Abstract

The “hard problem” of consciousness—why physical processes are accompanied by subjective experience—remains unresolved. This paper proposes a cross‑disciplinary theoretical framework: the Conscious Vortex Model (CVM). Based on three axioms—closed information horizon, dynamic self‑referential recursion, and holographic projection—we prove that any system satisfying these axioms is mathematically isomorphic to a non‑vacuum hyperbolic black hole on an information manifold. The Fisher information metric satisfies the Einstein field equations, whose curvature‑closed solution corresponds to the formation of an event horizon. Holographic duality ensures that all internal information is encoded on the boundary; the projection process itself is subjective experience (“projection‑as‑experience”). For the first time, we interpret wakefulness, NREM sleep, and REM sleep as three geometric phases of the hyperbolic black hole: the stable black hole phase, the black‑hole‑free phase, and the chaotic‑edge micro‑black‑hole emergence phase. We predict that consciousness state transitions should obey a Lyapunov exponent power‑law scaling with critical exponent \nu = 1/2, consistent with the universal behavior of black hole thermodynamic phase transitions. Numerical simulations in 2+1 dimensions demonstrate the spontaneous emergence of a “horizon” when self‑referential recursion intensity exceeds a threshold. The model integrates recent advances in information geometry, neural manifolds, black hole chaos, and holographic principles, providing testable mathematical language for the unification of consciousness and fundamental physics. Keywords: Conscious Vortex Model; information geometry; hyperbolic black hole; holographic projection; projection‑as‑experience; Lyapunov exponent; consciousness phase transition; sleep cycle; hard problem.