Galaxy Rotation Curves from Baryonic Field Geometry

What if dark matter is not a substance but a shadow of the gravitational potential itself? We show that the discrepancy between observed and Newtonian rotation curves across 175 SPARC galaxies can be captured by a single formula involving only the baryonic gravitational potential 𝜙 and its derivatives — no dark matter, no modified force law, no free parameters per galaxy. The observed acceleration boost 𝑉obs^2 /𝑉bar^2 is empirically linear in 1/|𝜙|, with a slope that scales universally with the total baryonic mass encoded in (1/𝜙)′. This yields a one-constant model, 𝑎tot = 𝑎𝑛(1 + 𝐶/√⟨(1/𝜙)′⟩ ⋅ 1/𝜙) with 𝐶 ≈ 10e−5, that matches MOND to within a few percent on median performance — and outperforms it at mass-to-light ratios independently favored by stellar dynamics. The baryonic Tully-Fisher relation 𝑉^4 ∝ 𝑀 emerges as an unimposed consequence. The numerical coincidence 𝐶 ≈ √𝑎0 ≈ √𝑐𝐻0 hints at a cosmological origin. We do not claim finality for the formula, but for the observation behind it: the Newtonian potential field of baryonic matter already contains the information that dark matter was invented to provide.