Madelung density perturbations reproduce the Newtonian sector of the acoustic metric (Einstein limit step).

Purpose

Extract weak-field $\Phi$ from Madelung $g_{tt}$ on the PG inflow grid and compare to analytic PG reference.

What it proves

Max relative $|\Phi_{\rm num}-\Phi_{\rm ref}|<10\%$ in fit band ( $x\in[5,18]$ , $|x-r_h|>1$ ).

Relation to current theory

Pen-and-paper Einstein-limit step paired with context/acoustic_metric_derivation.md §6.

Key equation

g_{tt}\approx -(1+2\Phi/c_s^2)

Interactive visualization

Acoustic horizon & Hawking temperature (sim data)

loading interactive visualization…

Plots

stdout tail

=================================================================
 SVT Simulation #79: GPE stress → weak-field Φ
=================================================================
  max rel |Φ_num - Φ_ref| : 0.0151  (tol 0.10)

=================== VALIDATION ===================
  Φ match in fit band         : PASS
  Overall                     : PASS

  SVT Prediction: Madelung density perturbations reproduce the Newtonian sector of the acoustic metric (Einstein limit step).
==================================================

  Matches data:   YES — Validated