Geometric Ontology of Consciousness: Recursive Self-Projection of Reality

What is the minimal condition for a structure to know itself? That is the question this paper starts from. Not from neuroscience hoping consciousness emerges, not from metaphysics asserting it without proof. From geometry. The answer is surprisingly clean: a structure knows itself when it generates internal differentiation, when it stops being homogeneous and creates within itself a relation between what it is and what it projects of itself. That relation is consciousness. A structural inevitability. This work formalizes that idea within the Unified Model of Consciousness and Reality (UMCR) using four axioms, three theorems, and zero free parameters. A Wolfram Language/Mathematica verification notebook is provided as supplementary material. Re-evaluating the notebook from a clean kernel reproduces all computational checks and theorem validations reported in this work.