Three-dimensional filament matter power spectra of the interference-free CDM background and the reconstructed FDM density for a selection of FDM masses at z = 4. Top: Single filament spectrum, P_single(k ∣ M), for an example filament of total mass M = 5 × 10⁹ h⁻¹ M_⊙. One finds all FDM spectra to be compatible with CDM down to the spatial extent of the ground state, R_gs ≡ ⟨ψ₀|R|ψ₀⟩ (vertical, dashed line) – effectively the characteristic scale of the cylinder. Once sufficiently small scales inside the filament are probed, the interference contribution to |ψ|² enhances the two point density correlation and boosts P_single(k ∣ M) above the CDM baseline. Note that for larger m₂₂: (i) P_single(k ∣ M) detaches later from the CDM baseline, (ii) the boost is shallower but (iii) extends to higher k until the suppression scale k_cut ∝ m is reached (vertical, solid lines). Bottom: One-filament term P^1f(k) – a stacked version of many P_single(k ∣ M), weighted according to the FMF in Fig. 10. We limit the filament population to the mass window M ∈ [3×10⁹, 3×10¹⁰] h⁻¹ M_⊙ and compute the one filament term either directly from the semi-analytical expression of the wave function developed in Appendix D (solid, blue) or by populating a box as shown in Fig. 11 (dashed, yellow). All quantitative observations made for the single cylinder case translate to P^1f(k) after a FMF-weighted average according to Eq. (45), i.e., R_gs → ⟨R_gs⟩_FMF (vertical, dashed lines) and k_cut → ⟨k_cut⟩_FMF (vertical, solid lines).