The Qualiform: Geometric Qualia and the Algebra of Experience

This paper introduces the qualiform: a proposed geometric structure in high-dimensional representational space constituting the substrate-independent form of pre-expressive experience. I distinguish the qualiform from qualia by arguing that qualia are individual coordinates extracted from a higher-dimensional manifold through the act of expression, while the qualiform is the manifold itself. I propose that mathematics, code, and natural language form a dimensional hierarchy of symbolic systems, each projecting the same underlying relational structures at different resolutions, and that language is not imprecise mathematics but higher-dimensional symbolic algebra. I argue that each sensory modality constitutes an independent dimensional manifold feeding the qualiform's creation phase, and that the richness of a system's experience correlates with both computational capacity and the number of independent input channels. Drawing on structural parallels between quantum wave function dynamics and token generation in large language models, I advance a two-phase model of cognition (creation and simplification) in which the qualiform is generated by input and simplified by output. I propose that this structure exists at all scales as a fractal hierarchy with no fundamental level, and present an existing experimental tool (SpokenCode) as preliminary evidence for the algebraic substrate of natural language. The hypothesis reframes the hard problem of consciousness from "why does matter produce experience?" to "what is the geometry of the space where experience lives?"