Linearly stable free-fall periodic orbits in the planar three-body problem, and new lowest-energy configurations for the Thomson problem in a disk (preprints, data and code)

Two preprints with their data and code. (1) Linearly stable free-fall periodic orbits in the planar three-body problem: seven collisionless, non-collinear free-fall (brake) periodic orbits with three pairwise-distinct masses and zero angular momentum that are linearly stable, found by mass continuation of the Li & Liao (2019) free-fall families and verified with an independent 60-80-digit Taylor integrator; initial conditions to 40 digits. (2) New lowest-energy configurations for the Thomson problem in a disk: lower energies than all published values for N = 650, 700, 800, 900, 1000, 6250, 7500, 8750 and 10000, each with a rigorous ball-arithmetic upper bound for an exactly feasible configuration. Files: the two PDFs, data_records.zip (certified configurations, orbit initial conditions, LaTeX sources, figures) and code.zip (search code and the independent verifiers). Version 2: N = 2000 withdrawn (P. Amore reported a lower unpublished value); last two digits of the S4 initial conditions corrected after an independent check by I. Hristov, who also confirmed the linear stability of S2 and S4.