What Could Cézanne Have Painted? Geometric Search for Stylistic Gaps in Embedding Spaces

Can generative models produce images faithful to a historical artist yet genuinely original–images the artist could have painted, but never did? We propose a geometric framework for discovering such stylistic gaps in visual embedding space, using an augmented dimension with an external filter (GPT-5.4). Results show that the method produces a moderately diverse set of images that are both distinct from Cézanne's corpus and accepted as genuine by the filter. An adversarial test with Renoir and Rembrandt, conducted without the augmented dimension, exposes fundamental limitations of current embedding spaces. Our findings highlight both the promise and the limits of geometrically-guided stylistic exploration.