The fourth QGEFT manuscript established a narrow but nontrivial Phase 4 result: on a frozen Higgs-condensed random graph background, a Wilson-fermion sector develops a sharply Yukawa-sensitive onset window when the bare mass is tuned near a Wilson-critical band. The immediate objection is that this onset might be an artifact of the chosen shell geometry rather than a robust property of the fermion sector. In particular, the production observable in paper4 uses topology-only breadth-first shells on the graph. The present paper addresses that objection directly by performing a metric-blindness test on the same frozen background and over the same focused Yukawa window. Using the giant connected component of the N=256 Phase 3 snapshot `phase3ₚrobeN256ₘ01ₖ030T020. json`, we compare four inequivalent shell metrics for the graph-local effective mass proxy m₄₅₅= (0) /G (1): the original topological shells, a weighted shortest-path metric built from the effective Phase 4 hopping strengths, a rank-based shortest-path metric that discards all absolute edge scales, and a thresholded binarized support graph. The central result is mixed but scientifically useful. The topological benchmark reproduces the previously reported sharp onset over y0. 50, 0. 60. A weighted metric also shows a clear delayed light-to-heavy transition in the same window, although on a different numerical scale. A rank-based metric strongly compresses the absolute gap values, but it still turns on in the upper part of the same Yukawa interval. By contrast, the default aggressive thresholded metric at quantile q=0. 75 over-prunes the graph near the source shell and leaves the onset unresolved. The narrow conclusion is therefore neither trivial success nor complete universality. The onset is not confined to one shelling prescription; it survives under materially different weighted and rank-based definitions of graph distance on the same frozen geometry. At the same time, not every binarized metric is admissible, and the present evidence does not yet justify the stronger claim that the onset is invariant under all shell constructions. The proper interpretation is that the Phase 4 Yukawa onset passes a first meaningful metric-blindness test and is therefore less likely to be a one-metric artifact, but a full universality-class statement still requires broader ensemble averaging and threshold-systematics studies.
Yaniv Cohen (Thu,) studied this question.