Why the Projective Consciousness Model Must Be True: A Formal Demonstration from Sensorimotor Dependencies, Invariance, and Control

Conscious experience is unified, multimodal, and perspectival: sensory contents appear in a single egocentric scene that remains coherent as the organism senses and acts. We provide a conditional necessity proof for the Projective Consciousness Model (PCM). From four minimal premises, (P1) approximately central projection of visual input, (P2) coherent integration across viewpoint changes, (P3) maximal invariance with minimal added structure, and (P4) normative control of viewpoint (e.g., information seeking under active inference or related optimal-control schemes), we derive that any internal state sufficient for coherent first-person spatial awareness and closed under viewpoint updates is, up to isomorphism, the three-dimensional real projective space RP 3 . Viewpoint changes act as collineations in P GL(4, R), while Euclidean and affine judgments arise only through a context-dependent metric gauge layered on the projective backbone. Strictly Euclidean maps and purely topological formats either implement an equivalent projective layer to reconcile perspective with coherent updating, or violate at least one premise. This geometry yields principled accounts of perceptual constancies and systematic geometric illusions (including the Moon illusion), provides a compact control parameterization for whole-field prediction and information gain, and links naturally to known neural mechanisms for spatial updating (gain fields and predictive remapping). The same projective scaffold can be extended beyond vision to multisensory integration, valuation, social cognition, and planning. Thus, given P1-P4, projective organization is the uniquely parsimonious representational format for coherent egocentric spatial experience.