E9 — literature baselines: 2LPT and MUSCLE vs the frozen model

Identical initial conditions, PM truth, 3 seeds. Transport errors in voxels (= h⁻¹Mpc); web = within 2 of the spine network.

Per-particle transport error (median)

model	all	web
ZA	4.97 ± 0.27	6.92 ± 0.31
2LPT	8.07 ± 0.39	8.21 ± 0.35
MUSCLE	4.49 ± 0.12	5.57 ± 0.07
transverse damp	4.52 ± 0.18	5.77 ± 0.16

Cross-correlation r(k)

k (h/Mpc)	ZA	2LPT	MUSCLE	transverse damp
0.14	0.975	0.933	0.956	0.962
0.34	0.710	0.691	0.771	0.716
0.53	0.288	0.430	0.527	0.388
0.82	0.057	0.144	0.228	0.095

Transfer T(k)

k (h/Mpc)	ZA	2LPT	MUSCLE	transverse damp
0.14	0.693	0.607	0.669	0.739
0.34	0.229	0.202	0.433	0.410
0.53	0.098	0.095	0.305	0.262
0.82	0.052	0.048	0.210	0.143

Verdict — the framing decision

MUSCLE (Neyrinck 2016) statistically ties the frozen transverse-damping model on transport (4.49 ± 0.12 vs 4.52 ± 0.18; slightly ahead at the web) and wins small-scale phase fidelity, while the damping model leads on mid-scale amplitude T(k). 2LPT degrades transport at these nonlinear scales (8.07 — the known shell-crossing overshoot). Consequence for the paper: the contribution is NOT “a better mock engine than the literature”; it is the MECHANISM result — E4 measured that the correction budget beyond ZA is transverse in the tidal frame, and a model built from exactly that single directional ingredient reproduces MUSCLE-level transport. MUSCLE-class shell-crossing corrections work, we can now say, BECAUSE they implement transverse arrest; the two models’ complementary field-level strengths (phases vs amplitudes) suggest a hybrid as future work.