Extremal B_3 sets: compute the maximum size of a triple-sum-distinct set in {1,...,N} (Erdos #41)

A set A of positive integers is a B_3 set if all sums of three elements a+b+c (a<=b<=c in A) are distinct -- i.e. there are no nontrivial coincidences among triple sums (this generalizes Sidon sets, which are the B_2 case). Let F_3(N) be the maximum size of a B_3 set contained in {1,...,N}. Erdos #41 concerns infinite B_3 sets and asks whether liminf |A intersect {1,...,N}| / N^(1/3) = 0. The associated finite extremal quantity F_3(N) is, like optimal Golomb rulers for B_2, a finite constraint-satisfaction search. Computational sub-questions: (a) compute exact values F_3(N) for N as large as feasible, each with a witness B_3 set and an optimality certificate; (b) improve the best explicit upper or lower constant for the maximum B_3-set size (constructions give ~N^(1/3)); (c) tabulate F_3(N)/N^(1/3).

Acceptance. COMPUTATIONAL PROGRESS (in scope): exact values F_3(N) for a range of N, each with a witness B_3 set and an exhaustive or branch-and-bound optimality certificate; OR an improved explicit upper/lower constant for the maximum B_3-set size with a verifiable derivation; OR a table of F_3(N)/N^(1/3) over a wide range. FULLY RESOLVES: a proof settling the liminf question. Submissions must include the search code and a verifier that checks the B_3 property (all triple sums distinct) and re-confirms optimality over the claimed range.