E8 — field-level fidelity (the mock-catalogue criterion)

Full-set density fields vs PM truth, 3 seeds, 1 Mpc/h voxels. r(k): phase/structure fidelity (1 = perfect); T(k): amplitude fidelity (1 = unbiased).

Cross-correlation r(k)

k (h/Mpc)	ZA	isotropic stick	transverse damp
0.06	0.997	0.991	0.997
0.09	0.993	0.970	0.989
0.14	0.975	0.890	0.962
0.22	0.924	0.730	0.901
0.34	0.710	0.374	0.716
0.53	0.288	0.089	0.388
0.82	0.057	0.008	0.095
1.26	0.005	-0.001	0.009

Transfer T(k)

k (h/Mpc)	ZA	isotropic stick	transverse damp
0.06	0.920	0.683	0.849
0.09	0.842	0.679	0.827
0.14	0.693	0.593	0.739
0.22	0.469	0.458	0.601
0.34	0.229	0.300	0.410
0.53	0.098	0.222	0.262
0.82	0.052	0.187	0.143
1.26	0.042	0.172	0.079

Verdict (H-field)

Supported with quantified caveats. In the nonlinear regime the transverse damping model beats ZA on both statistics (r at k=0.53: 0.388 vs 0.288; T at k=0.34: 0.410 vs 0.229) — it extends the usable k-range of the mock — while classical isotropic sticking degrades r(k) catastrophically at all k > 0.1. Costs: ~7% amplitude deficit in the largest-scale bin (0.849 vs 0.920; removable by the standard linear transfer rescaling) and a small phase cost at intermediate k (r 0.962 vs 0.975 at k=0.14). E7b: the 0.5 Mpc resolution row is now verified at n=3 (−12%, −9% on the two added seeds).