The Minimum Distance of Unshifted Spherical Fibonacci Lattices

For every Fibonacci number N=F_n>=2, we prove that the unshifted rational spherical Fibonacci lattice has least Euclidean distance2/sqrt(N), uniquely attained by the north pole and the next point. This answers the separation question in Brauchart's contribution to Oberwolfach Report40/2012,p2438 (UnsolvedMath OWR-12012-001). The proof combines a global Lambert-map distance inequality with Zaremba's classical formula for the Fibonacci lattice figure of merit. More generally, a rational N-point Lambert lift with Zaremba index rho>=N/4 has exactly this minimum; rho>N/4 also gives uniqueness. The construction includes a pole and uses the exact rational Fibonacci angle; the claim does not concern the different shifted irrational Fibonacci spiral, discrepancy, or optimal packing among all point sets. The four-page written proof is accompanied by symbolic and integer regression checks and separately labelled floating-point diagnostics. This is a self-audited, unrefereed preprint prepared with AI assistance, without independent review, formal proof-assistant verification, or an absolute-priority claim.