We prove that any additive, faithful, contractively monotone seminorm on Banach presheaf 1-cochains must be a positive scalar multiple of the ℓ¹ coboundary norm. The result explains why ℓ¹ appears as the canonical diagnostic of presheaf coboundary defects and serves as a functional-analytic companion to Single Obstruction Theory.
JEREMY H. CARROLL (Sat,) studied this question.