Order Parameter Spacetime Theory: A Unified Framework of Irreversible Geometry

This paper establishes the complete mathematical and physical framework of the Order Parameter Spacetime Theory. Starting from three postulates — the principle of least irreversible cost, the information bottleneck theorem, and the spacetime emergence hypothesis — we derive the irreversible equation of motion, the Information–Einstein equations, and all physical predictions. The theory re-describes the physical world as the motion of the field Φ in order-parameter space, governed jointly by the inertial resistance coefficient gᵢᵢ⁻¹ and the information dissipation tensor Υμν. Under different parameter regimes, the projections of this unified dynamics give rise to the three appearances of physics: force, geometry, and quantum. We formally introduce the concept of the Geometric Mode (defined in §4.1) as the microscopic form of gravity — gravity is not a force mediated by particles, but the macroscopic cumulative effect of geometric modes. The paper contains the definitions of all physical quantities, the derivations of the core equations, a hierarchical classification of all projections, a summary of seven classes of solutions, and a complete list of over twenty exclusive predictions. Natural units (c = ħ = k_B = 1) are used throughout; all equations are dimensionally self-consistent, and every physical quantity is explicitly defined in the text.