Contextual Vectors Are Not Awareness: Reinterpreting Representation Geometry after the Tensor Test

Contextual vectors are the working objects of contemporary language models: a token, once placed in a window, is assigned a vector that depends on that window. A growing literature then reads geometry in the resulting space as evidence of intelligence, of a consciousness spectrum, or of situational awareness. This article reinterprets that move with the criterion isolated in the companion teaching note. A multidimensional array is not a tensor. It becomes the component representation of a geometric object only when a transformation law is stated and an invariant is named. Applied here, the criterion separates three things that the consciousness literature collapses. The first is a representation map from contexts to a fibre. The second is a self-locating competence, measured behaviorally by out-of-context reasoning and by the Situational Awareness Dataset. The third is an identity claim, associated with integrated information theory, on which experience is a cause-effect structure. Only the first is mathematics of the vector. The second is a family of tasks. The third is a metaphysical identification that no embedding entails. 1. The conflation KS The reinterpretation is constructive. Context is treated as a base, the contextual vector as a coordinate representation of a section, and situational content as an invariant functional of that section, stable under the redescriptions the theory itself allows.

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