Squared-Norm Uniqueness under Orthogonal Additivity and Invariance: An Admissibility Lemma for Stable Comparability Functionals (IM-B002, v0.3)

This document is part of the Informational Mechanics (IM) framework and is published in the IM-B (Calculus & Admissibility) series within the IM v0.3 corpus. The paper establishes a structural uniqueness result for admissible strength functionals on inner-product spaces under orthogonal additivity, isometry invariance, and minimal regularity conditions. It shows that any such functional must be proportional to the squared norm, up to a positive multiplicative constant. The result is purely mathematical and introduces no physical axioms, dynamics, interpretations, or empirical claims. Its purpose is to provide a domain-neutral lemma intended for potential downstream use in IM-E (Measurement & Operators) and IM-D (Core Physics) papers when formalizing operator-defined comparability or outcome-weight structures. No claim is made that any particular physical system must satisfy the assumptions stated here.