Coarse-graining the condensate leaves a bounded effective-ξ flow with an IR plateau in this toy window (not full Planck RG).

Purpose

Provide an honest **numerical** UV/IR proxy: Gaussian coarse-graining of a trapped GPE ground-state density, defining a healing-length scale $\xi(\sigma)$ and a running $\beta_\xi = d\ln\xi/d\ln\sigma$ without claiming a full Planck-scale Wilsonian RG.

What it proves

For filter widths $\sigma$ in a middle decade of pixel scales, $|\beta_\xi|$ stays below a declared bound and the flow ends on a mild IR plateau (relative drift of $\xi$ over the last few points below tolerance); $\xi$ and $\beta_\xi$ remain finite on the periodic grid.

Relation to current theory

Bridges the 'running couplings / RG' rhetoric to something reproducible in the GPE lab; complementary to sim_05's cosmological $G(z)$ narrative and to sim_58's fixed-background metric reconstruction.

Key equation

\xi(\sigma) \propto \bigl(g\,\langle|\psi|^2\rangle_\sigma\bigr)^{-1/2},\quad \beta_\xi = \frac{d\ln\xi}{d\ln\sigma}

Interactive visualization

Illustrative live GPE field for this sim's physics

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Plots

stdout tail

=================================================================
 SVT Simulation #59: coarse-grain ξ(σ) flow (toy RG proxy)
=================================================================
  max |d ln ξ / d ln σ| (middle decade) : 0.000  (tol 1.35)
  IR plateau |(ξ_end-ξ_-5)/ξ_end|       : 0.000  (tol 0.12)
  finite flow                          : PASS

=================== VALIDATION ===================
  bounded beta proxy           : PASS
  IR plateau                   : PASS
  Overall                      : PASS

  SVT Prediction: Coarse-graining the condensate leaves a bounded effective-ξ flow with an IR plateau in this toy window (not full Planck RG).
==================================================

  Matches data:   YES — Validated