Rational Harmonic Arithmetic in Base-7 (RHA-7): Coherence Validation, Constant Alignment, and Harmonic Prediction of Planet X

This document validates the Rational Harmonic Arithmetic system in base 7 (RHA-7) by testing its predictive coherence across updated physical constants, particle mass ratios, and trans-Neptunian orbital parameters. Assuming that universal constants align on a discrete logarithmic spectrum of the form x = 7^n, RHA-7 predicts known values with minimal deviation where experimental precision is high (e.g., electron-to-proton mass ratio, neutron-to-proton ratio, pion mass, Makémaké’s orbit). It also redefines the Planck constant as h7 = (1/2) × 7^(-39), and introduces a speculative extrapolation: the harmonic prediction of a trans-Neptunian Planet X with semi-major axis a ≈ 7^18.861 ≈ 120,588 AU. The study highlights that high deviations often correlate with unstable or evolving reference data (e.g., W, Z, top quark masses), reinforcing RHA-7’s structural consistency. This extension confirms that the harmonic base-7 alignment persists across both fundamental constants and orbital dynamics, and may reflect a deeper numerical structure behind physical parameters. Original reference: https://doi.org/10.5281/zenodo.15379622