Pre-Registered Predictions for the External Field Effect's Environmental-History Dependence

Abstract

Pre-registration No. 3 of a series (No. 1: doi:10.5281/zenodo.21893592; No. 2: doi:10.5281/zenodo.21890749). The registration text is frozen at deposit; any clarification will be issued as a separately deposited supplement, never as an edit. Rotation curves of field disk galaxies show the external field effect (EFE) of modified dynamics at 4–11σ. Velocity dispersions of ultra-diffuse galaxies in the Coma cluster, in a field ten times stronger, show no EFE at all, and simulations of UDGs inside Coma in the same framework conclude that tides cannot explain it. The deepest tidally undisturbed Milky Way satellite, Crater II, shows the EFE again. This note registers, before history-resolved data exist, one mechanism for all three: the screening response relaxes toward its instantaneous equilibrium with a memory time set by the expansion rate at the epoch, τ = α/H(z), so what a galaxy shows depends on how long it has been where it is. The window α ∈ [0.5, 2] is earned from below by a population test on eighteen cluster UDGs with measured dispersions and phase-space classifications, and bounded above by the mechanism's own testability. Six predictions are registered with stated bands (the infall clock and its sign, a bath-variability ordering, a wide-binary phase bound, an orbit-shape razor against tidal stripping, backsplash recovery, and a population discriminant), and each carries the condition under which it is false. The decisive condition is a single object: a structurally undisturbed cluster UDG resident for ≥ 8 Gyr with σ/σ_iso ≥ 0.9 falsifies the mechanism at every α. Three Coma objects and three Hydra I objects are named as the places to look, with the mechanism's number attached (0.44–0.82). On the current sample the population instrument leaves the memory hypothesis indistinguishable from the isolated null at α ≳ 0.85 and disfavours the first-infall-only alternative at ln B = −10.9. Files: the registration (PDF and Markdown), the supplementary material (assumption ledger, exhaustion table, source classes, dimensionless groups; PDF and Markdown), the companion script n3_companion.py (numpy only, under one minute) that reproduces every quantitative claim in the note's order, its printed output, and Figure 1. AI assistance was used throughout, for derivations, code, literature search and drafting, under a discipline in which every number is reproduced by the deposited script, every load-bearing citation is verified against full text, and every external suggestion is verified independently before adoption; the physical hypotheses, the decisions, and the responsibility are the author's.