The Signature Is Global

2605195701046

The Signature Is Global

05/19/2026

sig(J(z)ᵀGJ(z)) = (2,2)
for all z, β ∈ ℝ, β ≠ 0.
Not only at the fixed point.
Q is not globally preserved.
The differential signature is.
Sylvester’s Law: invertible J preserves the signature of G under pullback.
det(J(z)) = β².
The rest follows.​​​​​​​​​​​​​​​​