Topological Phase-Locking and the Dynamical Origin of Galactic Acceleration Scales

We investigate the dynamical origin of the universal galactic acceleration scale a0 withintheframeworkofq-deformedEffectiveFieldTheory(q-EFT).Startingfromanonlinearback-ground field equation with an axisymmetric soliton ansatz γϕ= A(r) sinnθeiWϕ, we deriveanalytically the saturation amplitude A2∞ = (ξ2Φ2q/λ)·(I2n+1/I4n+1) and a characteristicequilibrium radius r∗= W√2/(ξΦq) from the equatorial pressure balance condition. Theseresults establish Πsat as a dynamical vacuum expectation value rather than a phenomeno-logical constant.We then introduce a quantum symmetry conjecture: requiring the topological field to beconsistent with angular momentum eigenstates YWW enforces n= W. Under this conjecture,the fractional rotational energy takes the purely geometric form ϵ(W) = (2W+1)/(4W+1),which modulates the effective acceleration scale as a0(W) = a(∞)0 4W/(4W + 1). Thisfunction saturates to a constant for large topological charge W and systematically decreasestoward zero for small W. If W ∝√Mb, the model predicts a mass-dependent drift of a0that qualitatively accounts for the systematic residuals of MOND in low-mass dwarf galaxysamples without introducing additional free parameters beyond a dimensionless mass-chargecoupling β ∼O(1). Quantitative validation against the full SPARC sample is deferred to acompanion paper.