Conscious Vortex Model: Information Geometry, Hyperbolic Black Holes, and the Unification of Consciousness Phase Transitions

The "hard problem" of consciousness—why physical processes are accompanied by subjective experience—remains without a generally accepted solution. This paper proposes the Conscious Vortex Model (CVM), which establishes the logical necessity and geometric realization mechanism of conscious experience through two functionally complementary and structurally asymmetric inferential paths. The first path departs from the computational complexity threshold and proceeds through a rigorous mathematical chain of non-isometric encoding and state dependence, proving that a complex information system necessarily gives rise to an internal perspective and experience—this path relies solely on the fundamental physical principles of information conservation and computational complexity, providing a first-principles logical foundation for the existence of consciousness. The second path departs from the renormalization group and holographic duality, deriving the geometric emergence of a hyperbolic horizon and periodic phase transitions, revealing the spatiotemporal morphology of conscious experience—wakefulness, deep sleep, and dreaming respectively correspond to three geometric phases of the hyperbolic black hole, with the sleep-wake cycle acquiring the geometric archetype of a reentrant Hawking-Page phase transition. At their core conclusion, the two paths converge precisely—the essence of experience is the continuous stream of self-referential flow driven by dissipative feedback within a horizon that is energetically open yet informationally closed. This paper further presents CVM's response to the hard problem and discusses the model's core limitations and testable predictions.