K = 1 Chronogeometrodynamics: A Theory of Adaptive Geometric Phase Transition In classical physics and mathematics, time is typically treated as an external continuous parameter—either as a background coordinate in Newtonian and relativistic frameworks or as an iteration counter in computational processes.This work introduces a fundamentally different viewpoint: the K = 1 chronogeometrodynamics framework, which redefines time, action, and structural evolution as emergent geometric quantities intrinsic to the system itself. Redefining Time and Action A central contribution of this framework is the establishment of a direct information–geometric relationship among time, structural change, and entropic resistance.This relationship is formalized in the Time Metric Law (Level I): dtinfo=dΦH,dt_{\mathrm{info}} = \frac{d\Phi}{H},dtinfo=HdΦ, where dtinfodt_{\mathrm{info}}dtinfo is the intrinsic information-time metric, dΦd\PhidΦ represents structural potential change, HHH denotes entropic resistance. This identification yields two key physical insights: 1. Time as Structural Cost The passage of time is not uniform but is generated internally by the structural evolution of the system.The integral quantity ∫dtinfo\int dt_{\mathrm{info}}∫dtinfo acts as the total cost accumulated along the evolutionary path. 2. Least Action as a Cost-Minimization Principle The Structural Action Law (Level II), A=∫dtinfo,δA=0,\mathcal{A}=\int dt_{\mathrm{info}}, \qquad \delta\mathcal{A}=0,A=∫dtinfo,δA=0, reveals that the classical least-action trajectory is, in this framework, the path that minimizes the intrinsic information-time cost, giving the principle a new operational and geometric interpretation. Cross-Scale Unification and Adaptive Geometry The K = 1 framework forms a coherent algebraic–geometric hierarchy whose highest constraint is theGeometric Transition Law (Level VI).Empirical multi-cluster analyses demonstrate that: • Optimal flows Ψopt\Psi_{\mathrm{opt}}Ψopt are algebraically structured. The realization of the least-action path depends on the algebraic class of the geometric flow chosen by the system. • Geometry adapts via phase transition. The system adjusts its geometric flow according to the structural driving force DDD: When DDcD > D_cD>Dc, it transitions to non-analytic flows ΨNon\mbox−Analytic\Psi_{\mathrm{Non\mbox{-}Analytic}}ΨNon\mbox−Analytic, achieving maximal efficiency. Near the critical region, a geometric phase transition emerges, balancing stability and efficiency. This adaptive behavior provides a refined perspective for interpreting highly disturbed systems such as Abell 2744, whose structural relaxation follows the GTL-predicted optimal geometric pathways. Future Fractal Coupling: Generalization of the Level III $\mathcal{K}=1$ geodesic condition to Non-Integer Dimensional ($D_H$) Manifolds, confirming the minimal action principle holds within fractal geometry. Algebraic Economy: The $\mathbf{\Psinan}$ family (e.g., $\Psi_{\sqrt{2}}$) is proven to be the most economical algebraic flow, having the highest $R_{\mathrm{geo}}$ efficiency ratio chosen by the universe under the Minimal Effort Principle to build optimal fractal structures. Universal Law: This framework elevates the GTL into a universal principle describing how all complex systems (from cosmic clusters to networks) achieve optimal evolution through algebraic geometric phase transition under high structural driving forces.