Einstein's theory of special relativity was incomplete as originally formulated since it did not include the rotational effect described twenty years later by Thomas, now referred to as Thomas precession. Though Thomas precession has been accepted for decades, its relationship to particle structure is a recent discovery, first described in an article titled "Electromagnetic effects and structure of particles due to special relativity". Thomas precession acts as a velocity dependent counter-rotation, so that at a rotation velocity of SQRT(3)/2 c, the magnitude of precession is equal to the magnitude of rotation, resulting in an inertial frame of reference. During the last year and a half significant progress was made in determining further details of the role of Thomas precession in particle structure, fundamental constants, and the galactic rotation velocity. In this article, these discoveries are described and proofs are provided, with results matching experimentally determined values to between eight and thirteen significant digits. Among the discoveries described and proven herein are 1) the observed galactic rotation velocity and elementary particle spin interact due to Thomas precession, 2) the basis for Planck's constant and quantized energy levels is Thomas precession, 3) the fine structure constant is a function of galactic rotation velocity and the maximum value of rotation velocity minus precession velocity. Also discovered and proven is that, due to the inertial frame of reference resulting from Thomas precession, distance and time, with units meters and seconds, within three dimensional space are sufficient to describe the structure of particles and their interactions. Einstein showed that energy is dependent on frame of reference with his equation E =γ mc^2 , and he formulated E = mc^2 as rest energy. Proven herein is that particle mass and rest energy are functions of rotational velocity due to Thomas precession. These far reaching discoveries are all interrelated, and based in Thomas precession. The theory, models, and equations give results that match experimental data to very high precision.