A First-Principles Derivation of the Cosmological Constant from an Eleven-Dimensional Covariant Master Action

The normalized cosmic inventory and the absolute cosmological constant are distinct observables: the first compares the gravitational response carried by different physical sectors, whereas the second fixes the dimensional coefficient of the homogeneous metric term in the gravitational field equation. This paper derives both quantities from a single stationary reduction of an eleven-dimensional covariant master action. The construction is the cosmological specialization of the information-projection framework previously developed by the author. Information projection supplies the generative architecture of the admissible higher-dimensional branch, while the calculation is carried out in the conventional language of covariant gravity, constrained effective actions, dimensional reduction, ADM geometry, free-boundary variation, and Noether charge. On a regular stationary 4 + 7 branch, a transported observer coframe and a stationary 1 + 6 splitting of the internal cotangent space decompose the 66-dimensional symmetric metric-response space into sectors of ranks 3, 18, and 45. After the seven action terms are assembled and their shared auxiliary variables are eliminated in a single stationary reduction, generalized traces of the physical Hessian give the cosmic composition Ω_b : Ω_cdm : Ω_bg = 3 : 18 : 45, with (Ω_b, Ω_cdm, Ω_bg) = (1/22, 3/11, 15/22) on the universal response branch. The absolute scale is obtained from the derivative of the same reduced on-shell action with respect to physical four-volume. The stationary-envelope, homogeneous-metric, finite-volume, dual, ADM, and Iyer–Wald representations are shown to yield the same cosmological coefficient on the finite stationary family. The dimensional realization solves the proper-time lapse, spatial coframe, York momentum mode, source profile, and source-determined boundary together. For the positive genus-zero solution constructed in the paper, the resulting cosmological constant, curvature radius, and proper-time expansion rate are Λ_bg = 1.0890639698897008 × 10⁻⁵² m⁻², R_Λ = 1.659716579066454 × 10²⁶ m, and H_prop = 67.499884050046 km s⁻¹ Mpc⁻¹. The derived curvature coefficient differs by 1.392567232 × 10⁻⁴ from the representative value formed from the Planck 2018 base-ΛCDM central parameters, with observational data entering only after the stationary branch has been determined. The same reduced theory gives an exact w = −1 plateau, nearby stable time-dependent backgrounds, and a vacuum susceptibility controlled by the inverse stationary response operator. A separate finite event–boundary realization exhibits delayed feedback, a numerically attracting periodic orbit, and nonlinear geometric boundary bifurcations. The calculation shows how event dynamics can act on a finite boundary and how the resulting boundary motion can in turn modify the event dynamics. A conditional map from this internal periodic response to physical spatial volume and proper time is formulated explicitly, thereby identifying the additional conditions required to interpret the internal cycle as an expanding and contracting cosmological history. The cosmological-constant result applies to the regular, positive, finite stationary branch defined in the paper.