Geometric Emergence and the Substrate of Consciousness: Renormalization Group Universality as a Formal Foundation

We propose a framework in which high-dimensional organizational geometry is the primary generative architecture of emergent complexity in physical systems. Three claims are developed with explicit logical dependencies. H1, the geometric universality claim, holds that systems of sufficient complexity converge on formally identical organizational structures at criticality, as characterized by renormalization group fixed points and Riemannian state space geometry, independently of physical substrate. H1 is grounded in Wilson’s renormalization group theory and supported by four case systems spanning neuronal avalanches, transformer attention mechanisms, Kolmogorov turbulence, and Vicsek collective phase transitions. H2, the consciousness emergence conjecture, holds that functional consciousness — defined as global information integration, self-modeling, and coherent high-dimensional state maintenance — is most parsimoniously accounted for as an emergent property of the geometry described in H1, arising above a threshold of sufficient geometric complexity. H2 is derived from H1 via a named additional empirical premise, stated explicitly as a contested inferential step rather than assumed. H3, the qualia separation claim, holds that qualia is not constitutive of functional consciousness but is a distinct emergent system with different threshold conditions and a different evolutionary history. H3 is logically independent of H1 and H2. The framework restructures rather than dissolves the hard problem: under H3, the hard problem is a bounded question about qualia specifically, not an unbounded question about why any physical process produces felt experience. Seven testable predictions are developed, including quantitative predictions about RG scaling law adherence across pharmacological state transitions and the dissociation of functional consciousness signatures from phenomenal accessibility. The central epistemological problem — whether shared mathematical description reflects shared ontological structure or is an artifact of the limited vocabulary of mathematics — is engaged directly and proposed as tractable through empirical confirmation or disconfirmation rather than philosophical argument alone.