Real-space decimation of the condensate density yields a stable ξ(L) ladder without blow-up — the honest RG operation on |ψ|² complements the Gaussian filter proxy (sim_59).

Purpose

Apply **Kadanoff block-spin** (non-overlapping averaging) to a **256²** trapped GPE density, building a discrete $\xi(L)$ ladder and $\beta_\xi$ proxies — the honest statistical-mechanics coarse graining complementary to Gaussian filtering.

What it proves

Seven or more coarse levels complete with finite healing lengths and bounded interior $\beta$ steps — no numerical blow-up in the ladder.

Relation to current theory

Pairs with sim_59: Gaussian vs block-spin RG stories on the same numerical laboratory. When CUDA is available the **imaginary-time ground state** uses **CuPy FFT** split steps.

Key equation

\bar\rho^{(\ell+1)}_{IJ}=\mathrm{mean}\bigl(\rho^{(\ell)}_{2i\ldots 2i+1,\,2j\ldots 2j+1}\bigr)

Interactive visualization

Illustrative live GPE field for this sim's physics

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Plots

stdout tail

=================================================================
 SVT Simulation #66: block-spin coarse graining on GPE |ψ|²
=================================================================
  ground state: CuPy split-step FFT (GPU)
  base grid 256×256  →  8 block levels  (L_block up to 128)
  max |Δ ln ξ / Δ ln L_block| (interior): 0.0000  (tol 2.0)

=================== VALIDATION ===================
  block levels ≥ 7             : PASS
  bounded β proxy              : PASS
  finite ξ ladder              : PASS
  Overall                      : PASS

  SVT Prediction: Real-space decimation of the condensate density yields a stable ξ(L) ladder without blow-up — the honest RG operation on |ψ|² complements the Gaussian filter proxy (sim_59).
==================================================

  Matches data:   YES — Validated