N27 — Magnetic winding number $w = 2$
N27: Magnetic winding number $w = 2$. SKA, ngVLA, ngEHT polarimetry.
Status boundary
Falsification status is a program-side tracking label. It separates current internal stance from formal verification, empirical support, and external acceptance; it is not a claim that the wider scientific community has accepted the result.
Falsification Details
magnetic winding!prediction pred:n27 The RM winding theorem (V.T227): $w = (T^2) = 2$. Faraday rotation measure near BH jets encodes toroidal winding.
SKA, ngVLA, ngEHT polarimetry
2030–2035.
Context
N27: Prediction
The RM winding theorem (V.T227): $w = (T^2) = 2$. Faraday rotation measure near BH jets encodes toroidal winding. Experiment: SKA, ngVLA, ngEHT polarimetry. Timeline: 2030–2035.
Derivation Context
The Faraday rotation measure (RM) around the shadow of a $T^2$ black hole exhibits winding number
The toroidal magnetic field on the minor $S^1$ cycle causes two sign changes per azimuthal circuit, compared to one for a radial/dipolar field on $S^2$. The winding number $2$ is a topological invariant of genus$(T^2) = 1$.
The toroidal B-field wraps around the minor $S^1$
(Definition (def:ch42-toroidal-bfield),
Chapter (ch:book5-ch42-eht-reread)).
As the line of sight traces one azimuthal circuit
around the shadow,
it crosses two sectors
where the toroidal field component $B_$
reverses sign:
once at the top'' of the torus
and once at thebottom.’’
Each reversal produces a sign change in the RM integral
$RM = n_e \,B_ \,dl$.
For $S^2$ with a radial or dipolar field,
only one sign change occurs per circuit.
The winding number is
$w_RM = |number of sign changes|/1 = 2$
for $T^2$ and $1$ for $S^2$.
The Stokes $V$ circular polarization winding number around the shadow is
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