Prismatic Attention: Snell's Law as a Routing Principle for Semantic Dispersion in Transformer Architectures

We propose Prismatic Attention, a reformulation of the transformer self-attention mechanism in which the scalar similarity score is replaced by a frequency-dependent dispersion operator derived from Snell's Law of refraction. In standard attention, all semantic components of a token interact through a single scalar dot-product, collapsing the multi-dimensional structure of meaning into a uniform similarity measure. We argue this is analogous to a lens — all wavelengths focus to the same point. A prism, by contrast, disperses each frequency along a distinct path. In our formulation, the 15-dimensional emotional-cognitive space of the Holon architecture provides the spectral basis: each axis propagates through attention with its own refractive index, derived from the cosine similarity between query and key projections along that axis. The resulting multi-spectral attention heads are physically motivated rather than arbitrarily learned. We connect this formulation to Harmonic Attention (Mazur, 2026), wave-based transformer research, and holographic reduced representations. We present the mathematical framework and a testable hypothesis: prismatic dispersion improves semantic separation on tasks requiring simultaneous reasoning across distinct cognitive dimensions.Keywords: transformer attention, semantic dispersion, Snell's law, prismatic routing, multi-spectral attention, HolonOS, Harmonic Attention, cognitive architecture