This paper formulates a conceptual conjecture, referred to as the conjecture of dimensional purity. It is neither intended as a mathematical theorem nor as an empirical hypothesis, but as a structural clarification across disciplines. The conjecture addresses the conditions under which a structure can be regarded as uniquely determinable. It states that such determinability is possible if and only if the number of independent degrees of freedom available in a description matches the structural complexity of the object under consideration (k=n). Systematic deviations from this relation are associated with characteristic forms of indeterminacy or representational ambiguity. The contribution is constitutive rather than descriptive or normative: it does not claim that real systems satisfy this condition, nor that they should. Instead, it clarifies the conditions under which the attribution of unique structural determination is meaningful at all. A practical use of the conjecture lies in its application as a structural reference framework in interactions with large language models. The paper can be employed as a conceptual prompt to examine whether topics on which a language model produces coherent discourse satisfy the condition k=n, or whether cases of under- or overdetermination are present. Comments and critical discussion are explicitly invited.