Pre-registered prediction for the Gaia DR4 wide-binary gravity test from the Entropy Potential Field Theory (EPFT)

I pre-register a quantitative prediction for the Gaia DR4 wide-binary gravity test, written before the data release scheduled for 2 December 2026. In the Entropy Potential Field Theory (EPFT), the local rate of change at a point combines a directional local part g and an isotropic cosmological background part g_b in quadrature. Attributing this total to its two contributions in an order-independent, continuous way gives a Bekenstein–Milgrom-type field equation with μ(x) = x/√(1+x²). The scale g_b = 1.6 × 10⁻¹⁰ m s⁻² (±20%) was fixed beforehand from disk-galaxy data, not from binaries. Solving the nonlinear field equation numerically for binaries in the Galactic external field (2.1 × 10⁻¹⁰ m s⁻²) and converting the result into the observable used by current analyses with a mock population, I predict, in the zones of the pre-registered DR4 protocol of Boufourou (2026): γ = G_eff/G = 1.09 (1.05–1.15) for projected separations 2–30 kAU, and γ = 1.13 (1.07–1.23) in the deep bin (g_N/a0 = 0.03–0.3). This is 0.32 on the Newton (0) – standard MOND (1) scale. EPFT also predicts an orientation signature of the external field effect (γ ≈ 1.12 for separations aligned with the projected Galactic field, ≈ 1.06 perpendicular to it). The rule is disfavoured if DR4 robustly finds γ < 1.03 or > 1.20 at 2–30 kAU, γ < 1.04 or > 1.30 in the deep bin, or an orientation dependence of the opposite sign. I disclose that one robust DR3 re-analysis (γ = 1.045 [1.025, 1.068] at 2–30 kAU; 1.11 ± 0.07 in the deep bin) already places the central test-zone prediction under mild tension, while the deep-bin prediction agrees. The package contains the PDF, all code and intermediate results; run_all.py reproduces every number.