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

Version 2.0 — Includes Supplementary MaterialsThis work presents a structural interpretation of the Baryonic Tully–Fisher Relation (BTFR) within the framework of Newtonian disk equilibrium and marginal stability.We demonstrate that:• The BTFR slope emerges from empirical size–mass scaling (R_d ∝ M_b^0.48) through geometric cancellation.• The intrinsic scatter floor (~0.09 dex) arises naturally from structural dispersion in disk scale length (σ_log R_d ≈ 0.18 dex).• The apparent galactic acceleration scale (~10⁻¹⁰ m s⁻²) emerges as a stability-driven fixed point under Toomre Q ≈ 1, without requiring modification of gravity.• High-redshift evolution provides a falsifiable observational discriminant between structural regulation and redshift-invariant acceleration hypotheses.Using the SPARC sample and mock JWST survey validation, this framework proposes that the BTFR represents a condition of structural self-organization in rotating stellar disks rather than a fundamental externally imposed law.The accompanying Supplementary Materials provide high-redshift predictions, mock catalog validation, and explicit observational discriminants.