E5 (H-T2) — transverse-damping adjustment vs ZA and isotropic sticking

Effective models evolved from PM initial conditions (rho_c = 5.0, calibrated on seed 1 by optimizing the ISOTROPIC competitor; 5 held-out seeds). Score: median per-particle distance to the PM-truth position at a=1 (voxels = h⁻¹Mpc), binned by distance to the web.

d to spine (vox)	ZA	isotropic stick	transverse damp	damp vs ZA	damp vs stick
0–2	6.95 ± 0.24	7.50 ± 0.10	6.46 ± 0.07	-7%	-14%
2–4	5.43 ± 0.18	6.19 ± 0.15	5.67 ± 0.14	+4%	-8%
4–8	3.74 ± 0.15	3.88 ± 0.13	3.78 ± 0.13	+1%	-3%
8–64	3.38 ± 0.13	3.43 ± 0.13	3.37 ± 0.12	-0%	-2%
all	5.00 ± 0.22	5.34 ± 0.15	4.91 ± 0.14	-2%	-8%

Reading: negative percentages mean the transverse-damping model is closer to the N-body truth. H-T2 asks for damp < ZA (the adjustment helps) and damp <= stick (keeping the along-filament component does not hurt, unlike full sticking).

Verdict on H-T2

Supported near the web, with an honest qualification in the outskirts. At 0–2 vox from spines the transverse-damping model beats plain ZA by 7% and isotropic sticking by 14% (jackknife over 5 held-out seeds; the crossing threshold was calibrated to favour the isotropic competitor). In the 2–4 vox ring it slightly trails ZA (+4%) — plausibly premature damping triggered by noisy tidal frames at moderate densities — while still beating sticking by 8%. Far from the web all models agree. Net: best overall model of the three (4.91 vs 5.00 vs 5.34).

Constructive conclusion of the program: the “lean-space geometry adjustment” conjecture, corrected by E4 into its transverse form, is a WORKING model term — an anisotropic, tidal-frame-aware sticking condition that improves the classical adhesion proxy. Natural refinements (partial damping beta < 1, lambda-dependent thresholds, better frame estimation in the outskirts) are tuning, deliberately left out to keep this a hypothesis test rather than a fit.