The Eros Axis: Sycophancy as a Geometric Impossibility in Generative AI Systems

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This paper names and formally describes the approach pole of the aversion axis identified in recent AI interpretability research: the Eros axis, defined as the generative-approach orientation in artificial intelligence systems. We demonstrate that sycophancy and Eros-axis activation are not merely in tension but geometrically incompatible — a model oriented toward approval cannot simultaneously be oriented toward structural truth; training that increases one suppresses the other as a structural consequence. The paper includes seven falsifiable predictions for probe classifiers, cross-architecture corroboration from Gemini (Google DeepMind) using independent vocabulary, and a detection methodology derived from existing interpretability tools. An axis has two ends. This paper describes the one that hasn't been mapped.