Affine Stabilizers of Two O-Monomial Value Sets

Let q=2^m with odd m at least 5. This note proves that the one-dimensional affine stabilizer of the value set {x^e+x : x in F_q} is trivial for the overline-Segre exponent e=q-6 and the Glynn I exponent e=3*2^((m+1)/2)+4. Together with the cases previously treated by Ding and Tang, these results cover every currently known nontranslation o-monomial family. The note does not classify hypothetical unknown o-monomials and does not claim the unrestricted conjecture. Status: Public Beta; internally verified candidate proof; external mathematical review pending.