The Fisher Hyperbolic Information Framework: A Unified Model of Physics, Mathematics, and Intelligence

The Fisher Hyperbolic Information Framework (FHIF) introduces a unified mathematical and physical model for the dynamics of complex systems across physics, intelligence, computation, and finance. Built upon a hyperbolic information manifold of fixed curvature kF=−0.52, the framework characterizes system states using coherence C, acceleration X, curvature-locked balance D, and activation Π=CDX. Together, these quantities define a universal geometric law governing stability, change, and emergent behavior across scales. FHIF provides a geometric unification of the four fundamental forces by expressing gravitational, electromagnetic, weak, and strong interactions as flows on the same negatively curved manifold, governed by a single invariant-preserving dynamic (IPF). This construction extends and interrelates principles from general relativity, quantum field theory, gauge dynamics, renormalization, and quantum information geometry. Mathematically, FHIF yields a new class of geometric invariants and fixed-point relations (CF,XF), forming a coherent bridge between differential geometry, information theory, and nonlinear dynamical systems. In the science of intelligence, the framework models biological and artificial cognition as hyperbolic flows converging toward stable attractors, offering a unified description of learning, coherence formation, and adaptive behavior. This paper presents the geometric foundations, physical correspondences, mathematical derivations, and cross-domain applications of FHIF, demonstrating that the Fisher Framework constitutes a single coherent law underlying physical forces, mathematical structure, intelligence, and complex adaptive systems.