A Zero-Parameter Prediction for the Baryonic Tully–Fisher Relation from the Golden-Ratio Gravitational Closure

The baryonic Tully–Fisher relation (BTFR), Mb ∝ V 4f , is one of the tightest empirical scalinglaws in extragalactic astronomy, yet its origin remains debated. We show that the Energy–Space–Displacement (ESD) gravitational closure—a parameterless modification of Newtonian dynamicsin which every constant is fixed by the golden ratio φ and its logarithm—yields a specific BTFRprediction with a mass-dependent prefactor G(u) that is absent in the deep-MOND limit. Testingthis prediction against 129 quality-filtered SPARC galaxies using rotation-curve-derived Newtonianaccelerations, we find: (i) the ESD achieves a residual RMS of 0.268 dex versus 0.283 dex for thedeep-MOND prediction, a 5.3% reduction in scatter with zero free parameters; (ii) the ESD meanresidual is −0.017 dex (consistent with zero bias), compared to +0.103 dex for MOND; (iii) the ESDpredicts an effective BTFR slope of α ≈ 3.84 through the mass-dependent tilt factor G(u), closerto the observed α = 3.75 ± 0.11 than MOND’s exact 4; and (iv) G correlates with baryonic mass(1.01–3.57 across the SPARC range), providing a testable surface-brightness-dependent signaturethat may help distinguish the ESD from MOND.