Transfer function T(k) = Re⟨ŝ s*⟩ / ⟨|s|²⟩ · two-point correlation
Erasure is scale dependent.
Templates are smooth, so the subspace they span sits at low wavenumber. A single retention number hides where the damage lands; the transfer function does not.
Transfer by scale
Simulation 10 worlds per ρ.
ρ
Scale-resolved signal transfer
wavenumber k in cycles per box; small scales to the right
Large-scale minus small-scale transfer
k < 6 vs k ≥ 6 · negative = large scales damaged more
Two-point correlation
ξ(corrected) / ξ(true) by separation
1 = clustering preserved · ρ = 0.3 · 5 worlds