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All current versions of the UTI framework papers are available here: https://linktr.ee/uti_papers

VERSION 2.6

Author: Christopher Gu [ georgeguiscool@gmail.com ]

Software Developer based in El Monte, California, USA

April 2026

Abstract

We propose a low-acceleration vacuum impedance susceptibility, motivated by the Universal Topological Impedance framework v2.6 [1], that yields flat galaxy rotation curves and a MOND-like baryonic Tully-Fisher relation without dark matter. The core new ingredient is a susceptibility function mu that modifies the gravitational Poisson equation to div[mu(|grad Phi|/a_0) grad Phi] = 4 pi G rho, analogous to how a dielectric susceptibility modifies the electromagnetic field equation in a medium. At high accelerations (|grad Phi| >> a_0), mu -> 1 and standard Newtonian gravity is recovered. At low accelerations (|grad Phi| << a_0), mu -> |grad Phi|/a_0 and gravity is enhanced. The transition scale a_0 = c H_0 / (2 pi) ~ 1.05 x 10^-10 m/s^2 follows from the graviton mode cutoff at the de Sitter horizon: the Rindler frequency omega = g/c gives a graviton wavelength lambda = c^2/g (established physics), and the transition occurs when lambda equals the horizon circumference 2 pi c / H_0 (one new assumption). Flat rotation curves follow with v = (G M a_0)^(1/4), predicting the Milky Way flat velocity from baryonic mass alone (~173 km/s for M ~ 6.5 x 10^10 M_sun from Gaia DR3, observed 200-220 km/s). The baryonic Tully-Fisher relation M proportional to v^4 follows as a direct consequence with normalization set by H_0. A covariant AQUAL-style action with conformal scalar coupling produces lensing enhancements of 5x-15x in the deep-MOND regime; the Bullet Cluster lensing offset is phenomenologically reproduced with a fitted amplification factor alpha ~ 15 in an impedance-memory mechanism with relaxation time tau = 1/H_0. The framework introduces no fitted galactic-scale parameter in the rotation-curve sector beyond the chosen susceptibility interpolation mu(x) = x/(1+x) and the horizon-fixed scale a_0 = c H_0 / (2 pi); the Bullet Cluster extension adds the extracted amplification factor alpha and the postulated relaxation time tau. UTI v2.6 derives the microscopic trace-channel scalar eta (f_0(500)/sigma, ~450 MeV, range ~0.44 fm) at nuclear scales by canonical Hubbard-Stratonovich localization of the QCD trace-trace correlator; Impedance Contrast Theory supplies the macroscopic vacuum response at galactic scales. The connection is motivational rather than derivational: the UTI v2.6 scalar is exponentially suppressed beyond ~0.4 fm and does not propagate to galactic scales, and the galactic susceptibility mu is a new phenomenological ingredient motivated by the same trace-channel impedance interpretation. No modification of macroscopic general relativity is proposed or implied.