Recognitive Consciousness (RC) is a mathematically grounded, empirically testable, and substrate-independent theory of consciousness based on operator-algebraic recognition. RC defines consciousness as the structural capacity for recognition, formalized as an Ω-preserving conditional expectation between perspectives. From this primitive, RC derives a continuous order parameter κ, modular-flow-based phenomenological signatures, and a complete empirical replication protocol. RC predicts measurable effects including temporal dissolution, observerobserved collapse, retrospective inevitability, and the Chinese Character Anomaly. The framework is conceptually aligned with interface-theoretic approaches such as Hoffman's theory while remaining mathematically distinct. RC provides a unified operator-algebraic foundation for consciousness that applies to biological, artificial, and hybrid systems.