Structural Fixed-Point Theory of Disk Galaxies: Geometric Cancellation, Scatter Floor, and Acceleration Convergence in the Baryonic Tully–Fisher Relation

This work presents a structural equilibrium explanation of the Baryonic Tully–Fisher Relation (BTFR) using Newtonian disk dynamics combined with empirical size–mass scaling from the SPARC sample.We demonstrate that:(1) The BTFR slope emerges from geometric cancellation under exponential disk equilibrium.(2) The intrinsic scatter floor (~0.09 dex) arises inevitably from structural dispersion in disk scale length.(3) Structural regulation is strongly mass-dependent and dominates low-mass galaxy scatter.(4) The galactic acceleration scale (~10⁻¹⁰ m s⁻²) emerges as a stability-driven dynamical fixed point in stellar-dominated disks.The results suggest that the BTFR and the acceleration scale are manifestations of structural self-organization in rotating disks rather than modifications of gravity.