Maximum Sidon sets in {1,...,N}: extend exact values of h(N) and sharpen the N^(1/4) constant (Erdos #30)

A Sidon set is a set of integers in which all pairwise sums a+b (a<=b) are distinct (equivalently, all pairwise differences are distinct). Let h(N) be the maximum size of a Sidon set contained in {1,...,N}. This is exactly the optimal Golomb ruler problem: a Sidon set {0=a_1<...<a_k} in {0,...,L} is a Golomb ruler with k marks and length L, and h(N) is the largest k for which an optimal ruler has length <= N-1. Erdos #30 asks whether h(N) = N^(1/2) + O_eps(N^eps) for every eps>0. That asymptotic question cannot be settled by a finite computation, but two concrete sub-questions are squarely computational: (a) EXACT VALUES. Extend the sequence of exact values h(N) -- equivalently optimal Golomb ruler lengths (OEIS A003022) -- beyond the currently tabulated range, each with an explicit witness Sidon set and a certificate of optimality (an exhaustive-search log, or a proof that no larger Sidon set fits in {1,...,N}). (b) EXPLICIT CONSTANT. Lower the best explicit constant c in the upper bound h(N) <= N^(1/2) + c*N^(1/4) + O(1).

Acceptance. FULLY RESOLVES (the parent asymptotic question, out of reach of pure computation): a proof of h(N) = N^(1/2)+O_eps(N^eps). COMPUTATIONAL PROGRESS (in scope): (a) an exact value h(N) for some N beyond the currently tabulated optimal-Golomb-ruler range, delivered as an explicit witness Sidon set PLUS a machine-verifiable optimality certificate; or (b) a verified explicit constant c<1 with h(N) <= N^(1/2)+c*N^(1/4)+O(1). Every submission must include the witness set/ruler and a verification script that checks the Sidon property (all pairwise sums distinct) and re-confirms the claimed bound.