A minimal k/(aH) screening of the sim_63 μ(a) law recovers GR at high k while preserving large-scale enhancement — the standard quasistatic shape for falsifiable scale dependence.

Purpose

Extend sim_63 with a **scale-dependent** $\mu(a,k)=1+(\mu_{\rm SI}-1)/(1+(k/k_0(a))^2)$ , $k_0\propto aH$ , so large- $k$ modes recover GR while large-scale modes keep the SVT enhancement — standard quasistatic screening vocabulary.

What it proves

Batched **RK4** advances hundreds of $k$ bins in parallel on **CuPy** (fallback: vectorised NumPy); high- $k$ tail matches GR to $<1.2\%$ on mean $D/D_{\rm GR}$ ; low- $k$ tail matches the scale-independent $\mu_{\rm SI}$ run to $<4\%$ .

Relation to current theory

Bridges sim_63 to scale-aware modified gravity forecasts without altering $\Lambda$ CDM $H(z)$ .

Key equation

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

Interactive visualization

SVT predictionA minimal k/(aH) screening of the sim_63 μ(a) law recovers GR at high k while preserving large-scale enhancement — the standard quasistatic shape for falsifiable scale dependence.

Plots

stdout tail

=================================================================
 SVT Simulation #67: μ(a,k) growth — GPU-batched RK4 (CuPy if available)
=================================================================
  backend : {'backend': 'cupy 14.0.1', 'has_gpu': True, 'device': 0, 'free_gb': 15.814, 'total_gb': 17.171}
  k modes : 448  time steps : 6000  GPU batch : True
  D_SI/D_GR (z=0, scale-indep. ref) : 1.2292
  high-k mean |D/D_GR - 1|          : 0.0108  (tol 0.012)
  low-k mean D/D_GR vs SI ref       : 1.2293 vs 1.2292

=================== VALIDATION ===================
  GR f(z=0) check              : PASS
  high-k → GR restoration      : PASS
  low-k ↔ SI μ(a)              : PASS
  finite growth                : PASS
  Overall                      : PASS

  SVT Prediction: A minimal k/(aH) screening of the sim_63 μ(a) law recovers GR at high k while preserving large-scale enhancement — the standard quasistatic shape for falsifiable scale dependence.
==================================================

  Matches data:   YES — Validated