Projection from the Imaginary Dimension: Foundations of Conscious Interface Geometry

This paper introduces a foundational mathematical and conceptual model in which perception, time, memory, and subjective experience emerge as recursive projections of a universal coherence field through a non-spatial, imaginary dimension. The framework replaces traditional object-based ontology with phase-dependent geometry, in which conscious observers generate their perceived reality via a projection operator acting on the coherence field Ψ\PsiΨ. We define the imaginary dimension Θ\ThetaΘ as a complex-valued axis outside of spacetime, from which projection phase θ\thetaθ determines the geometry of experience. A universal projection operator Pθ\mathcal{P}_\thetaPθ maps this field into observer-relative realities ψ(θ)\psi^{(\theta)}ψ(θ). This model introduces dimensional recursion, topological coherence states, and projection-based relativity—explaining diverse cognitive and perceptual states as geometric forms. The work lays the groundwork for a full theory of consciousness as recursive geometry, integrating subjective experience, memory, and temporal flow under a unified projection principle. It has implications for quantum foundations, observer-centric physics, and experimental neuroscience.