Covariant Hamilton phase-space deformation of relativistic generalized uncertainty principle kinematics: Analytical solutions and observables of dynamically closed and testable inflation

We formulate inflation from a covariant Hamilton phase-space deformation motivated by relativistic generalized-uncertainty-principle kinematics. A quartic Hamilton invariant generates a unique Hamilton co-metric whose single-clock pullback gives 𝑃 ⁡ ( 𝑋 , 𝜙 ) = 𝑋 + 6 ⁢ 𝛾 q ⁢ 𝑋 2 − 𝑉 ⁡ ( 𝜙 ) . The background equations, scalar and tensor quadratic actions, stability conditions, sound speed, spectral tilts, runnings, tensor ratio, consistency relation, and equilateral bispectrum follow from the same action. The deformation closes through 𝑦 ⁢ ( 1 + 𝑦 ) 2 = 4 ⁢ 𝛾 q ⁢ 𝑉 ⁢ 𝜖 𝑉 . Quadratic, Starobinsky, D-brane, and natural inflation are solved analytically and numerically. Dense scans of ( 𝑁 ⋆ , 𝑦 ⋆ ) and fixed- 𝛾 q trajectories reveal model-dependent tensor responses, controlled running corrections, and sharply distinct scalar-tilt surfaces. The resulting framework is dynamically closed, perturbatively stable, and directly testable through correlated primordial observables.