Structural Fixed-Point Theory of Disk Galaxies: Geometric Cancellation, Scatter Floor, and Acceleration Convergence in the Baryonic Tully–Fisher Relation (Version 2.0)

This work presents a structural interpretation of the Baryonic Tully–Fisher Relation (BTFR) using the SPARC sample of 175 disk galaxies. We show that: • The BTFR slope emerges from Newtonian disk equilibrium combined with empirical size–mass scaling (R_d ∝ M_b^0.5).• The intrinsic scatter floor (~0.09 dex) arises from structural dispersion in disk scale length.• A mass-independent acceleration scale (~10^-10 m s^-2) appears as a stability fixed point under Toomre Q ≈ 1.• Structural regulation is strongest in low-mass galaxies. The results suggest that the BTFR and galactic acceleration scale reflect structural self-organization in rotating stellar disks rather than modified gravity.