Physical Intelligence: A Bound Dynamical Framework of Five-Dimensional State Mechanics, Morphological Dissipation, and Non-Zero-Sum Horizon Arbitration

Contemporary artificial intelligence remains largely bounded by the Church-Turing discrete paradigm and probabilistic auto-regressive statistical optimization. While capable of generating coherent symbolic sequences within unconstrained, zero-consequence digital manifolds, these systems systematically suffer catastrophic dynamic breakdown upon deployment in the physical universe. This failure stems directly from an ignorance of fundamental thermodynamic bounds, material constitutive limits, and strict conservation laws. Here, we formally establish the foundational paradigm of Physical Intelligence (PI). Rather than treating intelligence as an ungrounded inference engine or an anthropomorphic cognitive proxy, we define it as an open thermodynamic dissipative structure executing homeostatic self-preservation and goal-directed actuation across non-smooth, non-differentiable physical contact manifolds. We formalize the YQ Five-Dimensional State Equation, which unifies five mutually orthogonal, coupled system primitives: Capacity (C): measuring state-space topological volume and noise absorption without locality collapse; Velocity (V): defining the Lyapunov convergence rate and microsecond-scale causal deadline preservation; Elasticity (E): governing constitutive mechanical strain buffering and dynamic topology preservation under unmodeled impulse shock; Orientation (O): providing the non-conservative potential gradient vector field driving macroscopic anti-entropic traversal; Arbitration (A): executing non-reversible symmetry breaking and deterministic phase-state collapse at critical bifurcations. We demonstrate that physical trial-and-error operates not as numerical noise, but as an indispensable "friction probe" that purchases structural manifold parameters via controlled local entropy production. Furthermore, we decouple the system into a high-level strategic framework ("谋", managing global phase-space shaping, time-integrated value, and ecosystem attractors) and a deterministic, low-level execution substrate ("算", implemented strictly via zero-heap, deterministic C99 operators anchored to hardware-in-the-loop realities). This work completes the hyper-closed loop spanning theoretical cosmology, non-equilibrium statistical mechanics, differential topology, and safety-critical deterministic control, providing an axiomatic baseline for verifiable autonomous agents in physical reality.