Why Dark Matter Is Not Needed for Galactic Rotation Curves

The dark-matter hypothesis exists to explain flat rotation curves. It posits invisible mass — about five times more than visible mass — distributed in a halo around each galaxy. Nobody has detected a dark-matter particle directly.

The explanation: the rotation curves are flat because the tension field provides a residual acceleration below the transition scale a₀ = cH₀/(2π). Below a₀, the Newtonian contribution fades and the topology takes over. The field lines must close. The closure provides the residual acceleration. The stars are held not by invisible mass but by the substrate’s own coherence. No new particles. No new fields. No new free parameters beyond the axioms.

The transition scale a₀ = cH₀/(2π) is derived from the closure geometry (4.3) and matches the empirical value to within ≈8%. The phenomenology derived from the transition scale is structurally identical to Modified Newtonian Dynamics (MOND, Milgrom 1983). The argument provides a candidate theoretical foundation for MOND — something MOND has lacked. This is a downstream observation, not an input: the argument derives the transition from the tension field, and the result matches MOND. It also inherits MOND’s known challenges at larger scales: the cluster mass discrepancy (KS-40) and the difficulty of reproducing structure formation without cold dark matter (KS-41).

7.1 — What the argument predicts

Flat rotation curves. v² ≈ √(GM × a₀) at r > rₜ. The tension field holds the outer stars. Status: DERIVED (conditional on the transition scale).

Tully-Fisher. v⁴ = GM × a₀ ∝ M. Fourth-power law. Status: DERIVED (conditional on the transition scale).

The radial acceleration relation. In the transition region, the observed acceleration g_obs relates to the Newtonian acceleration g_bar. The empirical McGaugh relation (2016) is g_obs = g_bar / (1 − e^{−√(g_bar/a₀)}). The argument suggests such a smooth interpolation should exist, determined by the record-density distribution in the transition region; the specific interpolation function has not been derived from the axioms. Status: CONJECTURAL FORM, not yet derived (KS-43).

Galaxy cluster dynamics. The same tension field operates at cluster scales. Not yet computed. Status: UNTESTED (KS-40).

Large-scale structure formation. Not yet computed in AP17; addressed structurally in AP21. Status: UNTESTED here (KS-41). The hardest test.