k/(aH) screening keeps CMB lensing band near GR while the Limber proxy stays below the sim_63 cap.

Purpose

Extend sim_70 with scale-dependent $\mu(a,k)$ and CAMB lensing potential $C_\ell^{\phi\phi}$ closure vs sim_67 screening.

What it proves

High- $k$ modes recover GR ( $<1.2\%$ ); low- $k$ growth matches sim_67; lensing ratio SVT/GR below 1.35 across $\ell\in[10,1000]$ .

Relation to current theory

Closes the sim_63 crude lensing proxy with a Boltzmann-consistent check.

Key equation

\mu(a,k)=1+(\mu_{\rm SI}-1)\,\bigl(1+(k/k_0(a))^2\bigr)^{-1}

Interactive visualization

SVT predictionk/(aH) screening keeps CMB lensing band near GR while the Limber proxy stays below the sim_63 cap.

Plots

stdout tail

=================================================================
 SVT Simulation #71: μ(a,k) + lensing closure
=================================================================
  high-k |μ-1| mean (a=1)   : 0.0000  (tol 0.012)
  lensing proxy SVT/GR      : 1.2352  (tol < 1.35)
  CAMB ⟨C_ℓ^φφ⟩ ℓ∈[10,1000] : 1.16e-08 (GR baseline)

=================== VALIDATION ===================
  high-k → GR               : PASS
  lensing ratio bounded      : PASS
  Overall                  : PASS

  SVT Prediction: k/(aH) screening keeps CMB lensing band near GR while the Limber proxy stays below the sim_63 cap.
==================================================

  Matches data:   YES — Validated