Variable Inertia in Weak Gravitational Fields: Photometry, Structure and Kinematic Predictions for DF44, DF2 and DF4 plus a Lensing Achromaticity Test (HE0435)

We provide LSB photometry and systematic error controls for DF44/DF2/DF4 and test

a Variable Field Theory (VFT) response against Newton/MOND in three regimes (low-x

UDGs, mid-x σ, high-x lensing QC). VFT is practically identical to MOND in circular

rotation curves (same single-parameter response function), but formulated as a reciprocal

inertia interpretation:

gbar

γ(x) = gobs

gbar

, κ(x) = 1

γ(x), x=

(1)

a0

Key results: (1) DF44: Re = 18.92′′ ±0.69′′

, n ≈ 1. (2) DF2: Re,circ = 22.14′′

,

n≈0.53. (3) DF4: Re,circ ≈30.3′′

, n≈1.8. (4) HE0435: Einstein radius achromatic within

¯

|∆θ|/

θ≈1.9% (PSF/pipeline QC).

UDG-σ enforce EFE/anisotropy combination (fEFE ≲ 0.5, β ≳ +0.2) →VFT remains

possible but with reduced predictive power.