This work presents a geometric inverse formulation of the Baryonic Tully–Fisher Relation (BTFR) and demonstrates that the observed BTFR slope directly constrains the baryonic size–mass relation of disk galaxies.Under Newtonian disk equilibrium, a tight BTFR with slope n requires the baryonic size–mass slope to satisfy:β = (n − 2) / nFor the observationally measured range n ∈ 3.5, 4.0, this implies β ∈ 0.43, 0.50. The framework is parameter-free and does not assume a specific cosmological model.The study further derives a geometric scatter floor for the BTFR, showing that intrinsic velocity dispersion (~0.09–0.10 dex) arises naturally from structural size dispersion, independent of detailed galaxy formation physics.The framework is explicitly falsifiable and provides observational tests across redshift, galaxy morphology, and future HI surveys (e.g., WALLABY, MHONGOOSE). The results reinterpret the BTFR not merely as a consequence of galaxy structure, but as a constraint on it.This manuscript is released as Version 2.0 (February 2026).
Alim ul haq khan (Wed,) studied this question.