)\mathrm{.}$$ The argument uses a vector-valued convolution inequality in which several smoothing kernels cooperate to produce a boundary majorant while their $L^2$ energies are averaged. For fixed kernels and mixing weights, the boundary optimization is a strictly convex quadratic program with an explicit dual. An eight-kernel numerical candidate is converted into a finite rational certificate and verified using exact arithmetic only.