This work applies the Sobolev–Ozok Lattice (SOL) model, a discrete Planck-scale spacetime framework, to the baryonic Tully–Fisher relation (BTFR) observed in rotationally supported galaxies. In the SOL approach, large-scale gravitational dynamics emerge from coherence corrections to the Newtonian potential, without introducing dark matter or empirical tuning parameters. A specific coherence mode with index k = 2 produces a scale-invariant, logarithmic correction to the gravitational potential at large radii. This term naturally yields the observed flattening of galaxy rotation curves and predicts a BTFR slope of approximately four from first principles. Using the SPARC database of 175 disk galaxies, we test the SOL prediction against multiple velocity definitions, finding excellent agreement with low scatter and high coefficient of determination values. The analysis includes regression fits, residual studies, and cross-velocity comparisons. The results demonstrate that the SOL framework can account for the BTFR and the shape of galaxy rotation curves in a parameter-free manner, offering a viable alternative to both dark matter halo models and modified gravity theories such as MOND. This dataset and code package provide the numerical results, figures, and plotting scripts necessary to reproduce all analyses in the paper. Decleration of Tools Used: This paper was prepared and formatted using Overleaf (LaTeX editor). Text refinement and language polishing were assisted by Overleaf AI Editor. all scientifit content, derivations, and conclusions are original and autored by the undersigned. This paper is part of the Sobolev–Ozok Lattice (SOL) research program. Project webpage (papers, figures, updates): https://ozokozcasol.github.io/Sobolev-Ozok-Lattice/