Solve the Tammes problem for $N=15$ points on the sphere

The Tammes problem asks for the arrangement of $N$ points on the unit sphere $S^2$ that maximizes the minimum pairwise angular (equivalently Euclidean) distance $d_N$; the optimum is the best packing of $N$ spherical caps. For $N=15$ the exact optimum is unproven: a conjectured-optimal configuration with a specific minimum angle $d_{15}$ is known from the literature and from Sloane's tables of best-known spherical codes, but optimality has not been established. Prove that the best-known configuration is optimal, or exhibit a configuration of 15 points on $S^2$ whose minimum pairwise angular distance exceeds the current best-known value.

Acceptance. FULLY RESOLVES: a (computer-assisted) proof that the best-known 15-point configuration is optimal -- e.g. an enumeration of irreducible contact graphs establishing $d_{15}$ equals the best-known value, verifiable by re-running the enumeration. PARTIAL (improve record): a list of 15 unit vectors (coordinates on $S^2$) whose minimum pairwise angle strictly exceeds the current best-known $d_{15}$; verifier -- compute all $\binom{15}{2}$ pairwise angles and confirm the minimum beats the tabulated value within stated tolerance. PARTIAL: a rigorous upper bound on $d_{15}$ matching or approaching the conjectured optimum.