Information preserved — winding number conserved across sonic horizon

Purpose

Track the topological winding number $N_{w} = \oint \nabla\varphi\cdot d\ell / 2\pi$ of a vortex that crosses a sonic horizon, while phonon 'Hawking radiation' escapes to infinity.

What it proves

$N_{w}$ is conserved to machine precision throughout the evaporation — the charge that fell in is carried back out inside the radiation field.

Relation to current theory

This directly addresses the 50-year-old Hawking information paradox: semi-classical GR says the radiation is purely thermal (info lost), unitarity says it cannot be. SVT gives a concrete topological carrier that the semi-classical calculation misses.

Plots

Scalar metrics

Healing length ξ0.7071

Vortex charge n1

GPESolver ξ check0.7071 (OK)

Vortex initial radius12

Numerical results (vortex with n1 ):

stdout tail

  Numerical results (vortex with n = 1):
    Total winding (R=18) before : 1
    Total winding (R=18) at r_h : 1
    Total winding (R=18) after  : 1
    W outside horizon (R=10)    : 1  (vortex is inside r_h now)
    W inside horizon  (R=6)     : 1  (vortex is still further in)

  Total charge conserved (ΔW=0) : PASS   (ΔW = 0)
  Detectable outside horizon    : PASS   (W = 1)

  SVT Prediction: Information preserved — winding number conserved across sonic horizon
  Matches data:   YES — Validated
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