Solving the Hard Problem: A Formal Information-Manifold Model of Consciousness

This work introduces a substrate-independent mathematical model of consciousness based on an information manifold structure. Conscious experience is defined as a globally integrated, self-referential manifold equipped with temporally continuous evolution and dimension-reducing observational projections. Four core results are proven: (1) unity of experience, (2) privacy of qualia, (3) diachronic identity through manifold invariants, and (4) substrate independence. A minimal toy model is constructed to explicitly instantiate these properties. The resulting framework bridges phenomenology, mathematical topology, and computational modeling, providing a foundation for empirical predictions, physical grounding, and distinctions between conscious systems and mere computational aggregates.