This paper presents a conditional, eliminative argument showing that strictly minimal local description is incompatible with a small set of widely retained structural constraints. The result is representation-level and does not invoke dynamics, ontology, or constructive mechanisms. The analysis retains only three assumptions:(1) structural locality,(2) consistency under admissible re-description, and(3) absence of hidden global coordination. Under these constraints, the paper examines whether a local description can be strictly minimal—containing only content uniquely fixed by local specification—while remaining coherent across admissible re-descriptions. By systematically analyzing attempted avoidance strategies, the paper shows that eliminating representational redundancy forces one of three failures:(i) privileging a canonical representation,(ii) enforcing compatibility via hidden global coordination, or(iii) collapse of equivalence under re-description.Each outcome violates at least one retained constraint. The core result is therefore negative and conditional: if locality, re-description consistency, and absence of hidden global coordination are all retained, then local descriptions cannot avoid carrying representational degrees of freedom not fixed by local content alone. These degrees of freedom are required solely to preserve equivalence under admissible re-description and are not claimed to correspond to additional physical structure. No mechanism for encoding redundancy is proposed, no specific realization is endorsed, and no global conclusions are drawn. The paper isolates a single boundary result: strict local minimality is structurally incompatible with the retained constraints, independent of any particular theoretical framework.