= Normalizer action determines axial branch parity
The <normalizer> of an axial isotropy subgroup preserves its one-dimensional <fixed-point subspace of a group action>. If its quotient by the isotropy contains an element acting as minus one, the reduced scalar vector field is odd, forcing a <pitchfork bifurcation> rather than a generic quadratic branch. For odd dihedral groups the reflection normalizer has no such quotient; an even-degree anisotropic term can distinguish the two half-axes at higher order.
// Target: algebra.bigb
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